MECHANICAL ENGINEERING REVIEW Problem Set no. 1 MULTIPLE CHOICE
1.
A spherical spherical tank is full of water that has has a mass of 10 10 000 kg. If the outside diameter of the tank is 2722 mm, how thick is the wall of the tank?
m V 10,000 00 0 V 1000
ρ
10 m3
4 πr 3 V 3 r 1.337 33 7 m
d t
2(1.337) 2.674 m
2722 - 2674 2
2674 mm
24 mm
2. A cylindrical tank is filled with water at the rate of 5000 5000 Gal/min. The The height of water in the tank after 15 minutes is 20.42 ft. What is the diameter of the tank? (Note: (Note: 1 ft 3 = 7.481 Gallons)
V
V
D 3.
5000 (15) π
75000 Gallons
10,025.4 ft 3
D2H ; H 20.42 ft
4 25 ft
At what what temperature temperature in which the reading reading in Fahrenheit Fahrenheit scale sc ale is the same as as the Centigrade Centigrade scale. sc ale.
Conversion C
F 32
1.8 F 1.8(C) 32 x C F x 32 1.8 x 40 x
4.
A new new temperature temperature s cale is desired with with freezing freezing point of water water at 0 X and boiling occurring occ urring at 1000X. Derive the conversi conversion on between C and X and what is 0 K in X.
1000 0 100 0 m 10 y
10
mx b
K C
0K
273
C
C
273
-273
X 10( 273 ) X
2730
0
5.
A pressure pressure gage at elevation elevation 8 m on the side of a tank containing a liquid reads 57.4 KPa. Another gage at elevation elevation 5 m reads reads 80 KPa. Compute the specific weight and density of the liquid. (use (use g = 9.81 m/sec 2)
ΔP γ(Δh)
(57.4 80) γ(8 5) γ 7.53 γ
KN m3
ρg
1000
ρ 767.9 6.
kg m3
An open tank contai ns 5 m of water covered covered with 2 m of oil ( = 8 KN/m 3). Find the absolute pressure at the at the bottom of the tank. (Assume P atm = 101 KPa)
101 (2)(8) 5(9.81) PBottom PBottom 7.
166.05 KPa
A skin diver diver wants to determine the press pressure ure exerted ex erted by the water on her body after a descent desc ent of 35 m to a sunken ship. The specific gravity of seawater is 1.02 times that of pure water. Determine the pressure in KPa.
P 0 35(1.02)(9.81) 8.
A water storage storage tank contains liquid and and vapor vapor in equilibrium equilibrium at 250 C,( l = 799.23 m 3/kg; v = 19.95 m 3/kg).The distance from from the bottom of the tank to the liquid level level is 10 m. What is the differen difference ce in pressure reading between the top of the tank and the bottom of the tank if the vapor vapor pressure is 3,973 KPa. (Assume g = 9.81 2 m/sec )
799 799 .23(9.81) (10) 4,051.4 KPa 1000 ΔP (3,973 - 4,051.4) 78.4 KPa
PBottom
9.
3,973 973
Compute the gravitat gravitational ional force between a proton ( m = 1.66 x 10 an atom whose whose radius of electron orbit orbit is 5.29 x 10 -11 m.
Fg
Gm1m2 Newton r 2 6.67(10 11 )(1.66)(10 5.29(10
Fg
27
)(9.11)(10 11 )
31
)
1.9x10
43
-27
kg) and an electron (m = 9.11 9.11 x 10 -31 kg)in
Newton
10. A pressure in the cylinder cy linder in the figure varies varies in the following manner with volume, P = C/V 2. If the initial pressure is 500 KPa, initial volume volume is 0.05 m 3 and the final press pressure ure is 200 KPa, find the work work done by the syst em.
For Fo r a NonFlow system W P dV
P2 V2 P1V1 1 n
PV 2 C; n 2 2
P1V1 P2 V2
2
500(0.05 )2 200 20 0V2 V2 0.08 m3 W 9 KJ
2
11. If the F scale s cale is twice the C scale, sc ale, what what will be the corresponding corresponding reading reading in each scale? C
F 32
1. 8
F 1.8C 32 F 2C
2C 1.8C 32 C
32 2 1. 8
160 0 16
F 32 0
12. A cylindrical tank 2 m diameter, 3 m high is full of oil. If the specific gravity gravity of oil is 0.9, what what is the t he mass of oil in the tank? (8482.3 kg)
Vcylinder S
π
4
D2H
π
4
(22 )3
3 π m3
ρ
ρ water ρ
0.9
1000 kg 900 90 0 3 ρ m m ρ V m 900 90 0(3 π )
8482.3 kg
13. 10 liters of an incompr essible liquid exert a force of 20 N at the earth’s surface. What force would 2.3 Liters of this liquid exert on the surface surface of the moon? The gravitat gravitational ional acceleration acc eleration on the surface of the moon is 1.67 m/sec 2. F ma
m V
1m3 kg m V (10.0) 1000 L 20
(10.0)
1000
9.81 N
kg m3 On the surface of the moon
203.874
2.3 (1.67) 0.783 N 1000
F 203.874
14. If the temperature temperature inside a furnace furnace is 700 K, what what is the corresponding corresponding reading reading in F? (800.6) Solution: t = 700 – 273 = 427 C F = (427)(1.8) + 32 F = 800.6F 15. A storage storage tank contains oil with a specific gravity gravity of 0.88 and and depth of 20 m. What is the hydrostati c pressure at the bottom of the tank in kg/cm2.(1.7) Solution: Using: g = 9.81 m/sec2
P0
0.88(1000)(9.81)(20) 1000
P = 1.7 kg/cm 2
172.656 KPa
16. A hiker carrying a barometer barometer that measures 101.3 KPa at the base of the mountain. The barometer reads 85 KPa at the top of the mountain. The The averag average e air density i s 1.21 kg/m3. Determine the height of the mountain.
dP
γdh
P2
P1
h2
h1
h
(P1
h
h
h
γ(h 2
h1 )
P2 )1000 ρg
(101 10 1.3 85 )1000 1.21(9.81)
1373 m
17. Water runs through a water main of cross sectional area of 0.4 m 2 with a velocity of 6 m/sec. Calculate the velocity and mass flow rate of the water in the pipe when the pipe tapers down to a cross sectional area of 0.3 m2. ( = 1000 kg/m 3)
m1
m2
A 1v 1
m
m
m 1000(0.4)6 2400
kg sec
A 1v 1 A 2 v 2
v2
A 1v 1 A 2
8
m sec
18. The 600 kg hammer hammer of a pile driv driver er is lifted 2 m above above the piling head. W hat is the change in potential energy energy ? If the hammer hammer is released, what will be its velocity velocity at the instant it strikes the filing? filing? Local g =9.65 mps2.(11.58 KJ; 6.21 mps) m = 600 kg Z = 2 m g = 9.65 m/sec2
mgZ KJ 1000 PE 11.58 KJ KE = PE 2 2 m( v f v i ) 11.58 2(1000) PE
vi v f
0 11.58(2000) 600 60 0
6.21
m sec
19. A lump of ice falls falls from from an aero plane as it comes into land. If the ice hits the groun ground d with a vertical vertical speed of 85 m/sec, m/sec , what was was the height of the plane when the ice fell fell off? off? (use g = 9.81 m/sec 2)
ΔKE
ΔPE
m 85 0 2
h
2(1000)
mg0 h 1000
h 368.25 meters
20. 5 kg of brass of specific heat 0.39 KJ/kg - C at a temperature of 176 176 C is dropped into a 1.2 kg of water water at 14 C. Find the resulting temperature temperature of the mix ture. (C (C PW = 4.187 KJ/kg - C)
mw
1.2 kg
mB
CPB
5 kg
CPW
0.39
KJ kg - C KJ kg - C
4.187
Heat rejectedby brass Heat absorbedby water QB
QW
mBCPB ( t B1 t ) m w CPW ( t t w1 ) 5(0.39)(17 176 6 t ) 1.2( 4.187)( t 14) t
40.4C
21. How much heat is removed removed to make ice of mass m = 0.720 kg at -10 C from a liquid at 15 C. Specific heat of ice = 2.22 KJ/kg-C Specific heat of water = 4.19 KJ/kg- C Freezing point temperature of water = 0 C hF of ice = 334.9 KJ/kg Answer: 302 KJ
Q Q1 Q 2
Q3
Q1
mC pw (15 0) sensible heat
Q2
m(hF ) latent heat
Q3
mC pi (0 10) sensible heat
Q 0.7204.19(15- 0) (334.9) 2.22(0 10) Q 302 KJ 22. A steam turbine turbine receives receives superheated superheated steam at 1.4 MPa and 400 C (h1 = 3257.5 KJ/k g). The The steam st eam leaves leaves the turbine at 0.101 MPa and 100 C (h2 = 2676 KJ/kg).The steam enters the turbine at v 1 = 15 m/sec and exits at v2 = 60 m/sec. m/s ec. The The elevation elevation differen difference ce between between entry and exit ports ports is negligible. The heat loss t hrough hrough the turbine walls is 2 KW. Calculate the power output if the mass flow through the turbine is 0.5 kg/sec.
Q h KE PE W h
m(h2
h1 ) 290 29 0.75 KW 2
KE PE
2
m(v 2 - v 1 ) 2(1000)
0.275 KW
0
Q 2 KW W
Q - h - KE - PE
W
2 290.75 - 0.275 - 0
288.475 47 5 KW
23. Steam with a flow flow rate of 1360 1360 kg/hr enters enters an adiabatic adiabatic nozzle at 1378 KPa, 3.05 m/sec with a specific volum volum e of 0.147 m3/kg and with a specific internal energy energy of 2510 2510 KJ/kg. The exit c onditions are, P = 137.8 137.8 KPa, specific volume = 1.099 m3/kg, and internal energy energy = 2263 KJ/kg. Determine Determine t he exit velocity velocity in m/sec. Given: m = 1360 kg/hr = 0.377 kg/sec P1 = 1378 KPa v1 = 3.05 m/sec 1 = 0.147 m3/kg U1 = 2510 25 10 KJ/kg
P 2 = 137.8 KPa 2 = 1.099 m3/kg U2 = 2263 KJ/kg
1
2
For Adiabatic Adiabatic Q = 0 and for a Nozzle W = 0
1
2 Wt
3
24. A s mall steam turbine operating operating at part part load produ produces ces 110 KW output with a steam flow flow rate of of 0.25 kg/s ec. Steam at 1.4 MPa, 250 C is throttled throttled to 1.1 MPa before before entering the turbine, turbine, and the turbine turbine exhaust pressur pressur e is 10 KPa. Find the steam quality quality (or temperature, temperature, if superhea superheated) ted) at the turbine turbine outlet. (x 2 = 96%) From table 3 at 1.4 MPa and 250 C: h = 2927.2 KJ/kg From table 2 at 10 KPa (0.010 MPa): hf = 191.83 KJ/kg; hfg = 2392.8 KJ/kg Q 0
h KE PE
h KE 0
W
0
KE h
v2
2
v1
2
2(1000) v2
(h 2 h1 )
2(1000)(h1
h2 )
v1
2
h U P
kg m 0.25 sec h1
h2
2927.2
h1
2510 (1378)(0.147 ) 2712.6 KJ/kg
h2
2263 (137.8 )(1.099 ) 2401.9 KJ/kg
v2
788.3 m/sec
KJ kg
Q h KE PE W Q 0; KE W
0 and PE
0
- h
110
m(h 2 - h3 )
110 m KJ h3 2487.2 kg h3
h2 -
h h f x(hfg ) 2487.2 - 191.83 0.96 2392.8 x 3 96% x3
25. A throttling calorimeter is connected to the de-superheated de-superheated steam line supplying steam to the auxiliary auxiliary feed pump of a ship. The The line l ine pressure pressure measures 2.5 MPa. The c alorimeter pressure i s 110 KPa and and the temperatur temperature e is 150C. Determine the line steam quality. From Superheated table, at 110 KPa and 150 C, h2 = 2775.6 KJ/kg From Saturated liquid and saturated sat urated vapor vapor table t able hf 1 = 962.11 KJ/kg; h f g = 1841.0 KJ/kg h1 = h f 1 + x 1(hf g1) h1 = h2
h1 hf 1 hfg1
x1
x1
98.5 %
2775.6 962.11 0.985 98 5 1841.0
26. An engineering engineering student wants wants to cool 0.25 kg of Omni Cola (mostly water) i nitially at 20 20 C by adding ice that is initially at -20C. How much ice should be added added so that that the final temperature temperature will be be 0 C with all the ice melted, if the heat capacity of the container neglected. Cwater = = 4.19 KJ/kg- C Cice = 2.010 KJ/kg-C hf of ice = 334.9 KJ/kg Qcola = Qice 0.25(4.19)(20 – 0) = m ice[(2.010)(0 [(2.010)(0 + 20) + 334.9] mice = 0.056 kg = 56 gram 27. 2.5 kg of brass of specific heat 0.39 KJ/kg -K at a temperature temperature of 176 176 C is dropped dropped into a 1.2 1.2 liters of water water at 14C. Find the resulting resulting tempera t emperature ture of the mixture. (At (At 14 C density density of water is 999 kg/m3)
mw
1.2 1000
(999) 1.1988 kg
Heat rejected by brass = Heat absorbed by water 2.5(0.39)(176 – t) = 1.1988(4.187)(t – 14) 171.6 – 0.975t = 5.02t – 70.3 t = 40.4C 28. An 85 Liters drum contains saturated sat urated water wat er and water water vapor vapor at 370 C. a. Find the masses of each if their volumes are equal b. Find the volume volume occupied by each if their mass es are equal From steam table at 370 C vf = 0.002222 0.002222 m 3/kg vg = 0.004193 m 3/kg a. V L = 0.0425 m3 ; V V = 0.0425 m3
v f
mL vg mV
VL mL
0.002222
0.0425 19.13 kg 0.002222 VV 0.004193 mV
0.0425 10.14 kg 0.004193
b.
VL VV 0.085 VL 0.085 VV eq. 1 v f
VL mL
0.085 VV eq. 2 0.00222 V vg V mV
mL
VV eq. 3 0.004193 mL m V mV
0.085 VV VV 0.00222 0.004193 0.085(0.004193) VV 0.002222 0.004193 VV 0.056 m3 VL 0.029 m3
29. An industrial power power plant requires requires 1.5 kg of dry dry saturated sat urated steam per per second sec ond at 165 165 C for heating purposes. This steam may be supplied from from an extracti extraction on turbine which receives receives steam at 4 MPa and 380 C and is exhauste exhauste d to a condenser at the rate of 0.8 kg/s ec at 0.0034 0.0034 MPa while rejecting 1400 KW to the cooling water. water. If the mechanical efficiency of the turbine generator unit is 95% and the heat heat loss los s in the turbine c asing is 10 KW, calculate the power generated by the plant. (Wo = 1540 KW) h at 4 MPa and 380 C = 3165.9 KJ/kg hg at 165C = 2763.5 KJ/kg hf at 0.0034 MPa = 109.84 KJ/kg
h1 P1 = 4 Mpa t1 = 380 C m = ______
10 KW Generator Efficiency = 94%
1 Wt’
1.5 kg/sec
2
165 C
h2
GP = Generator Power
3
0.8 kg/sec
QR = 1400 KW 4
h4
By mass balance kg sec By energy balance condenser m 1.5 0.8 2.3
QR
0.8(h3
h4 )
1400 0.8(h3 109.84) h3
1859.84
KJ kg
By energy balance in the turbine 2.3(3165.9) - 10 - 1.5(2763.5) - 0.8(1859.84) Wt Wt
1638.45 KW
WOUTPUT
1540.14 KW
30. Steam enters enters a turbine turbine with a velocity velocity of 1.5 m/sec and an enthalpy enthalpy of 2093 KJ/kg and leaves leaves with an enthalpy of 1977 1977 KJ/kg K J/kg and and a velocity velocity of 91.5 m/sec. Heat Heat loss es are are 8 KCal/min and the st eam flow rate is 27 kg/min. The inlet of the turbine is 3.5 m higher than its outlet. What is the work output of the turbine if the mechanical losses is 15% a) 32.4 KW b) 24.3 KW c) 34.2 K d) 48 KW
m sec m v 2 91.5 sec kg kg m 27 0.45 min sec KCal KJ 1 min Q8 x 4.187 x min KCal 60 sec z1 0 v 1 1 .5
z2
0.56 KW
(rejected)
-3.5 m
h1 2093
KJ kg
h2
KJ kg
1977
2
KE h
2
m( v 2 v1 ) 2(1000)
m(h2
1.883 KW
h1 ) 52.2 KW
KW
mg( z 2 z1 ) 0.015 KW 1000 Q h KE PE W PE
W
Q ( h KE PE) 49.77 KW
Power Output 49.77(1- .15) 42.3 KW 31. An air compressor handles 8.5 m 3/min of air with a density of 1.26 kg/m 3 and a pressure of 101 KPaa and discharges at 546 KPaa with a density of 4.86 kg/m 3. The The c hanges hanges in i n specific internal energy energy across the compressor is 82 KJ/kg and the heat loss by cooling is 24 KJ/kg. Neglecting changes in kinetic and potential energies, find the work in KW.
m
V m V 1.26(8.5 ) 10.71 kg/min 0.1785 kg/sec Q U (P ) KE PE W W Q - U - (P ) - KE - PE W Q - (U2 - U1 ) - (P2 2 - P1 1 ) - 0 - 0
P2
W Q - (U2 - U1 ) -
P1
2 1 KJ 546 101 W ( 24) (82) 138.2 kg 4.86 1.26
In KW W 0.1785(-138.2) 24.67 KW W 24.67 KW (Work is done on the system)
32. Calculate the change of entropy per kg of air when heated from 300 K to 600K while the pressure drops from 400 Kpa to 300 KPa. ( S = 0.78 KJ/kg-K) Given; R = 0.287 KJ/kg-K k = 1.4 T1 = 300K ; T2 = 600K P1 = 400 KPa ; P 2 = 300 KPal T P Cp ln 2 R ln 2 ΔS T1 P1
33. A certain mass of sulfur dioxide (SO 2) is contained in a vessel ess el of 0.142 m 3 capacity, at a pressure and temperature of 2310 KPa and 18C, respectively. respectively. A valve alve is open open momentarily and the pressure pressure falls immediately to 690 KPa. Sometime later lat er the temperature temperature is again again 18 C and the press pressure ure is observed observed to be 910 KPa. Es timate the value value of specific heat ratio. (k = 1.29)
8.3143 0.13 64 P1V1 m1RT1
R
m1
2310(0.142) 8.67 kg 0.13(291)
At V C P1 P2 T1 T2
P T2 2 86.92K P1 T1 34. Two Two unequal vessel ess el A and B are are connected connect ed by a pipe with a valv valve. e. Vessel Ves sel A contains 150 L of air at 2760 KPa KP a and 95C. Vessel B contains an unknown volume of air at 70 KPa and 5 C. The valv valve e is opened and when t he properties have have been determined, determi ned, it i t was was found out that the pressure press ure of the mixture is 1380 KP a and the temperature temperature is 45C. What is the volume of vessel B.(0.166 m3) Given: V A = 0.150 m 3 ; P A = 2760 KPa ; T A = 95 + 273 = 368 K P B = 70 KPa ; TB = 5 + 273 = 278 K P = 1380 KPa ; T = 45 + 273 = 318 K
V
V A
m m A m
VB mB
PV ; m A RT
P A V A ; mB RT A
1380(0.150 VB ) R(318 ) 0.65 4.34 VB VB
PB VB RTB
2760(0.150 ) 70( VB ) R(368 ) R(278 )
1.125 0.252 VB
(1.125 0.65) ( 4.34 0.252)
0.116 m3
35. A vess vessel el of volume volume 0.2 m3 contains nitrogen at 101.3 KPa and 15 C. If 0.2 kg of nitrogen is now pumped into the vessel, vessel, calculate t he new pressure pressure when the vessel vessel has returne returned d to its initial temperatur temperature. e. For nitrogen: nitrogen: M = 28; k = 1.399. (187 KP a) (Sample Prob. June June 18, 2014) 2014)
Given : V1 0.2 m3 ; P1 101.3 KPa; T1 15 273 288K ma - 0.2 kg (mass of N2 added PV
m R
mRT
PV RT 8.3143 KJ 28 kg - K
m1
101.3(0.2)28 8.3143(15 273)
m2
0.237 0.2 0.437 kg final mass
T2
15
0.237 kg
273 288K
mRT V V2 V1
P
P2
0.437(8.3143)(15 273) 186.82 KPa 28(0.2)
36. A certain perfect perfect gas of mass 0.1 kg occupies a volume volume of 0.03 m 3 at a pressure of 700 KPa and a temperature of 131C. The gas is allowed allowed to expand until the pressure is 100 KPa and the final volume volume is 0.2 m 3. Calculate; Calculate; a) the molecular molec ular weight of the gas (16) PV mRT b) the final temperature PV Given; R 1 1 3 m = 0.1 kg ; V 1 = 0.03 m ; P 1 = 700 KPa ; T1 = 131 +273 = 404 K mT1 P2 = 100 KPa ; V 2 = 0.2 m 3 KJ R 0.52 kg - K 8.3143 M 8.3143 kg 16 M R kgmol mol R
PV
T P1V1 T1 T2 t2
C
P2 V2 T2
T1P2 V2 P1V1
384.8K
111.8C
37. An ideal ideal gas with R = 2.077 2.077 KJ/kg-K and a constant k= 1.659 undergoes undergoes a constant pressure pressure process during which 527.5 K J are added to 2.27 kg of the gas. The The initi i nitial al temperature is 38 C. Find the S in KJ/K. Given: R = 2.077 KJ/kg-K; k = 1.659 Q = 527.5 KJ; m = 2.27 kg T1 = 38 + 273 = 311 K Process: P = C
Cp Q = mCp(T2 – T1) ; Q T1 352 T2 352 K mCp S mCp l n
T2 T1
RK
k 1
1.6KJ / K
5.72KJ / kg K
38. A certain perfect perfect gas of mass 0.1 kg occupies a volume volume of 0.03 m 3 at a pressure of 700 KPa and a temperature of 131C. The gas is i s allowed allowed t o expand until the pressure pressure is 100 KPa and the final volume volume is 0.02 m 3. Calculate; Calculate; a) the molecular molec ular weight of the gas (16) b) the final temperature (11.5 C)
700 70 0(0.03)
0.1(8.3143)(131 13 1 273 27 3) M
M 16 P2 V2mRT2 100 10 0(0.15) t2
0.1(8.3143)( t 2 273 27 3) 16
15.7C
39. What is the weight of a 114 L tank of oxygen (O 2) if the oxygen is pressurized pressurized t o 1.4 MPa, and the tank itself its elf weighs 445N, and the temperature is 10 C. 8.3143
R PV
32
m
0.26
1400(0.114)
KJ kg - K
mRT
0.26(10 273)
WO 2 Wt
2.17 kg
2.17(9.81) 21.29 N
445 21.29 446.29 N
40. Assume 2 kg of O 2 are mixed with wi th 3 kg of an unknown gas. The result ing mix ture occupies a volume volume of 1.2 m3 a) R and M of the unknown unknown gas constit uent b) the volumetric analysis c) the partial pressures For O2: M = 32 ;k = 1.395 Given; m O2 = 2 kg; m x = 3 kg V = 1.2 m3 ; P = 276 KPa; T = 338 K a) m = 5 kg xO2 = 0.40 ; x x = 0.60 R = 0.1361 KJ/kg-K R = .40(0.26) .40(0.26) + 0.60(Rx) Rx = 0.535 KJ/kg-K Mx = 15.54 15.54 kg/kgm b) c)
y O2 = 0.245 ; y x = 0.755 P O2 = .245(276) = 67.62 KPa ; P x = 0.755(276) = 208.38 KPa
41. How many kilograms of N 2 must be mix ed with 3.6 kg of CO 2 in order order to produce produce a gaseous mix ture that is 50% 50% by volume volume of each constit uents. Gas CO2 N2
M 44 28
y N2
y CO2
k 1.288 1.399
0.50
0.50
y iMi M M 0.50(28) 0.50( 44) 36 xi
R 0.231 x N2
x CO2 x N2
0.50(28 ) 0.389 36 1 .389 0.611
mN2
m
0.389
m N2
mCO2
m N2 m N2
(0.389 )mN2 mN2
mN2
3
0.389(3) mN2
0.389(3) (1 0.389 )
1.91 kg
42. Three Three moles of oxygen is compressed in a piston cylinder ass embly in a rev reversible ersible adiabatic adiabatic process from from a temperature temperature of 300 300 K and a pressure of 102 102 K Pa until the final volume volume is one tenth the init ial volume. volume. Determine the final temperature and the final pressure. Given; T1 = 300 K ; P 1 = 102 KPa ; V2 T2 T1
1
10
V1 ;
V1 V2
k 1
10
V V 1 ; T2 T1 1 V2 V2
k 1
k
k
; P1V1
k
P2 V2 ; P2
P1
V1 V2
k
For Oxygen; R = 0.2598 KJ/kg- K; k = 1.395 T2 = 745K ; P 2 = 2532.8 KPa
43. Two k ilograms of helium operates operates on a three process process cyc c ycle le where where the process processes es are constant volume volume (1 to 2); constant cons tant press pressure ure (2 to 3); and constant temperature t emperature (3 to 1). Given Given that P 1 = 100 KPa, T1 = 300 K, and 1/ 3 = 5. Determine the pressure, pressure, speci fic volume volume and temperature temperature around around the t he cyc le. For Helium: R = 2.077 KJ/kg-K ; k = 1.666
Given: 1/ 3 = 5 P1 = 100 KPa ; T1 = 300 K ; Processes: 1 to 2 (Isometric: V = C) 2 to 3 (Isobar (Isobaric: ic: P = C) 3 to 1 (Isothermal: (Isothermal: T = C or PV = C) T2 T1 υ1
υ
1
υ
2
υ1
P2
P1
υ 2
RT1 P1
6.231
2.077(300) 100
m3 6.231 kg
m3 kg
5
υ 3 υ υ 3
P1 υ1
1
5
6.231 5
1.245
P1 υ1
P3
P3
P2
T3
100(6.231) 1.245
υ3
T2
T2
T1
T1
P2 P1
500.5 KPa
500.5 KPa 300 K
300
500.5 100
1501.5 K
m3 kg
P3 υ3
44. Oxygen expands in a reversible reversible adiabatic m anner anner through through a nozzle nozzl e from from an init ial pressure and initial temperature temperature and with an initi al velocity velocity of 50 m/sec . there is a decrease decrease of 38 K in temperature across the nozzle. Determine a. the exit velocity b. for inlet conditions of 410 KPa and 320 K, find the exit pressure. 1
Given: v1 = 50 m/sec T = 38 K P1 = 410 KPa ; T1 = 320 K Fpr O2: Cp = 0.918 KJ/kg-K ; k = 1.395
2
Q h KE PE W Q 0; W 0; and PE 0
KE h -C p (T2 - T1 ) 2
v2 - v1 2000 v2
2
-C p (T2 - T1 )
v 1 - 2000Cp (T2 - T1 ) exit velocity 2
m
v 2 259.4
sec T2 T1 38 K T2 320 - 38 282 K k
T k 1 2 P1 T1 P2 262.4 KPa P2
45. A throttling calorimeter is connected to the main steam line where where the pressure is i s 1.75 1.75 MPa. The The calorimete r pressure is 90 KPa and 105C. Determine the main steam quality. From steam table T Aat 1.75 MPa; hf = 878.50 KJ/kg ; h g = 2796.4 KJ/kg At 90 KP a and 105 C; C; h = 2687.55 KJ/kg h1 = h at 1.75 MPa MPa and unk nown nown quality 1 x 1 = 94.32% h2 = h at 90 KPa and 105 C P 1 = 1.75KPa h1 = h 2 10 5 C 2 h1 = h f1 + x1(hfg1) = h 2 P 2 = 90 KPa 2687.55 = 878.5 + x1(2796.4 – 878.5) x1 = 0.9432 = 94.32%
46. A cylinder cyli nder fitted fitted with a frictionless frictionless piston contains 5 kg of superheated superheated water vapor vapor at 1000 KPa and 250 C. The system sy stem is now cooled at constant pressure until the water water reaches a quality of 50%. Calculate the work work done and the heat transferred. T
W
1 2
U S
Q
From Stea m Table: Table: At 1000 KPa KPa a nd 250C (superheated) h = 2942.6 KJ/kg U = 2709.90 KJ/kg S = 6.9247 KJ/kg- C = 0.2327 m 3/kg At 1000 KPa KPa a nd x = 50% h = 1770.46 KJ/kg U = 1672.64 KJ/kg S = 4.3626 KJ/kg- C = 0.097784 m 3/kg tsat = 179.91C
U1 2709.9 KJ/kg ; h1 2942.6 KJ/kg U2 1672.64 KJ/kg ; h2 1770.46KJ/kg Q U W
U m(U2 - U1 ) 5(1672.64 - 2709.9) 5186.3 KJ
2
W m Pd mP( 2 1 ) 5(1000)(0.97784 0.2327) 674.58 KJ (work is done on the system) 1
Q 5860.88 KJ (heat is rejected)
47. A 0.5 m 3 tank contains saturated st eam at 300 KPa. Heat is transfer transferred red until the pressure pressure reaches 100 100 KPa. Determine t he heat transferred and the final temperature. T 300 KPa
U
1 2
Q
100 KPa
Process: Constant Volume W=0 Q = U Q = m(U2 – U1) From St eam Table Table at P = 300 KPa KP a (sat (saturated urated vapor) U1 = 2543.6 KJ/kg 1 = 0.6058 m 3/kg υ
V
m
m 0.5
0.6058
0.825 kg
From steam Table at 100 KPa
g = 1.694 m 3/kg ; f = 0.0010432 m 3/kg f g = g - f = 1.693 m 3/kg Ug = 2506.1 KJ/kg ; U f = 417.36 KJ/kg ; Uf g = 2088.7 KJ/kg 2 = 1 2 = 0.0010432 + x 2(1.693) = 0.6058 x2 = 0.357 = 35.7% U2 = 417.36 417.36 + (0.357)(2 (0.357)(2088.7) 088.7) = 1163.465 1163.465 K J/kg Q = 0.825(1163.465 – 2543.6) = -1138.6 KJ Q = 1138.6 KJ (Heat is rejected from the system)
48. A rev reversible ersible nonflow nonflow constant volume volume process decreases the internal energy by 316.5 KJ for for 2.3 kg o f a gas for which R = 0.47 KJ/kg-K and k = 1.35. For the process, determine a. the work b. the heat c. the entropy change if the initi al temperature temperature is 478 K Given: U = -316.5 KJ m = 2.3 kg R = 0.47 KJ/kg-K k = 1.3 T1 = 478K Solution At V = C ; Q = U = mCv (T) R 0.47 1.567 KJ/kg - K Cv k 1 1.3 1 Q - 316.5 2.3(1.567)(T 2 - 478) T 2
a. b.
390K
W = PdV = 0 Q = -316.5 -316.5 KJ Q = 316.5 KJ (heat is rejected)
c.
mCv l n S mCv
T2 T1
2.3(1.567)ln
390 478
0.733
KJ K
49. In a turbine 4500 kg/min of air expands polytropically from 425 KPa and 1360 K to 101 KPa. The The exponent = 1.45 for the process. Find the work done and the heat transfer. Given: m = 4500 kg/min ; P 1 = 425 KPa; T1 = 1360K ; P 2 = 101 KPa; PV n = C n = 1.45 ; KE and PE are negligible For Air: R = 0.287 KJ/kg-K; k = 1.4; Cp = 1.0045 KJ/kg- K; Cv = 0.7175 KJ/kg- K
n
n 1 nmRT1 P2 n 1 W Q Δh 1 n P1
Q mCn (T2 T1 );
P k n ; T2 T1 2 1 n P1
Cn Cv
n 1 n
1.451 1.45 1 33.938 KW W 60(1 1.45) 425 1.45 1 4500(0.7175)(1.4 - 1.45)(1360) 101 1.45 1 2926 KW Q 425 60(1 1.45) Q 2926 KW (heat is rejected)
1.45(4500)(0.287)(1360) 101
50. Steam flows flows s teadily through through a turbine with a mass flow flow rate of 2.52 kg/sec . The The inlet steam conditions are 7000 KPa and 500 C. The exit steam pressure pressure is 20 KPa and the expansion is isentropic. Determine the turbine work in KW. From Steam Table Table (superheated (superheated state) At 7000 KPa and 500 C h1 = 3410.3 U1 = 3073.4 S1 = 6.7975 At S 1 = S2 to 20 KPa (saturated mixture region) h2 = 2239.45 U2 = 2110.47 x2 = 84.3%
m
1 W
2 Q=0
m
Q h KE PE W Q 0 (for adiabatic) KE and PE
are negligible
W -h -(h 2 - h 1 ) KJ/kg W m(h1 - h 2 ) KW where m is the mass flow rate in kg/sec W 2.52(3410.3 2239.45) 2959.54 KW 51. In In thermodynamics, a fixed fixed quantity of mass select ed for for the purpose purpose of study is called a: a. system b. closed system c. open sys tem d. control volume 52. In order order for a syst em to be in thermal equilibrium, which of the following following properties properties must be the same throughou throughou t the system? a. mass b. pressure c. temperature d. volume
53. A cy cle consists of a series series of processes processes that: a. eventually eventually return to the first state of of the first first process b. are continually repeated repeated c. are always in equilibrium equilibrium or quasi-equilibrium d. none of these thes e 54. A 0.5 m 3 container is filled with a fluid fluid whose specific volume volume is 0.001 0.001 m 3/kg. At standard standard grav gravitation al acceleration, the contents of this container weigh: a. 2010 N b. 3220 N c. 4905 N d. 7830 N
V
0.5 m3
V m 0.5 500 kg m 0.001 W 500(9.81) 4905 N
υ
55. Which Whic h a. b. c. d.
temperature temperature below i s equivalent equivalent to 125 °F? °F? 52 °C 125 °C 602 °R 315 K
C
F 32
1.8
125 32 1.8
51.7C
56. On a day when the barometer barometer reads reads 755 mm Hg, Hg, a tire pressure pressure gage reads 204 KPa. The The absolute pressur e in the tire is: a. 100 KPa b. 204 KPa c. 1.54 m Hg d. 2.29 m Hg
755 (101 101 .325 325 ) 755 305 KPa 2.29 m Hg 305 760 760
Pabs 204 204
57. The fan pressure differential differential gage on an air handler reads 12 cm H2O. What is this pressure differential differential in Kilo Pascals? a. 0 kPa b. 0.93 kPa c. 1.18 kPa d. 1.37 kPa 0.12 m H2O x
101.325 KPa 10.33 cm H2O
1.18 KPa
58. At a pressure of 4 Mpa, the temperature at which liquid water boils is: a. 29.0°C b. 100.0°C c. 143.6°C d. 250.4°C 59. The specific speci fic volume volume of a sys tem consisting of refriger refrigerant ant 134a at 1,000 KP a is 0.01 m 3/kg. The quality of the R134a is: a. 12.62 % b. 46.92 % c. 68.32 % d. Not applicable
At 1000 KPa (10 Bar) υ
f 0.870
L kg
υ
g 20.33
L kg
10 x
0.870 870 x(20.33 0.870 870 )
47%
60. A system contains water at 2,000 KPa, 220°C. The phase of this water is: a. Liquid b. Liquid-vapor Liquid-vapor mixture mix ture c. Vapor d. Solid 61. KNA thermodynamic system contains water at 10 m 3 of air whose press ure and temperature are 300 KPa, 127°C respectively. The weight for this system is: a. 92 KN b. 127 KN c. 192 KN d. 256 KN
From Steam Table at 300 KPa and 127 127 C m V m m 936 936 .75(10) 9367.5 kg ρ
936.75
kg
3
9367.5(9.8 1) 92 KN 1000 62. Air in a closed piston-cy linder device device arranged arranged to maintain a pressu re of 400 400 KPa K Pa is heated from from 27°C t o 227°C. Initially Initially the volume volume of the air is 1 lit er. What is the final air volume? volume? a. 0.5 liters b. 0.00167 m 3 c. 2.4 liters d. 0.036 m 3 V1 V2 T1 T2 W
mg
9367.5(9.8 1) 9367.5(9.8 1)
0.001 (27 273 ) V2
V2 (227 273 )
0.00167 m3
63. Propane Propane gas (Pc = 4.26 MPa, Tc Tc = 370 370 K) is maintained at 6.39 MPa and and 444 K. How muc h volume volume does 1 kg of this gas fill? a. 8.78 liters b. 12.3 liters c. 13.1 liters d. 15.7 liters C3H8 : Propane
M
R
PV
44 0.189
KJ kg - K
mRT
1(0.189)( 444) 0.131 131 m 3 13.1Liters 6390 64. Air (Cp = 1.005 kJ/kg-k) is heated from 27°C to 327°C. How much does the specific internal internal energy energy of the air change as a result of this heating? a. 301.5 kJ/kg decrease b. 301.5 kJ/kg increase c. 215.4 kJ/kg decrease d. 215.4 kJ/kg increase V
Cp
CV
R
Cv
005 0.287 287 1.005
0.718 718
KJ kg - K
KJ kg 65. Steam at 1 MPa, 250°C is contained in a rigid vessel. It is now cooled to 25°C. The final quality (if applicable) of the vessel contents is: a. 0.54 % b. 2.63 % c. 27.8 % d. Not applicable ΔU
C v ( t 2 t1) 215 215 .4
From Steam table 1000 KPa ; t ρ
4.2926
υ
0.233
250C (Superheat ed0
kg m3
m3 kg
U 2709 .5 25C (Saturated ) υL
0.001
υv
43.42
0.233 x
0.001 x(43.42 - 0.001)
0.54%
66. The interaction that occurs between a sy stem and and its surroundings surroundings as the syst em executes a process process,, which is the result result of the sy stem being at at a temperatur temperature e differen differentt from from the surroundin surroundings, gs, is: a. Mass transfer b. Heat transfer c. Work transfer transfer d. None of these thes e 67. Air is expanded from 1 MPa, 327°C to 200 kPa in a closed piston-cylinder device executing a PV 1.2 = c onstant onstant process. The work produced during this process is: a. 202.6 kJ/kg b. 263.4 kJ/kg c. 361.7 kJ/kg d. 422.8 kJ/kg n 1 nmRT 1 P2 n 1 W 1 n P1
m 1 kg ; R 0.287 W 201.57
KJ kg - K
KJ kg
68. Oxy gen (M = 32 kg/kg-mol) at 200 kPa, 27°C is contained in a piston-cy linder device device arranged arranged to maintain a constant pressure. How much work work is produced by t his sys tem when it is heated to 227°C? 227°C? a. 0 kJ/kg b. 11.2 kJ/kg c. 37.1 kJ/kg d. 52.0 kJ/kg
R
8.3143 32
W
P( V2
W
mR (T2
69. A 1000 a. b. c. d.
0.26
KJ kg - K
V1 ) Isobaric (Nonflo (Nonflow w) T1 )
52
KJ kg
kg automobile accelerates from 10 km/hr to 120 km/hr. How much work does this require? 0 kJ 501 kJ 552 kJ 80 kJ 2
W
2
m( v 2 v1 ) KJ 2(1000 )
m sec m v 2 33.33 sec 70. Steam at 1 MPa, 300°C flows through a 30 cm diameter pipe with an averag average e velocity of 10 m/s. The The mass flow rate of this steam is: a. 0.731 kg/s b. 2.74 kg/s c. 3.18 kg/s d. 3.78 kg/s v1
2.78
From Steam Table P
1000 KPa; t
ρ
3.8750
A
m
π
300C
kg m3
d2
4 d 0.30 m ρ Av
2.739
kg sec
71. Refrigerant-13 Refrigerant-134a 4a flows through t hrough a pipe at 800 KPa, 50°C. The spec ific flow work required t o move move this fluid fluid through a cross-section of the pipe is: a. 22.84 kJ/kg b. 31.60 kJ/kg c. 37.21 kJ/kg d. 40.70 kJ/kg
From R134a Table P 800 800 KPa KPa ; t 50C (Superheat ed) υ
28.547
L kg
28.547 547
E f PV 800 800
1000
22.84
KJ kg
72. A mixture of ideal ideal gases has an appar apparent ent molecular weight of 36.4 kg/k g-mole and a specific enthalpy of 273.2 kJ/kg when the temperature is 127 °C. The specific internal energy of this gas mixture is: a. 98.72 kJ/kg 8.3143 KJ b. 153.1 kJ/kg R 0.228 36.4 kg K c. 181.8 kJ/kg d. 273.2 kJ/kg hC t p
273.2
Cp (127 273 )
Cp
0.683
Cp
Cv
Cv
0.683 0.228
R
0.445
U 0.445(127 273 ) 182
KJ kg
72. A 12 V DC electrical motor draws draws a current current of 18 amps. How much work does this motor produce produce over over a 1010 minute period of operation? a. 97.42 kJ b. 129.6 kJ c. 216.0 kJ d. 318.2 kJ 73. Air at 1 MPa, 27°C is contained in a piston-cy linder device device that is arranged arranged to maintain a constant pressure. How much heat is required to raise the temperature of this air to 527°C? a. 180 KJ/kg b. 370 KJ/kg c. 502 KJ/kg d. 1040 KJ/kg KJ Q Cp (T2 T1 ) 1.0045 (527 27 ) 502.25 kg ΔU
W Q
0.7175 (527 27 ) 358.75
0.287(527 27) 143.5
ΔU
W
502.25
KJ kg
74. Two Two k ilograms of steam at 2 MPa, 250° C are contained contai ned in i n a rigid vessel. How muc h heat heat mus t be removed removed from this vessel to cool it to 25°C? a. 5030 kJ b. 2512 kJ c. -2512 kJ d. -5030 kJ At 2000 KP KPa a ; t 250 C
U1 2679 .6
KJ kg
0.11144 At 25C ; υ1 0.11144 υ 0 .001003 f Uf 104 .88 υ
1
υ
g
43.36
Ug 2409 .8 x 2 0.0025 U2 110 .75 Q -5137.7 KJ 75. Air is compressed in a piston-cylinder device. Using constant specific heats and treating the process as internally reversible, reversible, t he amount amount of work required to compress this air from from 100 KPa, KP a, 27°C to 2000 K Pa, 706°C is: a. -298.7 -298.7 kJ/kg P1 100 KPa KPa ; T1 27 273 300 K b. -512.2 -512.2 kJ/kg P2 2000 KPa KPa ; T2 206 273 979 K c. 721 kJ/kg n 1 d. 103 kJ/kg n T P 2
T1
2 P1
n 1.65 W
mR (T2 T1 ) 1 n
W 298.71
NonFlow
KJ kg
76. Air enters enters an adiabatic, st eady-flow turbine at 1 MPa, 527° C through through a 1m 1 m 2 duct with a velocity of 100 m/s. The air
leaves leaves a. b. c. d. P
the turbine at 100 kPa, kP a, 157C. The mass flow rate of the air is: 87.4 kg/s 137.3 kg/s 327.2 kg/s 435.34 kg/s
RT
m
ρ Av
ρ1
m
ρ
1000 0.287(527 273) 4.36(1)100
4.36
435.34 kg/sec
77. Air enters enters a steady state, s teady-flow teady-flow turbine at 1,000 1,000 KPa, K Pa, 550°C through a 1m 2 duct with a velocity of 100 m/s. The air leaves leaves this turbine at 100 KP a, 200°C 200°C through through a duct of the same size. Determine the work work produced produced by this Turbine Turbine for for an internally reversibl reversible e process . a. b. c. d.
107.62 102.67 106.27 201.71
MW MW MW MW
P1 1000 KPa; T1 550 273 823 K P2 100 KPa; T2 200 273 473 K m ρ Av ; A 1m2 ; v1 100 ρ1
m sec
P1 kg 4.23 3 RT1 m
m 423.4
kg sec
m ρ 2 Av 2 ρ2
P2 kg 0.74 3 RT 2 m
v 2 574.8
m sec
n 1 n
T2 P2 T1 P1 n 1.32
Q Δh ΔKE ΔPE W Q mC n ( T2 T1 )
k n 1 n Δh mC p (T2 T1 ) Cn C v
2
2
v 2 v1 ΔKE m 2(1000) ΔPE
z z1 mg 2 1000
W 107,618.2 KW
78. Steam at 4 MPa, 400° C enters enters a steady-flow, adiabatic turbine t hrough hrough a 20 cm -diameter-pipe -diameter-pipe with a velocity velocity of 20 m/s. It leaves leaves this t urbine at 50 kPa k Pa with a quality quality of 80% throu t hrough gh a 1 m-diameter pipe. W hat is the velocity velocity of the steam as it leaves the turbine? a. 10.3 m/s b. 28.2 m/s c. 32.6 m/s d. 73.3 m/s
At P 4000 KPa ; t 400C h 3214 .1
KJ kg
13.630
kg
ρ
m3 KJ U 2920 .6 kg P 50 KP KPa a ; x 80% h 2183 .9
0.3858 m ρ Av ρ
kg π 2 m 13.630 0.20 20 8.56 sec 4 8.56
v2
π 2 1 4
28.26
0.3858
m sec
79. Saturated Saturated liquid water enters an adiabatic s teady-flow throttle valv valve e at 500 kPa and leaves leaves at 100 kPa. W hat is the quality qualit y of the water water liquid-v liqui d-vapor apor mixture mix ture leaving leaving this valv valve? e? a. 9.87% b. 10.6% c. 14.3% d. 21.1% 80. Air enters enters the after after burner nozzle of a jet fighter fighter at 427°C with a velocity velocity of 100 m/s. It leaves leaves this adiabatic nozzle at 377°C. 377°C. Assuming that the air specific heats do not not change c hange with t emperature, emperature, the velocity velocity at the nozzle exit is : a. 142 m/s b. 178 m/s c. 227 m/s d. 332 m/s Q Δh ΔKE ΔPE W
0
Δh ΔKE
ΔKE
V2
2
h
Δ
2
V1
Cp (T2
2000 v2
00
T1 ) 2
2000 Cp (T1 T2 ) v 1
m sec
m sec 81. Air is compressed from 100 KPa, 300 K to 500 KPa, 500 K in a steady state, steady-flow compressor. Determine the work required for this compressor per kg: a. -132 kJ/kg b. -181 kJ/kg c. -203 kJ/kg d. -241 kJ/kg P1 100 KPa ; T1 300 K v2
332.34
P2 500 KPa ; T2 500 K n 1 n
P 2 T1 P1 n 1.46 T2
W
nmR nmR (T2 T1 ) KJ 180.8 1 n kg
82. A 3 m 3 drum contains a mixture at 101 KPa and 35 C of 60% Methane (CH 4) and 40% oxygen (O 2) on a volumetric basis. Determine the amount amount of oxygen t hat must be added added at 35 C to change change the volumetric volumetric analysis to 50% of each component. Determine Determine also the new mixture pressure. For mCH x CH CH 4: M = 16; k = 1.321 m O2: R = 32 ; k = 1.395 m 2.65 - 1.514 1.136 kg 4
4
CH4
1st Condition
2nd Condition
M
0.60(16) 0.40(32) 22.4
M
R
8.3143 22.4
x CH4
PV
0.371
KJ kg - K
m
101(3) 0.371(35 273)
m
mO2
2.65 kg
mCH4
yM xi i i M 0.60(16) x CH4 x 100% 42.857% 22.4 x O2 (100 42.857) 57.143% x O2 mO2
mO2 m 0.57143(2.65)
0.50(16) x 100% 33.33% 24 (100 33.33) 66.67%
x O2
mRT
0.50(16) 0.50(32) 24
x CH4
m
m
mCH4
m 1.136 3.41 kg 0.3333 2.65 mO2added
mO2added
3.41 2.65
P
mRT V
P
121.28 KPa
0.76 kg
3.41(8.3143)(35 273) 24(3)
1.514 kg
83. Air enter the nozzle as shown at a pressure pressure of 2700 2700 KPa KP a at a velocity velocity of 30 m/ sec and and with an enthalpy of 923 KJ/kg, and leaves leaves with a pressure pressure of 700 KPa and enthalpy of 660 KJ/kg. If the heat loss is 0.96 KJ/kg, find the exit velocity in m/sec if the mass flow rate is 0.2 kg/sec. a. 727 b. 635 c. 842 d. 574 Q Δh ΔKE ΔPE W
For a nozzle W
0; Δz
0
2
- 0.96 v2
(660 - 923)
727.2
v 2 - (30) 2 2000
00
m sec
84. A gaseous mixture composed of 25 kg of N 2, 3.6 kg of H 2, and and 60 kg of CO2 is at 200 KPa, 50 C. Find the respective partial press ures and compute the t he volume of each each component c omponent at its own partial press ure and 50 C. Given: m N2 = 25 kg ; m H2 = 3.6 kg ; m CO2 = 60 kg m = 25 + 3.6 + 60 = 88.6 kg xN2 = 0.282 ; x H2 = 0.041 ; x CO2 = 0.678 P = 200 KPa ; T = 323 K xi
yi Mi xi Mi xi 0.282 .041 .678 0.046 Mi 28 2 44 y N2 0.219 y H2 0.446 y CO2 0.335
yi
Pi P
P N2 = .219(200) = 43.8 KPa P H2 = .446(200) = 89.2 KPa P CO2 = 0.335(200) = 67 KPa
Pi Vi
miRi Ti
VN2
VH2
VCO2
25(0.297(323) 43.8 3.6( 4.16)(323)
54.76 m3
54.23 m3
89.2 60(0.189)(323) 67
54.67 m3
85. A centrifugal centrifugal pump compresses 3000 L/ min of water from from 98 KPa KP a to 300 KPa. The The inlet and and outlet temperatures temperatures are 3 25C (d = 994.36 kg/m ). The inlet and discharge piping are on the same level, but the diameter of the inlet piping is 15 cm wherea whereas s that of the disc harge harge piping is 10 cm. Determine t he pump pump work in Kilowatts.
3,000 00 0 Q 1000(60)
m3 0.05 sec
v1
0.05(4) 2 π(0.15)
2.83
v2
0.05(4) 2 π(0.10)
6.4
m sec
m sec
Q ΔU Δ(P υ) ΔKE ΔPE W 300 98 994.36 KJ W 0.22 kg
00
( 6.4)2 (2.83)2 2000
0W
kg sec W 0.22(218.8 ) 48 KW
m 0.05(994 99 4.36) 218.8
86. A closed gaseous gaseous sys tem under undergoes goes a reversible reversible process in which 30 KJ of heat heat are rejected and the volum volum e 3 3 changes 0.14 m to 0.55 m . The press pressure ure is constant at 150 KPa. Determine the change of internal energy U and the work done W. Q ΔU W
W
P( V2
- 30 ΔU
V1 ) 150(0.55 0.14 ) 61.5 KJ
ΔU 61.5
-91.5 KJ
87. Air in a piston cylinder occupies 0.12 m 3 at 552 KPa. the air expands in reversible reversible adiabatic adiabatic process in which 1.4 3 PV = C, doing work on on the piston until the volume volume is 0.24 m . Determine a) the work of the system b) the net work if the atmospheric pressure is 101 KPa Pr ocess : PV k 552(0.12) P2 W
Wa w net net
1.4
C
P2 (0.24) 1.4
209 KPa P2 V2
P1V1
40.2 KJ 1- k 101(0.24 - 0.12) 12.12 KJ
40.2 - 12.12
28.08 KJ
88. A piston piston cy linder contains air at 600 600 KP a, 290 K and and a volume volume of 0.01 m 3. A constant pressure process gives 54 KJ of work out. Determine the heat transfer of the process. Given: W P( V2 V1 ) mR (T2 T1 ) P 1 = P2 = 600 KPa T1 = 290 K P1V1 mRT 1 V 1 = 0.01 m 3 PV m 1 1 0.07 kg W = 54 KJ (work out) RT 1
T2
W
T1 478.4 K mR Q mC p (T2 - T1 )
Cp
Rk k -1
1.0045
KJ kg - K
Q 13.24 KJ
89. A 0.5 m 3 rigid tank containing hydrogen at 20 C and 600 K Pa is connected connec ted by a valve alve to another another 0. 5 m 3 rigid tank that holds hydrogen hydrogen at 30 30C and 150 KPa. K Pa. Now the valv valve e is opened and the t he sy stem st em is allowed to reach thermal equilibrium with surroundings which are at 15 C. Determine the final final pressure. As sume hydrogen hydrogen as an ideal gas. (For hydrogen R = 4.125 KJ/kg-K) PV Given: m RT Tank A 3 600(0.5) V A = 0.5 m m A 0.25 kg 4.125(293) T A1 = 20 + 273 = 293 K P A1 = 600 KPa 150(0.5) mB 0.06 kg Tank B 4.125(303 ) V B = 0.5 m 3 At equilibriu m state TB1 = 30 + 273 = 303 K V 0.5 0.5 1m 3 P B1 = 150 KPa m 0.25 0.06
0.31 kg
0.31(4.125 )(15 273) 1 P 368.28 KPa P
90. During During some actual expansion and compression processes in pist on cylinder cyl inder devices, devices, the gases have have been n observed observed to satisfy the relationship PV = C, where n and C are cons tants . Calculate Calcul ate the t he work work done when a gas 3 3 expands from a state of 150 KPa and 0.03 m to a final final volume of 0.2 0.2 m for the case of n = 1.3. Also show the process on the PV diagram. Given: PV n C P1 = 150 KPa ; V 1= 0.03 m 3 n n V2 = 0.2 m 3 P1V1 P2 V2 C For For a Closed system W P dV P
C
Vn By integratio n W
2 1 PdV n
P2
P1V1 V2
n
P2 V2 P1V1 1 n n
V 0.03 P1 1 150 0.2 V2
1.3
P2 12.74 KPa W
2 1 PdV
P2 V2 P1V1
W 6.533 KJ
1 n
12.74(0.2) 150(0.03) 1 1.3
91. Five F ive kg k g of methane gas is fed to a cylinder cyl inder having having a volume of 20 m 3 and initially containing 25 kg of methane at a press pressure ure of 10 bar. bar. Determine Det ermine the specific spec ific volume, volume, in m 3/kg, of the methane in the cylinder cy linder initially . Repeat Repeat for the methane in the cylinder after the 5 kg has been added. (For Methane: R = 0.5183 KJ/kg-K; k = 1.321) m1 = 25 kg ; V 1 = 20 m 3 ; P 1 = 10 Bar = 1000 KPa m2 = 25 + 5 = 30 kg P1V1
1
υ
T1
m1RT1
V1 20 m1 25
P1V1 m1R
1000(20) 25(0.5183 )
V2 m2
2
υ
0.8 m3 /kg
20 25 5
1543 .5K
0.66 m3 /kg
92. A vess vessel el of volume 0. 2 m3 contains contai ns nitrogen at 101.3 KPa and 15ºC. 15º C. If 0.2 kg of nitrogen i s now pumped into the vessel, calculate the new pressure when the vessel has returned to its initial temperature. For nitrogen: M = 28 and k = 1.399. (187 KPa)
8.3143 28 PV mRT R
0.297
101.3(0.2) 0.297 297(15 273)
m
mFinal PFinal
0.237 237
0.237 237 kg
0.2 0.437 437 kg
0.437(0.297)(15 273 273 ) 0.2
187 KPa
93. A certain perfect perfect gas of mass 0.01 kg occupies a volume volume of 0.003 m 3 at a pressure of 700 KPa and a temperature of 131ºC. The gas is allowed to expand until the pressure is 100 100 KPa KP a and and the final final volume is 0.02 m 3. Calculate: a) the molecular weight of the gas (16) b) the final temperature (111.5ºC)
PV R
mRT
700 700 (0.003 003 ) 0.01(131 131 273 273 )
8.3143 16 0.520 100 100 (0.02) 273 0.01(0.520 520 )
0.52
M t
111 111 .6C
94. A perfect gas has a molecular weight of 26 kg/kg mol and a value value of k = 1.26. Calculat e the heat rejected rejec ted a) when when 1 kg of of the gas in contained in a rigid vessel vessel at 300 KPa and 315ºC, and is then cooled until the pressur pressur e falls to 150 KPa. (-361 KJ) R
8.3143
Cv
26 R
0.32
1.23 k 1 T1 315 273 588 At V C P1 T1
T2
P2 T2 150(588)
294 300 Q mC v (T2 T1 ) 1(1.23(294 588) Q 361.2 KJ (rejected)
b) when 1 kg/sec mass flow rate of the gas gas enter a pipeline at 280ºC 280ºC and flows st eadily to the end end of the pipe where where the temperature temperature is 20ºC. Neglect c hanges hanges in kinetic and potential energies.( energies.( -403 KW KW))
Q Δh ΔKE ΔPE
W
Q Δh 0 0 0 Δh
CP
R CP
mC P (T2
Rk k 1 8.3143 26
T1 )
0.320
KJ kg - K
Rk KJ 1.550 k 1 kg - K
Q Δh 1(1.550)(20 - 280)
403.2 KW
93. The The mass analysi analysis s of hydrocarbon hydrocarbon fuel fuel A is 88.5% Carbo Carbon n and 11.5% Hydrogen Hydrogen.. Another hydrocarbon hydrocarbon fuel fuel B requires requires 6% more more air than fuel fuel A for complete combust ion. Calculate the mass analysi analysis s of Fuel Fuel B. Solution: Fuel A: C = 0.885 ; H = 0.115 Fuel B: C = ; H = (A/F)B = 1.06(A/F)A (A/F)A = 11.44(0.885 11.44(0.885)) + 34.32(0.115) 34.32(0.115) = 14.0712 kg/kg (A/F)B (A/F)B = 1.06(14.0712)= 1.06(14.0712)= 14.9155 kg/kg For fuel B: H + C = 1 H = (1 – C) 14.9155 = 11.44C + 34.32(1-C) C = 84.8% H = 15.2%
94. A diesel engine uses a hydrocarbon hydrocarbon fuel fuel represented represented by C12H26 and is burned burned with 30% excess air. The The air and fuel fuel
is supplied at 1 atm and 25 C. Determine a. the actual air-fuel air-fuel Ratio Ratio b. the m3 of CO2 CO2 formed formed per kg of fuel if the product product temp. t emp. is 400 400 C and a pressure of 1 atm. c. The M and R of the Products Produc ts d. The M and R of the dry flue gas Combustion with 100% theoretical air (basis 1 mole of fuel) C12H26 + aO2 + a(3.76)N2 bCO2 + c H2O + a(3.76)N 2 a = 18.5 b = 12 c = 13 Combustion with 30% excess air C12H26 + 1.30aO2 + 1.30a(3.76)N2 bCO=+ cH2O + dO2 + 1.30a(3.76)N 1.30a(3.76)N= = d = 5.55 nP = b + c + d + 1.3(18.5)(3.76) = 120.978
kg of ai r A 137.28(1 e)(n 0.25m) 19.42 a 12n m kg of fuel F nRT 12(8.3143)(400 273) VCO 662.7 m3 of CO2 P
2
101.325
3
m of CO2
662.7
3.9 kg of Fuel 12(12) 26 1 1 M niM 12(44) 13(18) 5.55(32) 90.428(28) n 120.978 M 28.7 R 0.2897 n d np c 107.978 M
1
1
niM 107.978 12(44) 5.55(32) 90.428(28) n
M 29.983 R 0.2773
95. The The analysis of the natural gas showed the following following percentages percentages by volume: volume: C 2H6 = 9%; CH CH4 = 90%; CO 2 = 0.2 0.2 %
and N2 = 0.8 %. Find the t he volume of air required per cu,m. cu,m . of gas if the gas and and air are at temperature of 16 C and a pressure of 101.6 KPa. Solution: basis 100 moles of fuel) 9C2H6 + 90CH4 + 0.2CO2 + 0.8N2 + aO2 + a(3.76)N2 bCO2 + cH2O + dN2 By Carbon balance: 2(9) + 90 + 0.20 = b b = 108.20 By Hydrogen Balance: 6(9) + 4(90) = 2c c = 207 By O2 balance: 0.2 + a = 108.20 + (207/2) a = 211.5 na = a(1 + 3.76) nF = 100 na/nF = 10.07 96. Calculate the internal energy and enthalpy of 1 kg of air occupying 0.05 m 3 2000 KPa. If the internal energy is increased by 120 KJ as the air is compressed to 5000 KPa, calc ulate the new new volume volume occupied by 1 kg of the air. For air: R = 0.287 0.287 KJ/k g-ºK and k = 1.4.( 250.1 KJ/kg; 350.1 350.1 K J/kg; 0.0296 m 3) PV mRT
T
2000 (0.05 ) 1(0.287 )
348.4K
U 0.7175 (348.4) 250.1 h
1.0045 (348.4) 350.1
97. When a certain perfect perfect gas is heated heated at constant pressure from 15ºC t o 95ºC, 95ºC, the heat required is 1136 KJ/kg. KJ/k g. When the same gas is heated at constant volume volume between between the same temperatures temperatures the heat required required is 808 KJ/kg. Calculate Cp, Cv, Cv, k, and M of the gas. (14.2 (14.2 KJ/kg; K J/kg; 10.1 KJ/k g; 1.405; 4.1 and 2.208) 98. A quantity quantity of a certain perf perfect ect gas is compressed compressed from from an initial stat e of 0.085 m 3, 100 KPa to a final final st ate of 0.034 3 m , 390 390 KPa. the Cv Cv = 0.724 KJ/kg-ºC and Cp = 1.020 KJ/kg-ºC. The observed observed temperature temperature rise is 146ºK. 146ºK. Calculate R, the mass present, and
U of the gas.(0.296 KJ/kg-K; 0.11 kg; 11.63 KJ)
99. A mass of 0.05 0.05 kg of air is heated at c onstant pressure pressure of 200 200 KPa until the volume volume occupied is 0.0658 m 3. Calculate Calculate the heat heat supplied, t he work work and the c hange in entropy entropy for the process process if the initial temperature is 130ºC. 130ºC. (Q = 25.83 KJ; W = 7.38 KJ) 100. A 1 kg of nitrogen is compressed reversibly reversibly and isothermally isothermally from 101 101 KPa, 20ºC to 420 KPa. Calculate the nonflow nonflow work work and the heat flow flow during during the process process assuming as suming nit rogen rogen to be a perfect perfect gas. ( Q = W = 124 kJ/KG) 101. Air at 102 KPa, 22ºC, initially occupying a cylinder cy linder volume of 0.015 m 3 is compressed isentropically by a piston to a pressure press ure of 680 KPa. Calculat e the final final tem t emperature, perature, the final final volume, the work done on the mass of air air in the 3 cylinder. (234.3 ºC; .00387 m ; 2.76 KJ) 102. 1 kg of air is compressed from 110 KPa, 27 ºC in a polytropic process where where n = 1.3 until the final final pressure pressure is 660 KPa. Calculate:
a) ∫PdV b) - ∫VdP c) S 103. There There are 1.36 kg of air at 138 138 KPa stirred with internal paddles in an insulated insul ated rigid ri gid container, whose volume volume is 0.142 m 3until the pressure becomes 689.5 KPa. Determine the work input and PV. ( 196.2 KJ; 78.3 KJ) 104. During During an isentropic process process of 1.36 kg/sec of of air, air, the temperature temperature increases from 4.44ºC 4.44ºC to 115.6 115.6 ºC. for a nonflow process and for a steady st eady flow flow process ( KE = 0 and PE = 0) Find: a) U in KW b) H in KW c) W in KW d) S in KW/ºK e) Q in KW
105. A certain perfect perfect gas is compressed reversibly reversibly from from 100 KPa, 17 17 ºC to a pressure pressure of 500 KPa in a perf perfectly ectly thermally insulated cylinder, cyl inder, the final temperature being 77 ºC. The The work done on the gas during t he compression is 45 KJ/kg. Calculate, k , Cv, R and M of the gas.( 1.132; 0.75 KJ/kg-ºK; 0.099 KJ/kg-ºK; 84) 106. 1 kg of air air at 102 KPa, 20 ºC i s compressed compressed reversibly reversibly according to a law PV 1.3 = C to a pressure of 550 KPa. Calculate the work done on the air and the heat supplied during the compression. (133.46 KJ/kg; -33.3 KJ/kg) 107. Oxy gen (M (M = 32) is compressed poly tropically in a cy linder from from 105 KPa, 15ºC to 420 420 K Pa in such a way that one third of the work work input is i s rejected rejected as heat to the cy linder walls. walls. Calculate the final final temperature temperature of the oxygen. Ass ume oxygen to be perfect perfect gas and take tak e Cv = 0.649 KJ/kg-K. (113 ºC) 108. Air at 690 KPa, 260ºC is throttled to 550 KPa before before expanding through the nozzle nozzle to a pressure pressure of 110 110 KPa. Ass uming that the air flows flows reversibly reversibly in steady flow through through the nozzle and that no heat is rejected, calculate the velocity of the air at exit exit from from the nozzle when the inlet velocity velocity is 100 m/sec. ( 636 m/sec) m/sec ) 109. Air at 40ºC enters enters a mixing c hamber at a rate rate of 225 kg/sec where it mixes with air at 15ºC entering at a rate rate of 540 kg/sec. Calculate The The tempera t emperature ture of the air air leaving leaving the chamber, ass uming steady flow flow c onditions. As sume that the heat loss is negligible. (22.4ºC)
A heat heat engine has a t hermal hermal efficiency efficiency of 45%. 45%. How much power does the engine produce when heat is transferre transferred d into it at a rate of 109 kJ/Hr? A) 50 MW B) 75 MW C) 100 MW D) 125 MW A refr refrigerator igerator has a coefficient of performan performance ce of 1.6. How much work must be supplied to this refr refrigerator igerator for for it to reject reject 1000 kJ of heat? A) 385 kJ B) 627 kJ C) 836 kJ D) 1000 kJ The thermodynamic thermodynamic efficiency efficiency of a heat heat engine t hat rejects rejects heat at a rate rate of 20 MW when when heat is supplied to it at a rate of 60 MW is: A) 33.3% B) 50% C) 66.7% D) 75%
A Carnot Carnot engine operates using a 527 °C energy energy reservoir reservoir and a 27 °C energy energy reservoir. reservoir. The The thermodynamic thermodynamic efficienc efficienc y of this engine is: A) 50% B) 62.5% C) 73.6% D) 103%
A Carnot Carnot heat pump uses thermal reservoirs reservoirs at -27 °C and 57 °C. How much power does this pump consume to produce produce a 100 kW heating effect? A) 9.1 kW B) 12.7 kW C) 15.3 kW
D) 20.7 kW
Saturated water vapor vapor at 150 kPa is condensed condensed to saturated liquid in a steady -flow, -flow, is obaric obaric heat exchanger. exchanger. The released released heat is transferr transferred ed to the surroun surrounding ding air whose temperature temperature is 20 °C. °C. The The increase of the entropy entropy ass ociated with this process process is : A) -4.731 k J/kg-K B) -2.366 kJ/kg-K C) 2.366 kJ/kg-K D) 4.731 kJ/kg-K
Steam at 2 MPa, 300 °C is expanded in a steady-flow, adiabatic turbine to 30 kPa. What is the lowest possi ble temperature temperature at the outlet of this turbine? A) 69.1 °C B) 101.1 °C C) 150.7 °C D) 203.2 °C Steam at 2 MPa, 300 °C is expanded through a steady-flow, adiabatic turbine to 30 kPa. How much work does this turbine produce? A) 478.7 k J/kg B) 523.2 kJ/kg C) 639.2 kJ/kg D) 741.6 kJ/kg
Air at 5 MPa, 967 °C is expanded through a steady -flow -flow device device to 100 kPa, k Pa, 27 °C. What is the change in the specific entropy of the air? A) -1.372 k J/kg-K B) -0.269 kJ/kg-K C) 1.742 kJ/kg-K D) 2.638 kJ/kg-K A 0.5-kg steel (C = 0.5 kJ/kg-k) kJ/kg -k) rivet cools from from 800 K to 300 K upon upon being inst alled in a riveted riveted building structure. The entropy change of this rivet is: A) -0.631 k J/K B) -0.245 kJ/K C) 0.245kJ/K D) 0.631 kJ/K
Oxygen at 100 kPa, 27 °C is compressed to 1 MPa in an adiabatic adiabatic compressor whose isentropic efficiency efficiency is 0.80. 0.80. The oxygen temperature at the compressor outlet is: A) 376 K B) 421 K C) 566 K D) 649 K Water undergoe undergoes s the reversible reversible process illust rated here here as it passes throu t hrough gh a steady -flow -flow device device that has has one outlet and one outlet. How much work does this device produce? A) 0 kJ/kg kJ/k g B) P (v2 (v2 - v1) v1) kJ/k g C) R (T2 - T1) kJ/kg D) cv (T2 (T2 - T1) kJ/k k J/kg g
Air is expanded in a closed clos ed sys tem from from 1 MPa, 327 °C to 100 kPa k Pa in an isentropic process. The sys tem surroundings surroundings are at 100 kPa, 27 °C. How much useful work did this system produce during this process? A) 91 kJ/kg
B) 103 kJ/kg C) 135 kJ/kg D) 210 kJ/kg
A 1 m3 vessel vessel contains air at 1 MPa, 327 °C. Ass uming standard conditions for for t he surroundings, surroundings, what is the t he maximum amount of work that can be done by the air in this vessel? A) 790 kJ B) 826 kJ C) 1012 kJ D) 1290 kJ Steam enters a turbine at 3 MPa, 350 °C with a velocity of 15 m/s. What is the specific exergy of this steam assuming the surroun surroundings dings are at standard c onditions? A) 678 kJ/kg B) 827 kJ/kg C) 968 kJ/kg D) 1116 kJ/kg
Steam at 3 MPa, 350 °C is expanded expanded through through an adiabatic, adiabatic, s teady-flow t urbine to t o a saturated vapor vapor at 100 100 kP a. The second law efficiency of this turbine is: A) 48.2% B) 63.7% C) 70.7% D) 82.1%
A heat exc hanger hanger maintains the air temperature temperature in a room at 25 °C by condensing saturated water vapor at 125 kPa t o saturated liquid water. The specific exergy destruction associated with this heat exchanger is: A) 932 kJ/kg B) 958 kJ/kg C) 1241 kJ/kg D) 1378 kJ/kg
Air is compressed from from 100 kPa, 27 °C to 900 kPa, 327 °C in an adiabatic piston -cylinder device. device. What is the irreversibility irreversibility of this process? process? A) 19.66 k J/kg B) 22.31 kJ/kg C) 28.73 kJ/kg D) 32.17 kJ/kg
An adiabatic, steady-flow heat exchanger condenses 10,000 kg/hr of saturated steam vapor at 200 kPa t o a saturated liquid also als o at 200 kPa. The The conden c ondensing sing steam heats 220,000 kg/hr of air at 100 100 k Pa, 25 °C to 100 100 k Pa, 125 °C. °C. What is the rate at which exergy is destroyed by this heat exchanger? A) 0 MJ/hr B) 270 MJ/hr C) 1327 MJ/hr D) 2295 MJ/hr
A Carnot vapor power power cyc le opera operates tes its boiler at 3.0 MPa and its condenser at 50 kPa. What is i s the t hermal hermal efficienc efficienc y of this cycle? A) 20% B) 30% C) 40% D) 50% A simple Rankine cycle cy cle operates operates the boiler at 3 MPa with an outlet temperature temperature of 350 350 °C and the condenser at 50 kPa. Ass uming ideal operation and process es, what is i s the t he thermal efficiency efficiency of this cy cle? A) 7.7% B) 17.7% C) 27.7%
D) 37.7%
A simple s imple Rankine cyc le opera operates tes its boiler at 3 MPa wit h an outlet temperature temperature of 350 °C and its condenser at 50 kPa. The turbine has an isentropic efficiency of 0.9 while all other operating conditions and process are ideal. What is the thermal efficiency of this cycle? A) 25.0% B) 30.9% C) 35.9% D) 40.9% A simple, s imple, ideal Rankine cyc le operates operates the boiler at 3 MPa and the condenser at 50 kPa. The temperature temperature at the boile r outlet is 400 °C. What is the rate rate at which heat must be s upplied to the water in the boiler for for a power production of 100 MW? A) 157 MW B) 218 MW C) 273 MW D) 352 MW
An ideal Rankine cyc le with reheat operates operates the boiler at 3 MPa, the reheater reheater at 1 MPa, and the condenser at 50 kPa. kP a. The temperature at the boiler and reheater outlets is 350 °C. What is the thermal efficiency of this cycle? A) 24.5% B) 26.5% C) 28.5% D) 30.5%
An ideal Rankine cyc le with reheat operates operates the boiler at 3 MPa, the reheater reheater at 1 MPa, and the condenser at 50 kPa. kP a. The temperature at the boiler and reheater outlets outlet s is 350 °C. The boiler and reheater are fired with a fuel that releases 9,000 kJ/k g of heat as it is burned. burned. What is the mass flow rate of the fuel fuel for such a cycle when when s ized to produce produce 50 MW of net work? A) 40 Mg/hr B) 50 Mg/hr C) 60 Mg/hr D) 70 Mg/hr
An ideal Rankine cycle cy cle with an open-fee open-feedwater-heater dwater-heater regenera regenerator tor operates operates the boiler at 3 MPa, the regenera regenerator tor at 125 kPa, and the condenser at 50 kP a. At the boiler outlet, the temperature temperature is 350 °C. °C. What percentage of the mass mass flow rate passing through the boiler is bled from the turbine for the regenerator? A) 4.85% B) 7.31% C) 10.6% D) 13.2%
An ideal Rankine cycle cy cle with an open-fee open-feedwater-heater dwater-heater regenera regenerator tor operates operates the boiler at 3 MPa, the regenera regenerator tor at 125 kPa, and and the condenser condenser at 50 kPa. At the boiler outlet, the temperature temperature is 350 °C. What is the thermal efficiency efficiency of this cycle? A) 24.6% B) 28.6% C) 32.6% D) 36.6%
A simple s imple Rankine c ycle ycl e opera operates tes the boiler at 3 MPa and the condenser at 50 kPa. The The temperature temperature at the boiler outlet is 350 °C. The The energy source is at 400 °C and the energy s ink is at 27 °C. What is the irreversibility irreversibility of this cy cle per unit of mass pass ing through through the boiler? boiler? A) 561.2 k J/kg B) 613.4 kJ/kg C) 694.2 kJ/kg D) 767.8 kJ/kg
A simple Rankine cycle cy cle produces produces 40 MW of power, power, 50 MW of process heat and rejects 60 MW of heat to the surroundings. surroundings. What is the utilizati on factor factor of this cogeneration cogeneration cyc le neglecting neglecting the pump pump work? A) 50% B) 60% C) 70% D) 80%
A basic R-134a, R-134a, ideal vapor-compr vapor-compression ession refriger refrigerator ator operates operates its evapor evaporator ator at -16 °C and its evapor evaporator ator at 1.4 MPa. How much power will the compressor require to service a 10 kW cooling load? A) 4.03 kW B) 5.97 kW C) 7.32 kW D) 10.0 kW
A basic R-134a, ideal vaporvapor-compress compress ion refriger refrigerator ator operates operates its evapor evaporator ator at 157 kPa and its evapor evaporator ator at 1.4 MPa. What is the rate at which which t he condenser condenser rejects heat when this refrigerator refrigerator services services a 100 100 kW k W load? A) 80 kW B) 103 kW C) 120 kW D) 141 kW An ideal R-134a vapor-compression apor-compression heat pump operates operates its evapor evaporator ator at 1.4 MPa and its condenser at -16 °C. The coefficient of performance performance of this heat pump is: A) 2.48 B) 2.79 C) 3.43 D) 3.79
A R-134a R-134a vapor-compressio apor-compressio n refriger refrigerator ator operates operates its evapor evaporator ator at 1.4 MPa and it s condenser at 157 kP a. All the cycle states and processes are ideal except for the compressor, which has an isentropic efficiency of 79%. How much power must be supplied to the compressor when t his refriger refrigerator ator serves serves a100 kW cooling load? A) 27.3 kW B) 34.2 kW C) 52.0 kW D) 100 kW A simple R-134a R-134a vapor-compression apor-compression refriger refrigerator ator system sy stem operates operates its evapor evaporator ator at 157 kPa and the exit of the compressor at 1.4 MPa. The working fluid enters enters t he throttle valv valve e as a saturated liquid at 1.2 MPa as a result of pressure pressure losses in i n the condenser condenser and connection l ines. What W hat is the coefficient coefficient of performance performance of this device? device? A) 2.64 B) 2.93 C) 3.26 D) 3.69
An ideal R-134a, R-134a, dual c ompressor ompressor vapor-compression apor-compression refriger refrigerator ator sys tem uses a flash c hamber to separate the vapo r in the evaporator evaporator feed line. This system sys tem operates the evaporator evaporator at 133 kPa, the flash flash c hamber at 400 kPa, and the condenser at 1.4 MPa. W hat fracti fracti on of the mass flow rate passing through the evapor evaporator ator passes through the condenser? A) 0.80 B) 1.00 C) 1.20 D) 1.50
An ideal R-134a, R-134a, dual c ompressor ompressor vapor-compression apor-compression refriger refrigerator ator sys tem uses a flash c hamber to separate the vapo r in the evaporator evaporator feed line. This system sys tem operates the evaporator evaporator at 133 kPa, the flash flash c hamber at 400 kPa, and the condenser at 1.4 MPa. What is the coefficient coefficient of performan performance ce of this device? device? A) 1.87 B) 2.63
C) 2.95 D) 3.17
A simple, ideal rev reversible Brayton cycle uses air as the working working fluid and has a pressure ratio of 6. What is the refriger refrigerat at o r COP of this cycle when when the temperature at the compressor entrance is -13 °C and that at the turbine turbine entrance is 37 °C? A) 0.33 B) 0.72 C) 1.48 D) 1.97
The composition of a mixture of of nitrogen nitrogen and carbon dioxide gases is 30% 30% -N2 and 70%-CO2 by mole fraction. fraction. What is the mass fraction of the nitrogen constituent? A) 15.2% B) 21.4% C) 30.2% D) 63.7%
A mix ture of helium and nitrogen is 50% -He and 50%-N2 by mass analysis. analysis . W hat is the mole fraction fraction of the helium in this mixture? A) 39.7% B) 43.2% C) 67.2% D) 87.5% The composition of a gas mixture is 40%-O2, 40%-N2, and 20%-He by mass analysis. What is the apparent molecular weight of this mixture? A) 6.71 kg/k g-mol B) 13.02 kg/kg-mol C) 15.70 kg/kg-mol D) 18.60 kg/kg-mol
The composi tion of a mixture of gases is 50%-CO2, 50%-CO2, 40%-O2, and 10%-He by volume volume analysis . What is the apparent apparent molecular weight of this mixture? A) 19.3 kg/k g-mol B) 24.6 kg/kg-mol C) 28.7 kg/kg-mol D) 35.2 kg/kg-mol
A 1 m3 container contains a mixture mixt ure of gases composed of 0.02 kg-mol of O2 and 0.04 kg-mol of He at a pressure of 200 kPa. What is the temperature of this ideal gas mixture? A) 300 K B) 350 K C) 400 K D) 450 K
A 200 liter c ontainer holds 0.5 k g of of air and 0.2 kg of helium at a temperature temperature of 350 350 K. What is the pressure of t his ideal gas mixture? A) 1.4 MPa B) 1.6 MPa C) 1.8 MPa D) 2.0 MPa
A mix ture composed of 70%-CO2 and 30%-He by volume volume analysis is c ontained at 1 MPa. What is the partial press ur e of the He in this mixture? A) 300 kPa B) 450 kPa C) 600 kPa
D) 700 kPa
A mix ture of 30%-Ar and 70%-CO2 by volume volume analysis. analysis . This mixture mixt ure is contained in a rigid vessel at 200 k Pa, 27 °C. The vessel is now now heated until the mixture temperature temperature is 127 °C. °C. Ass uming that the specific heats do not change, how much heat was required? A) 1.10 MJ/kg-mol B) 2.40 MJ/kg-mol C) 1.10 MJ/kg D) 2.40 MJ/kg
A mix ture consist s of 30%-Ar and 70%-CO2 by volume volume analysis. analysis . This mixture mix ture is contained c ontained in a rigid vessel at 200 200 kPa, 27 oC. oC. The vessel vessel is now now heated until the mixture mixt ure temperature is 127 127 oC. Ass uming constant specific heats, what is the change in the entropy of the mixture? A) 4.780 k J/kg-mol-K B) 6.900 kJ/kg-mol-K C) 4.780 kJ/kg-mol-K D) 6.900 kJ/kg-mol-K
A mix ture of 20%-CO2 and 80%-N2 by volume volume is expande ex panded d from 1 MPa, 227 °C to 200 kPa as it pass es through an adiabatic, adiabatic, steady-flow t urbine. urbine. As suming this process process is reversible reversible and the specific heats heats are const ant, how much work is produced produced by this expansion? A) 137.9 k J/kg B) 164.5 kJ/kg C) 174.3 kJ/kg D) 194.2 kJ/kg What is the specific humidity of air at 150 kPa whose dry bulb temperature is 20 °C and relative relative humidity is 70%? A) 0.000981 kg-wv/kg-da kg-wv/kg-da B) 0.00382 kg-wv/kg-da C) 0.00514 kg-wv/kg-da D) 0.00686 kg-wv/kg-da
Using saturated liquid water and 0 °C as the reference reference state, what is the specific enthalpy of humid air at 120 120 kPa, kP a, 20 °C, and 50% relative humidity? A) 32.71 k J/kg-da B) 35.63 kJ/kg-da C) 38.93 kJ/kg-da D) 41.72 kJ/kg-da What is the dew-point dew-point temperature temperature of humid air at 200 k Pa, 30 °C, °C, and 55% relative relative humidity? A) 10 °C B) 15 °C C) 20 °C D) 25 °C Humid air at 150 kPa, 30 °C, °C, and and 80% relative humidity undergoe undergoes s an isobaric cooling process until its temperature temperature is 25 °C. Will any liquid condensate form during this process? A) Yes B) No C) Not Not applicable D) Not Not applicable
Humid air is cooled, dehumidifie dehumidified d and reheated reheated during an isobaric process. Which Whic h one of the psyc psyc hometric charts below below correctly depicts these processes? A) a B) b C) c D) d
One-hundr One-hundred ed cubic meters per minute of humid air at 101 kPa, 35 °C, °C, 40% relativ relative e humidity is cooled to 25 °C in a constant pressure process. The cooling rate for this process is: A) 9.3 kW B) 17.8 kW C) 20.2 kW D) 22.3 kW Saturated humid air at 101 kPa, 20 °C is heated to 35 °C during an isobaric process. What is the final relative humidity of this air? A) 42% B) 53% C) 68% D) 75% Humid air at 101 kPa, 35 35 °C, 80% relative relative humidity is conditioned to 101 kPa, 25 25 °C, °C, 50% relative relative humidity. How much condensate is formed during this process? A) 0.0087 k g/kg-da B) 0.0168 kg/kg-da C) 0.0193 kg/kg-da D) 0.0231 kg/kg-da
Humid air at 101 kPa, 35 35 °C, 80% relative relative humidity is conditioned to 101 kPa, 25 25 °C, °C, 50% relative relative humidity. How much heat must be removed removed to accomplis h this when t he condensate condensate leaves leaves the system sys tem at 25 °C? °C? A) 41.7 kJ/kg-da B) 46.7 kJ/kg-da C) 52.3 kJ/kg-da D) 57.5 kJ/kg-da
A standard atmospheric pressure cooling tower uses humid air at 30 °C, 60% relative relative humidity to cool liquid water from 55 °C to 40 °C. °C. Saturated humid air leaves leaves this tower tower at 35 °C. How much make -up water must be s upplied to this tower? A) 0.0206 k g/kg-da B) 0.0313 kg/kg-da C) 0.0347 kg/kg-da D) 0.0404 kg/kg-da Five Five kilogram-mol of octane are burned with a stiochiometric amount of air. air. How much water is formed formed in the products products if the combustion is complete? A) 15 kg-mol B) 25 kg-mol C) 35 kg-mol D) 45 kg-mol
Methyl alcohol is burned burned with 30% 30% exc ess air. How much unburned unburned oxygen will t here be be in the products products if the combustion is complete? A) 0.35 kg-mol-o2/kg-mol-fuel kg-mol-o2/kg-mol-fuel B) 0.45 k g-mol-o2/kg-mol-f g-mol-o2/kg-mol-fuel uel C) 0.55 kg-mol-o2/kg-mol-fuel D) 0.65 kg-mol-o2/kg-mol-fuel
Gaseous methane fuel is burned burned with 100% exc ess air. This This combustion is inc omplete with 10% of the carbon in the fuel forming CO. The products of combustion are at 100 kPa. What is the partial pressure of the CO in the products? A) 0.51 kPa kP a B) 1.36 kPa C) 2.78 kPa D) 10.5 kPa
Gaseous methane fuel is burned burned with 50% excess air. air. When the temperature temperature of the products products is 30 °C and the pressur pressur e is 100 kPa, what fraction of the water in the products is liquid? A) 31%
B) 48% C) 62% D) 74% Dodecane Dodecane is burned burned at constant pressure with 150% 150% excess ex cess air. What is the air-fuel ratio for this process process ? A) 37.5 B) 42.3 C) 48.7 D) 51.3 Liquid octane fuel is burned in an isobaric, steady-flow burner with 80% excess air. The air and fuel enter the burner at 25 °C and the combustion products leave at 427 °C. How much heat is released by this burner when the combustion is complete? A) 18,530 k J/kg-fuel J/kg-fuel B) 31,800 k J/kg-fuel J/kg-fuel C) 38,460 kJ/kg-fuel D) 42,610 kJ/kg-fuel
One gallon of gasoline (octane) has a mass of 2.66 kg. What is the maximum amount of heat that can be produced when one gallon of gasoline is burned with air? A) 17,320 k J/gal B) 111,270 kJ/gal C) 116,320 kJ/gal D) 127,650 kJ/gal
In a metallurgical process, methane is burned burned at constant pressure, with a stiochiometric amount of air both of which are at 25 °C. W hat is the maximum temperature temperature of the product products? s? A) 1930 K B) 2320 K C) 2890 K D) 3170 K
How irreversible irreversible is the combustion of methane methane at standard atmospheric pressure with 20% excess air when when all reactants and products are at 25 °C and the water in the products is all liquid? A) 630,000 kJ/k g-mol-CH4 g-mol-CH4 B) 780,200 k J/kg-mol-CH4 J/kg-mol-CH4 C) 884,700 kJ/kg-mol-CH4 D) 1,110,000 kJ/kg-mol-CH4
What is the rev reversible ersible work for for CH4 burned with s tiochiometric air when all products products and reactants are at the standard referance state? A) 673,500 kJ/k g-mol-fuel g-mol-fuel B) 718,300 kJ/kg-mol-fuel C) 793,000 kJ/kg-mol-fuel D) 817,900 kJ/kg-mol-fuel At what temperature will 20% of carbon dioxide disass ociate to c arbon arbon monoxide when the pressure is 0.1 atm? A) 2240 K B) 2420 K C) 2690 K D) 3120 K
Exc ess air is used used in combustion reactions to control control flame temperatures. temperatures. Exc ess air will also ___________ _____________ __ __ _ _ when Dn is positive. A) Produce more incomplete combustion B) Produce more complete combustion C) Produce undesirable combustion D) Have no effect
A mixture of 1 kg-mol of CO and 1 kg-mol of O2 is heated to 3000 K at a pressure pressure of 1 atm. What fraction fraction of the original CO becomes CO2? A) 27.8% B) 37.6% C) 69.2% D) 90.1%
Increasing the temperature of an ideal gas increases ________________. A) The number of reactants i n the products products B) The The number of inert gases i n the product C) The number of disassociation products D) None of these
A mix ture c onsists onsist s of 1 kg-mol of CO, 1 kg-mol of O2, and 2 kg-mol of N2. Treating Treating the nitrogen as an inert gas, how much CO2 is formed formed when the t he temperature and pressure of this mix ture is 2600 K and 1 atm? A) 0.371 k g-mol B) 0.615 kg-mol C) 0.832 D) 0.957 kg-mol A mixture of 1 kg-mol of CO2, 1 kg-mol kg-mol of O2, O2, and 2 kg-mol of N2 is heated to 4000 K at a pressure pressure of 1 atm. As suming that the final final mix ture consis ts of CO2, CO2, CO, O2, O, and N2, how how much atomic oxygen oxy gen is present present in i n the final final mixture? mixt ure? A) 0.33 B) 0.50 C) 0.67 D) 0.90
What is the approximate approximate heat of reaction reaction at 3400 K for the dis association associ ation of CO2 CO2 to CO? A) 5961 kJ/kg-mol k J/kg-mol B) 7482 kJ/kg-mol C) 8785 kJ/kg-mol D) 9213 kJ/kg-mol
A sys tem is composed of gasoline liquid and vapor, apor, and air. Acc ording to Gibbs phase rule how many independen independen t properties are required for phase equilibrium? A) 0 B) 1 C) 2 D) 3 When the water temperature temperature of the Great Great Salt Lake is 20 °C, °C, what is the mass fraction fraction of the salt dissolved in the water? water? A) 26.5% B) 32.1% C) 36.7% D) 40.3% The contents content s of a can of soft drink consist consi sts s of CO2 dis solved in water and a vapor vapor space spac e fill filled ed with CO2 and H2O vapor vapor . At 17 oC and 2 atm, what is the mole fraction fraction of the CO2 in the liquid mixture? mixt ure? A) 0.00156 B) 0.00735 C) 0.0107 D) 0.0312 At one locat ion in i n a nozzle, the air temperature temperature is 400 K and t he air velocity velocity is 400 m/s . What is the stagnation enthalpy (based on temperature temperature dependent dependent specific heats) of of the air at this location? A) 300 kJ/kg B) 357 kJ/kg C) 470 kJ/kg D) 481 kJ/kg
At one locat ion in a nozzle, the air temperature temperature is 400 K and the air velocit velocity y is 450 m/s. What W hat is the Mach number number at this location? A) 0.97 B) 1.12 C) 1.37 D) 2.02
Air at 20 k Pa flows with a Mach number of 1.5. W hat is the st agnation pressure pressure of this air? A) 22.2 kPa kP a B) 41.7 kPa C) 56.2 kPa D) 73.4 kPa
Air in a large tank at at 350 K and 200 kPa is supplied to an isentropic isentropic c onverging-diverging onverging-diverging nozzle. What is the temperature at a point point in this nozzle where the M ach number number is 1.2? A) 198 K B) 271 K C) 360 K D) 395 K
An isentropic, isentropic, converging-diverging converging-diverging nozzle operates with stagnation st agnation conditions 400 k Pa, 500 K. K . This This nozz le has a throat throat area of 0.01 m2 and and is chocked. W hat is the mass flow rate through t his nozzle? A) 5.01 kg/s B) 7.23 kg/s C) 8.32 kg/s D) 9.81 kg/s
The exit of the div diverging erging section sect ion of of an isentropic nozz le has twice the area of the nozzl nozzle e throat. W hat is the Mach number at the exit when the exit flow is supersonic? A) 1.80 B) 2.00 C) 2.20 D) 2.40
The exit ex it of the divergin diverging g section secti on of an isentropic isentropic nozzle has twice t he area area of the nozzle throat. If the stagnation pressur pressure e at the throat throat is i s 200 kPa, what is the pressure pressure at the nozzl nozzle e exit when the exit flow is supersonic? A) 18.7 kPa kP a B) 32.2 kPa C) 87.3 kPa D) 137.2 kPa
An aircraft aircraft flies through through 80 k Pa, 270 K s till air with a Mach number of 1.30. A normal shock wave wave will form form directly in in front of this aircraft. What is the stagnation pressure acting on this aircraft? A) 61 kPa B) 73 kPa C) 101 kPa D) 193 kPa A normal shock wave wave forms forms in the diverging diverging portion of a nozzle at a point where where Mx = 1.5. The area at the exit of this nozzle is 50% larger t hen that where where the shock s hock wave wave forms. forms. What is the t he Mach number number at the nozzle exit ? A) 1.2 B) 1.12 C) 0.38 D) 0.24
Steam at 3.0 MPa, 500 500 °C, and negligible velocity is expanded expanded to 0.8 MPa through through an isentropic nozz le. What is the velocity of the steam at the nozzle exit? A) 268 m/s B) 522 m/s
C) 738 m/s D) 894 m/s
b.
A gaseous mixture has the following following volumetric volumetric analysis O2, 30%; CO 2, 40% N2, 30%. Determine a) the analysis on a mass basis b) the partial partial pressure of each component if the total pressure is 100 KPa and the temperature temperature is 32 C c) the molecular weight and gas constant of the mixture Gas O2 CO2 N2
yi 0.30 0.40 0.30
M 32 44 28
k 1.395 1.288 1.399
Cp 0.918 0.845 1.041
Cv 0.658 0.656 0.744
R 0.260 189 0.297
xi 0.27 0.494 0.236
Pi 30 40 30
Mixture Mixt ure M 35.6 R .234 P 100
69. Consider 2 kg of CO CO and 1 kg of CH4 at 32 C that are in a 0.6 m3 rigid drum. Find: a) the mixture pressure P in KPa b) the volumetric analysis c) the partial pressures in KPa d) the heat to cause a temperature rise of 50 C. 70. A gaseous gaseous mixture mix ture has has the following following volumetric analysisO analysis O 2, 30%; CO 2, 40% N2, 30%. Determine a) the analysis on a mass basis b) the partial partial pressure of each component if the total pressure is 100 KPa and the temperature temperature is 32 C c) the molecular weight and gas constant of the mixture 71. A gaseous gaseous mixture m ixture has the following following analysis on a mass mass basis , CO 2, 30%; SO 2, 30%; He, 20% and N 2, 20%. For a total press ure and temperature of 101 KPa K Pa and 300 K, Determine a) the volumetric or molal analysis b) the component partial pressure c) the mixture gas constant d) the mixture specific heats 72. A cubical t ank 1 m on a side, contains a mix ture of 1.8 kg of nitrogen nitrogen and 2.8 kg of an unknown gas. The mixture mix ture press pressure ure and temperature are 290 KPa and 340 K. K . Determine a) Molecular weight and gas constant of the unknown gas b) the volumetric analysis 73. A mixture of ideal gases at 30 C and 200 KPa is composed of 0.20 kg CO 2, 0.75 kg N2, and 0.05 kg He. Determine the mix ture volume. volume.
74. In determining the specific heat of a new metal alloy,0.15 kg of the substance is heated to 400 C and then placed in a 0.2 kg aluminum calorimeter cup containing 0.4 kg of water at 10 C. If the final temperature of the mixture is 30.5 C, what is the specific heat of the alloy.( ignore the calorimeter stirrer and thermometer)
75.
76.
77.
78. 79.
80.
81. 82.
83.
84.
85.
86. 87.
88. 89. 90.
91.
Cp Al = 0.92 KJ/kg-C; Cpw = 4.186 KJ\kg-C An air compressor handles 8.5 m 3/min of air with = 1.26 kg/m 3 and P = 101.325 KPa and it discharges at P = 445 KPag with = 4.86 kg/m 3. The U = 82 KJ/kg and the heat loss by cooling is 24 KJ/kg. Neglecting KE and PE, find W in KJ/min. A 0.1 kg of aluminum (Cp=0.92 KJ/kg- C) at 90C is immersed in 1 kg of water from 20 C . Assuming no heat is lost to the surroundin surroundings gs or container , what is the temperature temperature of the metal and water when they reached reached thermal equilibrium? Water is flowing flowing in a pipe with varying varying cross section secti on area, area, and at all all points the water completely fills the pipe. At point 1 the cross section area of the pipe is 0.070 m 2 and the velocity is 3.50 m/sec. a. What is the fluid fluid speed at points in the pipe pipe where th cross secti on area is 0.105 m 2 and 0.047 m 2. b. Calculate Calcul ate the volume volume of water disc harged from the open end of the pipe in 1 hour. hour. A sealed tank containing sea water t o a height height of 11 m also also contains air abov above e the water at a gage gage pressure of 3 atmosphere. Water flows out from the bottom through a small hole. Calculate the efflux speed of the water. A copper pot with a mass of 0.500 kg contains 0.170 kg of water at a temperature of 20 C. A 0.250 kg block of iron at 85C is dropped dropped into the pot. Find the final temperature, as suming no heat loss to the surroun surroundings dings . copper water iron C = = 0.390 KJ/kg-C; C = = 4.19 KJ/kg-C and C = 0.470 KJ/kg-C. At one one point in a pipeline pipeline the water speed is 3 m/sec and and the gage pressure is 50 KPa. Find the gage pressur pressure e at a second point in the line, 11 m lower lower than the first , if the pipe diameter at the second point is one half the first. A closed cl osed system containing a gas gas ex pands slowly in a piston piston cylinder cyl inder in accordance accordance to PV 2 = C. If the initial pressure is 500 KPa, init ial volume volume is 50 L and the final final pressure is 200 KPa, find find the t he work done by the sy stem. A steam turbine receives receives superheated superheated steam at 1.4 MPa and 400 C (h = 3121 KJ/k g). The The steam st eam leaves leaves the turbine at 0.101 MPa and 100 C (h = 2676 2676 KJ/kg).The s team enters enters the turbine turbine at 15 m/sec m/s ec and exits at 60 m/sec. m/sec . The The elevation elevation differen difference ce between between entry and and exit ports ports is negligible. The The heat loss through th e turbine turbine walls is 2 KW. Calculate the power power output if the mass flow flow through the turbine is 0.5 kg/sec. A small circular ci rcular hole hole 6 mm in diameter is cut in the side of a large large water tank 14 m below the water level level in the t he tank. The top of the tank is open to the atmosphere. Find the velocity of water exiting the hole and the volume discharged per unit time. Oxygen (M = 32) is compressed polytropically in a cylinder from 105 KPa, 15ºC to 420 KPa The decrease in internal energy of 1.36 kg of an ideal gas is –342.9 KJ when the pressure decreases from 689.3 KPa to 137.86 137.86 KPa K Pa and the volume volume increases inc reases from from 0.0425 m 3 0.127 m 3. Cv = 1.047 KJ/kg-K. Determine the value of k. The working fluid of a gas turbine pass es through through the machine at a steady rate of 10 10 kg/sec. kg/s ec. It enters with wit h a velocity of 100 100 m/sec and specific enthalpy of 2000 K J/kg and leaves leaves at 50 50 m/sec with a specific enthalpy enthalpy of 1500 KJ/kg. If the heat lost los t to surroundings surroundings as the fluid fluid pass es through through the turbine is 40 KJ/kg, c alculate the power developed. 0.07 m 3 of gas at 4.14 MPa is expanded in an engine engine cy linder and the pressure at the end of expansion is 1.35 310 KPa. If the expansion is polytropic with PV = C, find find the final volume. Helium gas ( R=2.077 KJ/kg-K; k= 1.667) enters a steady state – steady st eady flow flow expande ex panderr at 800 KPa, 300C and exits at 120 KPa. The The mass flow rate i s 0.2 0.2 kg/sec and the expansion process is PV 1.3 = C. Calculate W of the expander in KW. A pressure gage at elevation elevation 8 m on a side of a tank containing a liquid reads reads 57.4 KPa. Another gage at elevation elevation 5 m reads reads 80 KPa. Determine the density density of the l iquid. Gas at a pressure of 95 KPa, volume volume 0.2 cu.m. and temperature temperature 17 C, is compressed until the pressure is 275 KPa and the volume volume is 0.085 cu.m.. Calculate the final final temperature. A liquid of density 800 800 kg/cu.m. , specific heat of 2.5 KJ/kg-K KJ/kg -K and temperature temperature of 27 C is mixed with another liquid of density density 820 kg/cu.m., kg/c u.m., specific heat 1.9 KJ/kg -K and temperature temperature of 55 C in the ratio of one of the first liquid to three of the second by volume. Find the resulting temperature. A rigid container c ontains 1 mole of nitrogen nitrogen gas that slowly receives receives 3 KCal of heat. heat. What is the change in internal energy of the gas in KJ.For N 2: M = 28; K = 1.399
92. A certain perfect perfect gas of mass 0.01 kg occupies a volume volume of 0.003 m 3 at a pressure of 700 KP a and and a temperatu temperature re of 131ºC. The gas is allowed to t o expand unt il the pressure is 100 KPa KP a and the final final volume is 0.02 m 3. Calculate: Calculate: a) the molecular weight of the gas b) the final temperature
93. A c ubical tank 1 m on on a side, contains a mixture of 1.8 kg of nitrogen (M = 28; k = 1.399) 1.399) and 2.8 kg of an unknown gas. The mixture pressure and temperature are 290 KPa and 340 K. Determine a) Molecular weight and gas constant of the unknown gas
b) the volumetric analysis
94. A volume of gas having having initial init ial entropy of 5317.2 KJ/K is heated heated at constant c onstant temperature of 540 C until the entropy entropy is 8165.7 KJ/K. How much heat is added and how much work is done done during the process.
95. A 283 L drum contains a gaseous mixture at 690 KPa and 38 C whose volumetric composition is 30% O 2 and 70% CH4. How many kg of mixture must be bled and what mass of O 2 added in order to produce at the original pressure and temperature a mixture whose new volumetric volumetric composition i s 70% O 2 and 30% CH4. For O2: M = 32 ; k = 1.395For CH4; M = 16 ; k = 1.321
100. A certain perfect perfect gas of mass 0.01 kg occupies a volume of 0.003 m 3 at a pressure of 700 KP a and and a temperatu temperature re 3 of 131ºC. The gas is allowed to expand unt il the pressure i s 100 KPa KP a and the final volume is 0.02 m . Calculate: Calculate: a) the molecular weight of the gas b) the final temperature 101. When a certain certain perfect perfect gas is heated at constant pressure pressure from 15ºC t o 95ºC, 95ºC, the heat heat required required is 1136 KJ/kg. When the same gas is heated at const ant volume volume between the same temperatures temperatures the heat heat required required is 808 808 KJ/kg. Calculate Cp, Cv, k, and M of the gas. 102. A closed vessel of 0.7 m 3 internal volume contains contai ns a gas at 58 Kpa and 18 C and with R = 0.27 KJ/kg-K.If now 0 0.35 kg of another gas at 18 C and R = 0.29 KJ/kg-K is als o admitted into the vessel. Calculate the final pressure of the mixture. 103. A closed sys tem consist ing of of 2 kg of a gas gas undergoe undergoes s a process during during which th e relationship relationship between 1.3 pressure and and s pecific volume volume is PV = C. The process begins with P 1 = 1 bar, 1 = 0.5 m3/kg and ends with P 2 = 0.25 bar. Determine Determine the final volume, volume, in m 3, and and plot the process on a graph graph of pressure pressure versus versus specific volume volume .
104. Four kilograms of a certain gas is contained within a piston –cylinder cyl inder assembly. The The gas undergoe undergoes s a process for which the pressure pressure - volume volume relationship is P V 1.5 = C. The The initial pressure is i s 3 bar, bar, the initial i nitial volume volume is 0.1 m 3, and the final volume volume is 0.2 m 3. The The change in speci fic internal internal energy energy of the gas gas in the process process is U = - 4.6 kJ/kg. There are no significant changes in kinetic or potential energy. Determine the net heat transfer for the process, in kJ. (Q = -0.8 KJ) 105. Calculate the change of entropy per kg of air (R = 0.287 KJ/kg-K; k = 1.4) when heated from 300 K to 600K while the pressure drops from from 400 KP a to 300 300 KPa. ( S = 0.78 KJ/kg-K)
106. A 5 k g quantity quantity of oxy oxygen gen (M = 32; k = 1.395) is heated from from 250 K to 400 K at const ant pressure. pressure. Determine a. h b. U c. S d. W = P dV 107. A 5 m 3 tank contains chlorine (R = 0.1172 0.1172 KJ/kg -K) at 300 KP a and 300K 300K after 3 kg of chlorine has been used. Determine the original original mass and pressure pressure if the original original temperature temperature was 315 K. (45.66 kg ; 337.15 KPa) 108. A gaseous mixture has the following following volumetric analysis : O 2 = 30%; CO 2 = 40% ; N 2 = 30%. Determine the gravimetric gravimetric analysis the partial pressure of each component if the total pressure pressure is 100 KPa and the temperatur temperatur e is 32C the molecular weight weight and gas constant of the mixture For O2: M = 32 ; k = 1.395 CO2: M = 44 ; k = 1.288 1.288 N2: M = 28 ; k = 1.399
109. How many kilograms of N2 must be mixed with with 3.6 kg of of CO 2 in order to produce a gaseous mixture that is 50% by volume of ach constituents. 110. For the resulting mi xture, xt ure, determine determine M and R, and the partial partial pressure of the N 2 if that of the CO 2 is 138 KPa. 111. The exhaust from a diesel engine us ing a high grade hy drocarbon fuel has an an Orsat Analysis Analy sis of, 10.2% CO 2 ; 7.9% O2 and 81.9% N2.Determine a. the value value of n and m from from CnHm b. the ratio of H to C in the fuel fuel by mass c. the actual air fuel ratio d. the theoretical air – fuel ratio d the percent ex cess air Given: Orsat Orsat Analysis CO2 = 10.2 % O2 = 7.9 % N2 = 81.9 % Combustion Equation (Basis 100 moles of dry flue gas)
CnHm xO2 x(3.76)N2
10.2CO2 yH2O 7.9O2 81.9N2
By carbon, hydrogen hydrogen,, nitrogen and and oxy gen balance balance n = 10.2 ; m = 14.73; x = 21.78 ; y = 7.36
kg of H kg of C
m
12n
0.1203
21.78(32) (21.78)(3.76)(28) kg of ai r A 21.80 12(10.2) 14.73 kg of fuel F actual
CnHm aO2 a(3.76)N2
bCO bCO2 cH2O a(3.76)N2
a = 13.9; b = 10.2 ; c = 7.37
13.9(32) 13.9(3.76)(28) kg of ai r A 13.9 12(10.2) 14.73 kg of fuel F theoretical A F actual 1 e A F theoretical e 0.57 57% 112. A furna furnace ce burns burns natural natural gas that t hat has the following following volumetric analysis: analysis : CH4 = 90% 90% ; C2H6 = 7% and C 3H8 = 3%. The gas fuel flow rate is 0.02 m 3/sec and 25% excess air is required for complete combustion. The natural gas and
The The The The The The The
air enter at 25C and 101 KPa. The The exhaust ex haust gas (products) (products ) has a temperature of 1000 C and 101 KPa. Determine the following combustion equation volumetric analysis of the products molecular weight M and gas constant R of the products density of the products in kg/m 3 orsat analysis of the products flue gas velocity velocity exiting the smokestac k if the stack diameter is 1 m
0.9CH4
0.07C2H6
0.03C3H8
aO2
a(3.76)N2
bCO2
cH2O a(3.76)N2
a 2.2 b 1.13 c
2.13
combustion with excess air e 0.25 0.9CH4
0.07C2H6
0.03C3H8
(1.25)aO 2
0.07C2H6
0.03C3H8
2.74O2
(1.25)a(3.76)N2
bCO2
cH2O dO2
(1.25)a(3.76)N2
d 0.55 0.9CH4
10.32N2
1.13CO2
2.13H2O 0.55O2
10.32N2
Volumetric Volumetric analysis analysis CO2 = 8% H2O = 15.08% O2 =3.88% N2 = 73.04% M = 27.93 kg/kg m R = 0.298 KJ/kg-K Orsat Orsat analysis analysis CO2 = 9.42% O2 = 4.57% N2 = 86% 113. A gas gas fired thermal power power plant uses two types of of hydrocarbon fuel fuel with the following following molal (volumetric (volumetric analysis) analysis ) CH4 = 68% ; C 2H6 = 32%. Fuel and air is supplied to the boiler at 101 KPa and 25 C with 30% excess air requirement requirement for for c omplete combustion. P roduct roduct temperature temperature and pressure pressure are 1000 1000 C and 101 KPa, respectively. Determine t he following: following: a. the combustion equation b. the theoretic theoretical al and actual air fuel fuel ratio c. the Orsat analysis analysis of the produ products cts d. the molecular weight and gas constant of of the products products e. the kg of CO2 formed formed per kg of fuel burned f. the partial pressure press ure of H 2O in the products
Combustion with 100% theoretical air 0.68CH4 + 0.32C2H6 + 2.48O 2 + 9.32N2 → 1.32 CO2 + 2.32 H2O + 9.32 N2 a = 2.48 ; b = 1.32 ; c = 2.32 Combusti Combustion on with excess air e = 0.30 d = 0.74 0.68CH4 + 0.32C2H6 + 3.22O 2 + 12.12N2 → 1.32 CO2 + 2.32 H2O + 0.74O 2 + 12.12 N2
A 16.62 F T A 21.61 F a Orsat Orsat Analysis CO2 = 9.3% O2 = 5.24%
N2 = 85.45% Molecular Weight and Gas Constant M = 28.05 R = 0.296 Kg of CO 2/kg of fuel =58.08/20.48 = 2.84 kg/kg PH2O = 14.24 KPa
114. Air is contained in a cylinder cy linder fitted fitted with a frictionless pis ton. Initially the c ylinder contains 500 L of air at 150 KP a and 20 C. The air is then compressed in a polytropic process ( PV n = C) until the final final pressure pressure is 600 KPa, at which point the temperature temperature is 120 C. Determine the work W and the heat heat transfer Q. (R (R = 0.287 KJ/kg - K ; k = 1.4) Given: V 1 = 0.50 m 3 ; P 1 = 150 KPa ; T1 = 293 K P 2 = 600 KPa ; T2 = 393 K ; Process: PV n = C n1
T2 T1
P 2 P1
n1
ln
n
ln
n
T2 T1 P2 P1
m
P1 V1 RT1
0.892 kg
U mC v (T2
Cv
- T1 ) 64 KJ
R
k -1 Q 31 KJ
n 1.27 Q U W W
T2 1 95 KJ 1 n T1 P1 V1
115. A steam st eam turbine of a coal fired thermal t hermal power plant receives steam st eam at 7 MPa and 500 C (h1 = 3410.3 KJ/kg ; S 1 = 6.7975 KJ/kg-K) with a velocity velocity of 30 m/sec and expands expands isentropically to the condenser at a pressure pressure of 20 KPa with a veloci velocity ty of 90 m/sec. m/sec . Calculate Calcul ate the t he ideal powe r developed by the turbine for a steam flow rate of 37.8 kg/s k g/se ec assuming PE in the turbine to be negligible. At 20 KPa K Pa Sf = 0.8320 KJ/kg-K ; S g = 7.9085 KJ/kg-K ; Sfg = 7.0765 KJ/kg-K hf = 251.4 KJ/kg ; h g = 2609.7 KJ/kg ; hfg = 2358.3 KJ/kg SOLUTION: 6.7975 = O.8320 + x 2(7.0765) x2 = 0.839 h2 = 251.4 251.4 + (0.839)(2 (0.839)(2358.3) 358.3) = 2230.014 2230.014 KJ/kg
Q h KE PE W Q 0 and PE 0 W -h - KE
2 2 (90) (30) W mh KE 37.8(2230.014 3410.3) 2(1000) W 44,478.73 KW
116. Air which is initially at 120 KPa and 320 K occupies 0.11 m 3. It It is compressed isothermally until the volume is halved halved and then compressed it at constant pressure until the volume volume decreases to ¼ of the initial volume. volume. Sketc h the process on the PV and TS diagrams. Then determine the pressure, the volume and temperature in each state. (For air: R = 0.287 KJ/kg-K ; k = 1.4) Given: P1 = 120 KPa ; T1 = 320K; V 1 = 0.11 m 3; T2 = 320K; V 2 = ½V1; V 3 = ¼V ¼ V1 For air: R = 0.287 KJ/kg-K; k = 1.4 Processes:
1 to 2: T = C 2 to 3: P = C
T
P 3
2 T=C
1
P=C 1 3
V
Solution:
S
At 1 to 2: T = C P 1V1 = P 2V 2 T1 = T2 = 320K V 2 = ½V 1 = ½(0.11) = 0.055 m 3
V1 120(2) 240 KPa V 2
P2 P1
At 2 to 3: P = C P 3 = P 2 = 240 KPa V 3 = ¼V 1 = ¼(0.11) = 0.0275 m 3 T3 T2 T3
V3 V2
0.0275 320 160 K 0.055
From RT
P
1
2
3
RT1 P1
RT2 P2
RT3 P3
1 = 0.765 m 3/kg 2 = 0.383 m 3/kg 3 = 0.191 m 3/kg 117. A cy linder fitted with a frictionless frictionless piston contains 5 kg of superheated superheated water vapor vapor at 1,000 KPa & 250 C (h1 = 2942.6 KJ/kg ; U 1 = 2709.9 KJ/kg ; S 1 = 6.9247 KJ/kg-K). This system is now cooled at constant pressure until the water reaches a quality x 2 of 50%. Calculate the heat transferred transferred and the work work done during this process process,, and draw the process on the PV & TS plane. At 1000 KPa at saturation hf = 762.81 KJ/kg; h g = 2778.1 KJ/kg; h f g = 2015.29 KJ/kg Uf = 761.68 KJ/kg; U g = 2583.6 KJ/kg ; U f g = 1281.92 KJ/kg Sf = 2.1387 KJ/kg-K; S g = 6.5865 KJ/kg-K; S f g = 4.4478 KJ/kg-K
h2
762.81 (0.50)(2015.26)
U2
761.68 0.50(1281.92)
At P Q
1770.44 KJ/kg
1402.64 KJ/kg
C
m(h2 - h1 )
U
W
m(U2 - U1 )
Q - U
5(1770.44 - 2942.6) 5860.8 KJ
5(1402.64 - 2709.9) 6536.3 KJ
-5860.8 6536.3 675.5 KJ
P
T
1
1
2
2
S
V
118. A small sm all circ ular hole 6 mm in diameter is bored in the side of a large water tank t ank 14 m below the t he water water level i n the tank. The top of the tank is open t o the atmosphere atmosphere and the velocity velocity on the water surface is negligible. Find the t he velocity of water exiting the hole hole and the t he volume volume discharged in L/sec. ( water = = 1000 kg/m3)
1
Q U P KE PE W 14 m
U 0 P 0
2
W0 Q 0 KE PE
v2
2
v1
2
g(Z 2 Z 1 )
2000
1000 2
v2
2g(Z 1 Z 2 ) v 1
v1
0
; Z1
v2
2(9.81)(14) 16.57 m/sec
0
2
m
(0.006)
(16.57)
4
4.7 x 10
-4
3
m /sec 0.47 L/sec
119. A piston cylinder device, device, whose piston is resti ng on on a set stops, initiall y contains 3 kg of air at 200 KPa and 27 C. The The mass of the piston is suc h that a pressure of 400 KPa is require required d to move move it. Heat is now transferred transferred to the air air until its volume doubles. Determine the work done by the air and the tot al heat transferred to the air during during this process. Also, show the process on a P-V diagram. (For air: R = 0.287 KJ/kg-K ; k = 1.4)
P
T 2
3 2P = C
3 V=
1 1 Q
At
V
V1
V2
P2 P1
T2
Qv
T2 T1 600 K
3(0.7175)(600 - 300) 645.75 KJ
At P V3 V2
T2 2 V 1
2.6 1.3 T3
C
T3
V 3
C
2.6
m3
T3 600
1200 K
Qp
mCp (T3 - T2 ) 3(1.0045)(1200 - 600)
Qp
1808.1 KJ
W P(V3 - V2 ) 400(2.6 - 1.3) W 520 KJ QT
645.75 1808.1 2453.85 KJ
120.
121. A closed sys tem consist ing of 2 kg of a gas undergoe undergoes s a process process during which the relationship between pressure and and specific volume volume is PV 1.3 = constant. The process begins with P 1 = 1 bar, 1 = 0.5 m 3/kg and ends with P 2 = 0.25 bar. bar. Determine the final final volume, in m 3, and and plot the proces process s on a graph of press press ure versus versus specific volume. (Note: 100 KPa = 1 Bar) m = 2 kg P1 = 1 Bar = 100 KPa ; P2 = 0.25 Bar = 25 KPa 1 = 0.5 m 3/kg Process: PV 1.3 = C 1.3 1.3 P1 1 P2 2 1
2 P1 P2 1
1.3
1
3
m 100 1.3 2 0.5 1.45 kg 25 3 V2 m2 2(1.45) 2.9 m
122. Suppose that 42,200 KJ of heat energy are suppli ed in a small boiler to 25 kg of water at 90 C. What part of the water in kg will be vaporized, if the initial ini tial enthalpy of water is 376.78 KJ/k g and and latent heat of vaporizat vaporization ion (h f g)of water is 2257 KJ/kg. Neglect Neglect changes in kinetic and potential energies. energies.
Q m(h2 h1) h2
x2
42,200
376.78 2064.78 KJ/kg 25 h2 100(4.187) x2 (2257)
0.793
mv m mv 18.23 kg mass of water vaporized to vapor x2
123. Calculate Calcul ate t he heat required t o be given given to 2 kg of ice ic e at -15C to change into steam at at atmospheric pressure, taking the values Freezing point temperature temperature = 0C Specific heat of ice = 2.04 KJ/kg-K
Latent heat of fusion = 335 KJ/kg Specific heat of water = 4.2 KJ/kg-K Latent heat of of evaporation evaporation = 2256.7 2256.7 KJ/kg KJ/k g
Q m2.04(0 15) 335 4.2(100 0) 2256.7 Q 6084.6 KJ
124. A liquid of density density 800 kg/ m3 specific heat heat of 2.5 KJ/kg KJ/kg -K and and temperature temperature of 27 C is mixed with another li quid of density 820 kg/m3, specific heat 1.9 KJ/kg-K and temperatur temperature e of 55 C in the ratio ratio of one of the first first liquid to t o three of the second by volume. volume. Find the resulting temperature. temperature. Qh = Qc mh(Cph)(55 - t) = m c (Cpc)(t – 27)
Vc Vh
V
1 3
; Vh 3Vc
m V m
m V mc Vc c mh Vhh 3Vc (820)(1.9)(55 t) Vc (800)(2.5)(t 27) (55 t) 0.428(t 27) 55 t 0.428t 11.55 t
55 11.55 1.428)
46.6C
A 3 m diameter by 4.5 m height vertical tank is receiving receiving water ( = 978 kg/m 3) at the rate of 1.13 m 3/min and is discharging through a 150 mm with a constant velocity of 1.5 m/sec . At a given given instant, the tank is half half full. full. Find the water level and the mass change in the tank 15 minutes later.
Two Two gaseous streams containing the s ame fluid enter a mixing c hamber and leave leave as a single st ream. For the first first 2 3 gas the entrance entrance condition are: A 1 = 500 500 c m ; v1 = 730 m/sec ; 1 = 1.60 kg/m . For the second gas the entrance 2 condition are A 2 = 400 cm ; m 2 = 8.84 kg/sec ; 2 = .502 m 3/kg. The exit stream conditions is: v 3 = 130 m/sec and 3 = 0.437 m 3/kg. Determine
(a) the total mass flow leaving leaving the chamber (b) the veloci velocity ty of gas 2. In determining determining the specific heat of a new metal alloy,0.15 k g of of the substance is heated to 400 C and then placed in a 0.2 kg aluminum calorimeter cup containing 0.4 kg of water at 10 C. If the final temperature of the mixture mix ture is 30.5C , what is the specific heat of the alloy. (ignore (ignore the calorimeter s tirrer and thermometer) thermometer) Cpal = 0.92 KJ/kg- C; Cpw = 4.187 KJ\kg-C
It is required to lift five five people on an elevator elevator a distance dist ance of 100 m. The The work is found to be be 341.2 341. 2 KJ and g = 9.75 m/sec 2. Determine Determine the average average mass per person.
Twenty kilograms of ice at -8C is placed in a 120 kgs of water at 40 C. Assuming no heat lost to or absorbed from the surroundings, surroundings, what will be the resulting equilibrium equilibrium temperature temperature of the mixture. Specific heat of ice = 2.22 KJ/kg-C Specific heat of water = 4.19 KJ/kg- C Freezing point temperature of water = 0 C hF of ice = 334.9 KJ/kg
20 2.22(0 8) 334.9 4.19(t 0) 120(4.19)(40 t)
355.2 6698 83.8t 23464 502.8t
t 27.98C
A cup c up of coffee coffee of volume volume 0.3 L is heated from from a temperature temperature of 25oC 25oC to 60oC at a pressure of 100 kPa. Determine the change in the (a) internal energy, (b) enthalpy and (c) entropy. Assume the density and specific heat of coffee to be 1100 kg/m3 and 4.1 kJ/kg.K respectively. respectively. Employ the SL model. model. (d) What -if scenario: How would the answers change if the heating was done inside a chamber pressurized at 1 MPa? [Manual Solution] [TEST Solution] Answers: (a) 47.36 kJ (b) 47.36 kJ (c) 0.15 kJ/kg.K (d) No No changes
A block of solid with a mas s of 10 10 kg is heated from from 25oC to 200oC. 200oC. If the change in the specific internal energy is found found to be 67.55 kJ/kg, identify the material. [Manual Solution] [TEST Solution] Answers: Copper Copper A block of aluminum with a mass of 10 k g is heated from from 25oC to 200oC. 200oC. Determine (a) the total change in internal energy energy and (b) entropy of the block. (c) What -if-Scenario: -if-Scenario: How would the answer in (b) change if the block was made of copper instead? [Manual Solution] [TEST Solution] Answers: (a) 1578.5 k J/kg (b) 4.17 kJ/K (c) 1.783 kJ/K A 2 kg block of aluminum at 600oC is dropped dropped into a cooling tank. If the final final temperature temperature at equilibrium is 25oC, determine (a) Change Change in internal energy, and (b) change in entropy of the block as the system. Use Use the SL model for aluminum (c_v = 0.902 kJ/kg.K). [Manual Solution*] [TEST Solution*] Answers: (a) -1037.3 kJ (b) -1.939 kJ/K 10 A copper block of mass 5 kg, k g, initially at equilibrium equilibrium with the t he surrounding surroundings s at 30oC and 100 kPa is placed in a pressuriz ed chamber c hamber with a pressure of 20 MPa and a temperature of 200oC. 200oC. Determine (a) the change in the internal energy energy (b) enthalpy and (c) entropy entropy of the block after it comes to a new equilibrium. (d) W hat-if-Scenario: hat-if-Scenario: How would the answer answer in (a) (a) change if the block was made of silver? silver? [Manual Solution] [TEST Solution] Answers: (a) 65.62 kJ/kg (b) 67.85 kJ/kg k J/kg (c) 0.17 kJ/k g.K (d) 39.94 kJ/kg A 2 kg k g block of aluminum aluminum at 60oC is dropped dropped into a tank containing 5 kg of water at 25oC. If t he final final temperature temperature after equilibrium is 27.77oC. Determine (a) DU and (b) DS for the combined com bined syst sy stem em of aluminum and water before and afte afte r the process. [Manual Solution] [TEST Solution] Answers: (a) -52.35 k J (b) -0.1643 kJ/K ] A cup of coffee coffee cools down by transferring heat to the surroundings at a rate of 0.1 kW. k W. If the mas s of coffee is 0.2 kg and coffee coffee can be modeled as water, determine the rate of of change of temperature of coffee. coffee. [Manual Solution][TES T Solution] Answers: (a) 1.2 K/s K/ s Anim. 3-2-14 3-2-14 (click ) A pump raises the pressure of liquid water from 50 kPa to 5000 k Pa in an is entropic manner. manner. Determine (a) the chang e in temperature temperature and (b) specific enthalpy between the inlet and exi t. [Manual Solution] [TEST Solution]
Answers: (a) 0 (b) 4.965 kJ/kg Oil (cv=1.8 (cv=1.8 kJ/kg.K ) flows flows s teadily through through a long insulated cons tant-diameter tant -diameter pipe at a volume flow rate rate of 10 m3/min. The conditions at the inlet are p = 3000 kP a, T = 20oC, V=20 m/s and z= 100 m. The The conditions at the exit are are p = 2000 kPa, T = 21oC 21oC and z=0 m. (a) Use Use the mas s equation equation to evaluate evaluate the velocity velocity at the exit. (b) (b) Use the energy equatio n to show that j remains unchanged between the inlet and the exit. (c) Determine the exit temperature. [Manual Solution] [TEST Solution] Answers: (a) 20 m/s (b) 21.16oC 21.16oC Water flows flows steadily through a dev device at a flow flow rate of 20 kg/s . At the inlet the conditions are 200 kP a and 10oC. 10oC. A t the exit the conditions are 2000 k Pa and 50oC. 50oC. (a) Determine Determine the differen difference ce between the entropy entropy transpor t ransported ted by the flow flow a t the exit and at the inlet. (b) What are the possible reasons behind the increase in entropy transport? [Manual Solution] [TEST Solution] Answers: (a) 11.06 kW kW/K /K (b) heat addition and irreversibilities irreversibilities 19 In In an isentropic is entropic nozzle, operating operating at steady s tate, the specific flow flow energy energy 'j' and specific entropy entropy 's' remain remain constant along the flow. flow. The The following following properties properties are known at the inlet and exit ports of an isentropic isentropic nozz le disc harging harging water at a steady rate rate of 2 kg/s. Inlet: p=300 kPa, A=4 A= 4 cm2; Exit: Ex it: p=100 p=100 kPa. Determine (a) the exit velocity velocity and (b) the exit area. Use the SL model for liquid water. (c) What-if scenario: How would the exit velocity change if the inlet kinetic energy was neglected? [Manual Solution] [TEST Solution] Answers: (a) 20.65 m/s (b) 97.2 97.2 mm2 (c) 20.03 m /s Anim. 3-2-19 (clic k) A pipe carries saturated liquid water at a pressure of 500 kPa. Some water squirts out from from the pipe throu t hrough gh a small leak. As the water is expelled, it quickly achieves achieves mechanical equilibrium wit h the atmosphere atmosphere at 100 kPa. (a) Estimate the temperatur temperature e of water water inside and outside the pipe. What if scenar sc enario: io: How would the answers answers c hange hange if the fluid fluid was (b) R-134a or (c) R-12 instead? [Manual Solution] [TEST Solution] Answers: (a) 151.8oC, 99.6oC (b) 15.6oC, -26.6oC -26.6oC (c) 15.6oC, 15.6oC, -30.1oC -30.1oC A vertical vertical piston-cylinder piston-cy linder assembly contains water. The The piston has a mass of 2 kg and a diameter of 10 cm. Determine the vertical vertical force force necessary on the piston to ensure that water inside the cyl inder boils boils at (a) 120oC or (b) (b) 80oC. 80oC. Ass ume atmospheric pressure to be 101 kPa. (c) What-if scenario: How would the answer in part (a) change if the piston mass was neglected? [Manual Solution] [TEST Solution] Answers: (a) 0.746 kN (b) -0.441 kN (c) 0.766 kN Anim. 3-3-8 (clic k) A vertical vertical piston-cylinder piston-cy linder assembly contains a saturated mixture mixt ure of water at 120oC and a gage pressure of 108.5 kPa. The piston has a mass of 5 kg and a diameter of 12 cm. Determine (a) the atmospheric pressure press ure outside outs ide and (b) the external force exerted on the piston to maintain a constant pressure. [Manual Solution] Answers: (a) 90 kPa kP a (b) 1.178 k N downward downward A cooking pan with an inner diameter of 20 c m is filled filled with water and covered covered with a lid of mass 5 kg. If the atmospheric atmospheric pressure is 100 kPa. Determine (a) the boiling temperature temperature of water. water. (b) What -if-Scenario: -if-Scenario: How would would the answer answer change if a 5 kg block is placed on top of the lid? [Manual Solution] [TEST Solution] Answers: (a) 100.04 oC (b) 100.45 oC. Anim. 3-3-10 (click ) 11 A heat engine cycle is executed with ammonia in the saturation dome. The pressure of ammonia is 1.5 MPa during heat addition addition and 0.6 0.6 MPa during during heat rejection. rejection. What is the highest highest possible thermal efficiency efficiency ? Based on the temperatures of heat addition and rejection, could you comment on possible application of such a low-efficiency cycle? [Manual Solution] [TEST Solution] Answers: 9.44% Anim. 3-3-11 3-3-11 (click ) 16 A 10 L rigid tank contains 0.01 kg of steam. Determine the (a) pressure (b) stored energy E and (c) entropy S of steam if the quality is 50%. Neglect kinetic and potential energy. (d) What-if scenario: How would the answers change if the quality was 100%? [Manual Solution] [TEST Solution] Answers: (a) 83.7 kP a (b) 14.48 kJ (c) 0.043 k J/K (d) 175.4 kPa, 25.25 k J, 0.072 k J/K Anim. 3 -3-16 -3-16 (click )
A tank contains 20 kg of water at at 85oC. If half of it (by mass) is in the liquid liquid phase and the rest in vapor vapor phase, determine (a) the volumetric volumetric quality, and the stored energy energy in the (b) (b) liquid and (c) vapor vapor phases. [Manual Soluti on] [TEST Soluti on] Answers:(a) 99.96% (b) 99.96% (c) 3558.4 3558.4 kJ (d) 24,883.5 kJ A vessel having having a volume of 0.5 m3 contains 2 kg saturated liquid and saturated vapor mixture of H2O at 500 kPa. Calculate the (a) mass and (b) volume volume of each phase. phase. [Manual [M anual Solution] [ TEST Solution]
Answers: (a) 1.32 kg, 0.67 kg, (b) 0.001 m3, 0.25 m3 m3 A rigid tank of volume volume 83 m3 contains 100 kg k g of H2O H2O at 100oC. The tank is heated until the temperature temperature inside reaches 120oC. 120oC. Determine t he pressure inside the tank at the (a) (a) beginning beginning and (b) (b) end of the heating heating process . What -if-scenari -if-scenario: o: How would would the final final pressure c hange if the tank temperature increased to 125oC? 125oC? [Manual Solution] [TEST Solution] Soluti on] Answers: (a) 101 k Pa (b) 198.5 198.5 kPa (c) (c ) 216.2 kPa k Pa A rigid tank (v = constant) contains 8 kg of liquid and 2 kg of vapor vapor of H2O at 200oC. 200oC. To what temper t emperature ature should the tank be heated until all the liquid in the tank vapor vaporize? ize? [Manual Solution] [TEST Solution] Answers: 288oC
A piston pis ton cylinder cyl inder device device of volume 1 m3 contains 3 kg of water. The piston, which has an area of 100 cm2, exerts a force of 1.7 kN on the pin that keeps it from from moving. Determine the (a) temperature and (b) (b) quality qualit y of H2O inside insi de the cylinder. cyl inder. The The water is now heated. (c) Determine the force force on the pin when all the liquid in the tank vapor vaporize. ize. Ass ume the atmospheric pressure to be 100 kPa and neglect the piston mass. [Manual Solution] [TEST Solution] Answers: (a) 130 oC (b) 0. 497 (c) 4.64 kN Anim. 3-3-29 (click ) 30 A rigid tank with wit h a volume of 3.5 m3 contains 5 kg of saturated sat urated liquid -vapor -vapor mixture mix ture of H2O at 80oC. The tank is slowly heated until all the liquid in the tank are are completely vaporized. aporized. Determine the temperature temperature at which this t his happen happens s. Also show t he process process on T-v diagram diagram with respect t o saturation lines. [ Manual Soluti on] [TEST Solution] Answers: 128.33 oC A 50 L rigid t ank contains R-134a R-134a at a temperature of 50oC with a quality of 2.5%. Heat is added until the all the vapo r condense (due t o increased pressure) and the tank tank is filled filled c ompletely with saturated l iquid. (a) (a) With W ith the aid of a T -v diagram, show that this is quite possible. Also determine (b) the pressure and (c) temperature in the tank at saturation. [Manual Solution] [TEST Solution]
Answers: (b) 3469 k Pa (c) 93.25oC 32 A 1000 1000 L rigid tank contains saturated li quid water at 40oC. 40oC. (a) Determine Determine the pressure ins ide. (b) (b) The tank is now heated to 90oC. Use the compress compressed ed liquid table to determine determine the pressure pressure in the tank. [Manual Solution] [TEST Solution] Table Table B-4: Compressed Compressed Liquid Table of Water
Answers: (a) 7.39 kP a (b) 43.23 MPaoC A lid with negligible weight is s uddenly uddenly placed on a pan of boiling water and the heating is t urned urned off. off. After about about an hour, thermal equilibrium is reached between the water and the atmosphere, which is at 30oC and 101 kPa. If the inner diameter of the pan is i s 20 cm. Determine the force force necessary to t o open open the lid. (b) (b) What -if-Scenario: -if-Scenario: How would t he answer change if the lid weight of 1 kg was to be considered? [Manual Solution] [TEST Solution] Answers: (a) 3.04 kN (b) 3. 05 k N Anim. 3 -3-33 -3-33 (click ) Superheated water vapor vapor at 1.5 MPa and 280oC is i s allowed to cool at constant cons tant volume volume until the temperature drops to 130oC. 130oC. At the final final state s tate determine (a) the pressure (b) the quality quality and (c) the enthalpy. S how the process on a T-s diagram. [Manual Solution] [TEST Solution] Answers: (a) 270.1 kPa (b) 24.2% (c) 1072 kJ/kg 36 A rigid rigid tank t ank with a volume of 1 m3 contains superheated superheated steam at 500 kPa and and 500oC. Determine (a) the mass and (b) the total internal energy of the steam. The tank is now cooled until the total internal energy decreases to 2076.2 kJ. Determine Determine (c) the pressure pressure and (d) temperature temperature in the final state. [Manual Soluti on] [TEST Solution] Answers: (a) 1.407 kg (b) 4400.4 4400.4 kJ (c) 120.7 k Pa (d) 105.0oC 38 A large indust i ndustrial rial tank of volume 200 m3 is filled with steam at 450oC 450oC and 150 kP a. Determine Determine (a) the pressure and (b) quality quality of steam when t he temperatur temperature e drops drops to 25oC 25oC due to heat heat loss . (c) If the heat transfer for t his constant volum volum e process is given by Q=DU, determine the heat transfer. [Manual Solution] [TEST Solution] Answers: (a) 3.17 kP a (b) 5.4% (c) -255.57 -255.57 MJ A piston-cylinder pis ton-cylinder device device contains 3 kg of saturated mi xture of water with a quality of 0.8 at 180oC. Heat is added added until all the liquid liqui d vaporize. vaporize. Determine (a) the press ure (b) the initial volume volume (c) the final volume volume and (d) the work perform perform e d by the vapor vapor during the expansion process. (e) Show the process process on a p-v diagram. [Manual Solution] [TEST Solution]
Answers: (a) 1 MPa (b) 0.466 m3 (c) 0.582 m3 (d) 116 kJ Anim. 3-3-43 3-3-43 (click ) 45 A piston-cylinder device device contains 0.6 kg of steam at 350oC and 1.5 MPa. Steam St eam is now cooled at const ant pressur pressure e until half of the mass condenses. condens es. Determi ne (a) the final temperature t emperature and (b) the boundary work trans fer. (c) Show the process on a T-s diagram. [Manual Solution] [TEST Solution] Answers: (a) 198.3oC (b) -108 k J Water vapor vapor (1 kg) at 0.2 kPa and 30oC is cooled at a constant pressure process until condensation begins. Determin e (a) the boundary work transfer and (b) change of enthalpy, DH, treating water as the system. (c) What-if-Scenario: How would the answers answers c hange, hange, if all the vapor vapor condensed? [Manual Solution] [TEST Solution] Answers: (a) -18.9 kJ (b) -78.57 k J (c) -139.9, -2,916.1 -2,916.1 kJ A piston cylinder cyl inder device device contains 10 L of liquid water at 100 kPa and 30oC. Heat is transf t ransferre erred d at constant pressure until the temperature increases increas es to 200oC. 200oC. Determine Det ermine the t he change in the (a) total volume volume and (b) total internal energy of steam. Show the process on a T-s and P-v diagram. [Manual Solution] [TEST Solution] Answers: (a) 21.6 m3 (b) 25221 kJ A piston-cylinder device device contains a s aturated mix ture of water water with a quality of 84.3% at 10 kPa. IfIf the pressure is raised in an an isentropic (consta nt entropy) manner manner to 5000 kPa, kP a, (a) (a) determine determine t he final temperature. temperature. (b) What-if sc enario: enario: How would the answer c hange if water was at saturated vapor vapor state to start with? [Manual [Manual Solution] [TEST Solution] S olution] Answers: (a) 499oC (b) 994oC Anim. 3-3-48 3-3-48 (click) (clic k) Water at a pressure pressure of 50 MPa is heated in a constant pressure electrical heater from from 50oC to 1000oC. 1000oC. Spot the states on a T-s diagram and determine (a) the change of enthalpy and (b) entropy. Use compressed liquid model for liquid water. [Manual Solution*] [TEST Solution]
Answers: (a) 4241 k J/kg (b) 6.31 kJ/k g.K, A nim. 3 -3-52 -3-52 (click ) Determine (a) the mass flow rate and (b) the volume volume flow rate of steam st eam flowing through a pipe of diameter 0. 1 m at a pressure of 1000 kPa kP a and a temperature of 300oC 300oC with a veloci velocity ty of 50 m/s. (c) (c) Also Al so determine the t he rate of transport of energy by the steam. (d) (d) What -if-Scenario: How would the answer in (d) change if the temperature was 400oC? [Manual Solution] [TEST Solution]
Answers: (a) 1.52 kg/s (b) 0.392 0.392 m3/s (c) 4647 kW (d) 4182 4182 k W Figure 3-3-53 3-3-53 Refriger Refrigerant-134 ant-134 flows flows through through a pipe of of diameter 5 cm with a mass mass flow rate of 0.13 kg/s at 100 kPa, 10 m/s. Determine Determine (a) the temperature and (b) quality of the refrigerant refrigerant in the pipe. Als o determine the rate of transport of (c) energy and (d) entropy by the flow. [Manual Solution] [TEST Solution] Answers: (a) -26.6oC (b) 78.3% (c) 24.19 k W (d) 0.0983 k W/K W/ K Steam at a pressure of 2 MPa and 400oC flows through a pipe of diameter 10 cm with a velocity of 50 m/s. Determine the flow rates of (a) mass (b) energy and (c) entropy. [Manual Solution] [TEST Solution] Answers: (a) 2.6 kg/ s (b) 8446.8 kW (c) 18.51 kW .K Liquid water at 100 kP a, 30oC 30oC enters a boiler through a 2 cm -diameter pipe with a flow flow rate of 1 kg/s. It leaves leaves the boiler as a saturated vapor vapor through through a 20 cm-diameter cm -diameter pipe without any significant significant pressure loss . Determine (a) the exit velocity velocity , and the rate of transport transport of energy at the (b) inlet and (c) exit. Neglect potential energy, energy, but not kinetic energy. energy. (d) What if-Scenario: How would the answers change if kinetic energy was neglected? [Manual Solution] [TEST Solution] Answers: (a) 53.92 m/s (b) 125.8 125.8 k W (c) (c ) 2,676.95 kW (d) 125.79 125.79 k W, 2,675.5 kW Water is pumped pumped in an isentropic (constant entropy) entropy) manner from from 100 k Pa and 25oC to t o 40 MPa. Determine Determine the change in enthalpy, Dh, using the (a) compressed liquid table (b) compressed liquid model and (c) solid/liquid model. [Manual Solution] [TEST Solution] Answers: (a) 40.94 kJ/kg (b) 39.99 kJ/kg.K k J/kg.K (c) 40.02 kJ/kg In an an isentropic nozzle t he specific flow flow energy j and and entropy s remain const ant along the flow. flow. Superheated Superheated steam flows steadily t hrough hrough an isentropic nozzle for which which the following following properties properties are known at the inlet and and exit ex it ports. ports. Inlet: Inlet: p=100 kPa, T=400oC, T=400oC, A=100 cm2, Vel=5 m/s ; Exit: Exi t: p=200 kPa. Determine Determine (a) the exit exi t velocity (b) the exit temperature temperature and (c) the exit area. [Manual Solution] [TEST Solution] Answers: (a) 630 m/s m /s (b) 302oC( 302oC(b) b) 1.36 cm2 Anim. 3 -3-61 -3-61 (click )
1 Determine Determine (a) the mass of air at 100 kPa, 25oC in a room with dimensions 5m x 5m x 5m. (b) How How much air must leave leave the room if the pressure drops to t o 95 kPa at constant cons tant temperature? (c) How much muc h air must leave leave the room if the temperature temperature increased to 40oC 40oC at const ant pressure? pressure? [Manual [ Manual Solution] [TEST [TEST Solution] Answers: (a) 146 k g (b) 7.3 kg (c) 7.0 kg Figure 3-4-1 A cylinder c ylinder of volume volume 2 m3 contains 1 kg of o f hydrogen at 20oC. Determine the change in (a) pressure (b) stored st ored energy and (c) entropy entropy of the gas gas as the chamber chamber is heated to 200oC. Us e the PG model model for hydrogen. hydrogen. (d) What -if-Scenari -if-Scenario: o: How would would the t he answer change if the chamber contained c ontained carbon-dioxide carbon-dioxide instead? [Manual Solution] [TEST [TEST Solution] Answers: (a) 371.2 kPa (b) 1,833 k J (c) 4.88 k J/kg.K (d) 17 kPa, 118.3 kJ, k J, 0.315 k J/K Anim. 3 -4-2 -4-2 (click )
The gage press ure in an automobile tire is measured measured as 250 kPa when when the outside pressure i s 100 kPa and temperatur temperature e 25oC. If the volume volume of the tire is 0.025 m3, m 3, (a) determine the amount of air in kg that must be bled in i n order to reduce reduc e the pressure to the recommended value of 220 kPa kP a gage. Use the PG model for air. (b) (b) What -if-scenario: How would the answer in change if the IG model was used instead? [Manual Solution] [TEST Solution] Answers: (a) 8.77 g (b) No change A 1 L piston-cylinder piston-cyl inder device device contains air at 500 kPa and 300 K. An electrical resistance heater is us ed to raise the temperature of the gas to 500 K at constant pressure. Determi ne (a) the boundary work t ransfer, and the change in (b) stored energy and (c) entropy of the gas. (d) What-if scenario: Which part of the answers would not change if the IG model was used? [Manual Solution] [TEST Solution] Answers: (a) 0.333 kJ (b) 0.834 kJ (c) 0.00298 kJ/K (d) part a Anim. 3 -4-10 -4-10 (click (cl ick)) 11 A pist on-cylinder on-cy linder device device contains cont ains 0.01 kg of nitrogen at 100 kPa kP a and 300oC. Using Us ing (a) the PG model and (b) IG model, determine the boundary work transfer as nitrogen cools down to 30oC. Show the process on a T-s and a p-v diagram. [Manual Solution] [TEST Solution] Answers: (a) -0.8 kJ (b) -0.8 kJ Oxygen at 100 kPa and 200oC 200oC is compressed t o half its initial volume. volume. Determine Determine the final final s tate in terms of pressure and temperature i f the compression compression is carried carried out in i n an (a) (a) isobaric (b) isothermal and (c) isentropic manner. manner. Use t he PG model for oxygen. [Manual Solution] [TEST Solution] Answers: (a) -36.5oC (b) 200 k Pa (c) 263 kPa, 348oC 348oC Anim. 3 -4-12 -4-12 (click ) Air at 15oC and 100 kPa enters the diffuser diffuser of a jet engine s teadily with a velocity velocity of 100 m/s. The inlet area is 0.2 m2. Determine Determine (a) the mass flow rate of of the air, air, (b) What -if-sc -if-scenar enario: io: How would would the conclusion conclusi on change c hange if the entranc entranc e velocity was 150 m/s? [Manual Solution] [TEST Solution] Answers: (a) 24.2 kg/s (b) 36.3 36.3 kg/s Air flows through through a nozzle in an isentropic manner from from p = 400 kPa, k Pa, T = 25oC at the inlet to p = 100 KPa at the exit. Determine Determine the temperature temperature at the exit, exit, modeling air as a perfect perfect gas. [Manual Solution] [TEST Solution] Answers: -72.5 oC Anim. 3-4-20 3-4-20 (click ) A tank of volume volume 10 m3 contains nit rogen rogen at a pressure of 0. 5 MPa and a temperature temperature of 200 K. Determine the mass of nitrogen in the tank using the (a) (a) ideal gas and (b) real real gas model. (c) What -if-Scenario: -if-Scenario: How would the answer i n part part (a) change if the press pressure ure and temperature in the tank were 3 MPa and 125 K respectively? respectively? [Manual Solution] S olution] [TES T Solution] Answers: (a) 84.23 kg (b) 85.98 kg (c) 806.5 kg A closed rigid tank contains carbon-dioxide carbon-dioxide at 10 MPa and 100oC. 100oC. It is cooled until its temperature temperature reaches 0oC. Determine Determine the pressure pressure at t he final final state. Use (a) (a) the RG model wit h the Lee Lee Kesler K esler chart (b) (b) the RG model model with the t he Nelson Obert chart and (b) the PC model. [Manual Solution*] [TEST Solution] Answers: (a)3.87 (a)3.87 MPa (b) Out of Range (c) 3.48 MP a A 15 L tank contains 1 kg of R-12 refrigera refrigerant nt at 100oC. 100oC. It is heated until the temperature temperature of the refriger refrigerant ant reaches 150oC. Determine the change in the (a) internal energy DU and (b) entropy DS. Use the RG model with Lee Kesler charts. [Manual Solution*] [TEST Solution] Answers: (a) 28.02 kJ/kg kJ/k g (b) 0.07 kJ/kg. K A piston cylinder cyl inder device device contains 10 L of nitrogen at 10 MPa and 200 K. It is heated at a constant pressure to a temperature temperature of 400 K. Determine (a) DH and (b) DS. Use the RG model model with Lee K esler charts. (c) (c) What -if-scenari -if-scenario: o: How would the answers change if the PC model was used? If the PC model is always more accurate, then why should one use the RG model at all? [Manual Solution] [TEST Solution] Answers: (a) 490.5 kJ (b) 1.8 k J/K (c) 495.9 kJ, 1.77 k J/K Anim. 3 -5-13 -5-13 (click ) Consider an ideal gas at 400 K and 100 kPa. As a result of some disturbance, the conditions of the gas change to 404 K and and 98 k Pa. Estimate the change in the specific volume volume of the gas using the ideal-gas relation at each state. [Manual Solution*]
Determine Determine the enthalpy enthalpy change and the entropy change of carbon di -oxide per unit mass as it undergoe undergoes s a change of state st ate from from 250 K and 7 MPa to 280 K and and 12 MPa, (a) by assuming ass uming ideal -gas behaviour, behaviour, and (b) by accounting acc ounting for the t he deviation from ideal-gas bahaviour. Methane is compressed adiabatically by a steady-state flow compressor from 2 MPa and -10oC to 10 MPa and 110oC at a rate of 0.8 kg/s . Using the generalized generalized charts, determine t he require required d power power input to the compressor. compressor.
A cylindrical c ylindrical tank contains 4.0 kg of carbon monoxide at -45 oC has an inner i nner diameter of 0.2 m and a length of 1 m. Using the RG model model (L-K charts), determine determine (a) the pressure exerted by the gas. (b) (c) What-if-scenario: How would the answer in (a) change if the IG model is used instead? [Manual Solution] [TEST Solution]
Methane is adiabatically c ompressed ompressed by a piston-cy linder device device from from 1 MPa and 100oC to 4 MPa. Calculate (a) the work work done per unit mass . Assume the adiabatic efficiency efficiency to be 90%. Use the real real gas model. (b) What -if-scenario: -if-scenario: How would the answer in (a) change if the gas compressed were ethane instead? [Manual Solution*] Answers: (a) -277 k J/kg, (b) -149 kJ/kg __________ _________________ _______ ________ _________ ____ ___________ ______
BP2-91. In a Rankine Rankine cycle, cy cle, saturated liquid water at 1 bar is compressed compressed isentropically to 150 bar. First by reheating reheating in a boiler boiler and then by superheating at constant pressure of 150 bar, bar, the water subst ance is brought brought to 750K. After adiabatic adiabatic reversible reversible expansion in a turbine turbine to 1 bar, it is then cooled in a condenser to a saturated liquid. How much work work is generated generated in i n the turbine? turbine? (Steam properties h, kJ/kg, s , kJ/kg-K: @ 150 bar&750 bar&750 K, h = 3240.5, 3240.5, s1 = 6.2549; @ 1 bar, hf=417.46, hfg=2258, sf=1.3026, sfg=6.0568) a. 769.9 b. 796.9 c .967.9 d.976.9 d. 976.9 BP1-91. A reheat reheat steam s team has 13850 13850 kPa throttle throttle pressure at the turbine turbine inlet and 2800 kPa reheat reheat pressure. The throttle o and reheat reheat t emperature of the steam st eam is 540 C, condenser pressure is 3.4 kPa, engine efficiency efficiency of high high pressure and low pressure is 75%. Find the cycle thermal efficiency. a. 34.46 34.46% % b. 35.56 c. 36.66 d. 37.76 BP2-99 In a Rankine Rankine cyc le, steam enters enters the t he turbine at 2.5 MPa and condenser of 50 kPa. What is the thermal efficienc efficiency y of the cycle in percent? (Steam properties properties h, kJ/kg, s, kJ/kg -K: @ 2.5 MPa; h g = 2803.1 2803.1 s g = 6.2575; @ 50 kPa, h f = 340.49, 340.49, hf g= 2305.4, 2305.4, sf = 1.091, s f g= 6.5029, vf =0.001.3 m3/kg) a. 25.55 b. 28.87 c. 30.12 d. 31.79 BP2-95. A supercritical steam Rankine cycle has turbine inlet conditions of 17.5 MPa and 530 oC expands in a turbine to 7 kPa. The turbine and pump polytropic efficiencies are 0.9 and 0.7, respectively. Pressure losses between pump and turbine inlet are 1.5 MPa. What should be the pump work in kJ/kg. a. 27.13 b. 29.87 c. 32.47 d. 33.25 Sol. Wp = vf(P4-P3)/n; vf(P4-P3)/n; vf = 1000 m3/kg BP2-97 BP 2-97 Steam St eam enters the superheater of a boiler boiler at a pressure of 25 bar and dryness drynes s of 0.98 and and leaves at the t he same o pressure at a temperature of 370 C. Calculate the heat energy energy supplied per kg of steam supplied in the superheater. superheater. (Steam properties: @ 25 bar &370 oC, h = 3171.8 3171.8 kJ/kg; @ 25 25 bar, h f = 962.11, h f g = 1841.0 kJ/kg) a. 405.51 b. 504.15 c. 154.15 d. 245.25. A BP 2-94. A back pressure steam turbine of 100 MW capacity serves serves as a prime mover mover in a cogeneration cogeneration sys tem. The The o o boiler admit s the return water wat er at a temperature of 66 C and produces the steam at 6.5 MPa and and 455 C. Steam then enters a back pressure turbine and expands to the pressure of the process, which is 0.52 MPa. Assuming a boiler efficiency efficiency of 80% and neglecting the effect effect of pumping pumping and the pressure pressure drops at various various location, what is the incrementa incrementall heat rate for electric ? The following following enthalpies have have been found: at turbine entrance = 3306.8 kJ/kg, exit = 2700.8 kJ/kg; k J/kg; boiler entrance entrance = 276.23 kJ/kg, exit = 3306.8 kJ/kg) a. 22,504.23 kJ/kW -hr b. 52,244.32 kJ/kW -hr c. 12,435.72kJ/kW-hr d. 32,234.82 kJ/kW -hr BP2-98. In an open open feedwater feedwater for for a steam st eam power power plant, saturated st eam at 7 bar is mixed with sub -cooled liquid at 7 bar and 25oC. Just enough enough steam is supplied supplied to ensure that the mixed steam leaving leaving the heater heater will be satur ated liquid at 7
bar when heater efficiency is 90%. Calculate the mass flow flow rate of s ub cooled liquid i f steam flow flow rate is 0.865 k g/s. o (Steam properties properties h, kJ/kg, @ 7 bar, bar, h g = 2763.5, h f = 697.22; @ 7 bar & 25 C, hf = 105.5) a. 2.725 b. 2.286 c. 3.356 d. 3.948 BP2-95. A steam plant operates operates with an initi al pressure pressure of 1.7 1.7 MPa and 370 oC temperature and exhaust t o a heatin heatin g sys tem at 0.17 MPa. The The condensate from from the heating heating s yst em is returned returned to the boiler at 65.5 oC and the heating system utilizes utiliz es from from its intended purpose 90% of the energy transferred transferred from from the steam it receiv receives. es. The turbine efficiency efficiency is 70%. If the boiler boiler efficiency efficiency is 80%, what is the cogeneration cogeneration efficiency efficiency of the syst em in percent? Neglect pump work. work. (Steam properties properties h, kJ/kg, kJ/k g, s, kJ/kg-K: kJ/kg -K: @ 1.7 MPa & 370 oC; h = 3787.1, s = 7.1081; @ 1.7 1.7 MPa, h f = 483.20, 483.20, hfg= 2216.0, s f = 1.4752, s f g= 5.7062; @ 65oC, h f =274.14) a. 69 b. 78 c. 91.24 d. 102.10 BP1-96. In a cogeneration cogeneration plant, steam enters the turbine turbine at 4 MPa and and 400 oC. One fourth of the steam is extracted from from the turbine turbine at 600kPa pressure for process process heating. The remaining steam continues to expand to 10 kPa. The extracted steam is then condensed and mi xed with feedwa feedwater ter at constant pressure and t he mixture is pumped t o the boiler pressure of 4 MP a. The The mass flow flow rate of the steam through through the boiler boiler is 30 30 kg/s . Disregarding Disregarding any pressur pressure e drops and heat losses in the piping, and assuming the turbine and pump to be isentropic, how much process heat is required required in kW? (Steam (Steam properties h, kJ/k g, s, kJ/kg-K: @ 4 MPa & 400oC, 400oC, h = 3213.6 3213.6 s = 6.7690; 6.7690; @ 600 kPa, h f = f g f f g 670.56, h = 2086.3, s = 1.9312, s = 4.8288) a. 1,026.90 b. 2,468.2 c. 3,578.5 d. 15,646.8 BP1-96. A 23.5 kg/s at 5 MPa and 400 400 oC is produced by a steam st eam generator. generator. The feedwater feedwater enters economizer economi zer at 145 o C and leaves at 205 oC. The steam leaves the boiler drum with a quality of 98%. The unit consumes 2.75 kg of coal per second sec ond as received received having having an heating value of 25,102 kJ/kg. kJ/ kg. What would be the overall overall effic efficiency iency of the unit in percent? percent ? (Steam properties properties h, kJ/kg, s, kJ/kg-K: kJ/kg -K: @ 5 MPa & 400 oC, h=3195.7; @ 0 MPa, h f = 1154.23, 1154.23, hf g= 1640.1; @ 205 oC , hf = 610.63) a. 65 b. 78 c . 88 d. 95 BP2-94. BP 2-94. A coal-fired coal -fired power plant pl ant has a turbine-generato r rated at 1000 MW gross. gross . The plant required about 9% of this power for its internal operations. It uses 9800 tons of of coal per day. The The coal has a heating value of 6,388.9 k Cal/kg, Cal/k g, and the steam generator generator efficienc efficienc y is 86%. What W hat is the net station efficiency efficiency of the plant plant in percent? percent? a. 30.12 b. 33.07 c. 36.74 d. 40.01 BP2-97. Steam enters t he turbine of a cogeneration cogeneration plant at 7 MPa and 500 oC. Steam at a flow rate of 7.6 kg/s is extracted from from the turbine turbine at 600 kP a pressure for process process heating. The remaining remaining steam continues to expand to 10 kPa. kP a. The recovered recovered condensates condens ates are pumped back to the boiler. The mass flow rate of steam that enters enters the t he turbine is 30 kg/s. Calculate the cogeneration cogeneration efficiency efficiency in percent. percent. (Ste am properties properties h, kJ/kg, s, kJ/kg-K: kJ/kg -K: @ 7 MPa & 500oC, 500oC, h = 3410.3 3410.3 s = 6.7975; 6.7975; @ 600 k Pa, h f = 670.56, hf g= 2086.3, s f = 1.9312, s f g= 4.8228; @ 10 kPa, h f = 191.83, hf g= 2392.8, 2392.8, sf = 0.6493, s f g= 7.5009) a. 50 b. 55 c. 60 d. 65 BP2-96. BP 2-96. A 60 60 MW turbine generator running at 3600 3600 rpm receives receives steam st eam at 4.0 MPa and 450 oC with back pressure of 10 kPa. Engine efficiency is 78% and the combined mechanical and electrical efficiency is 95%. What would be the exhaust enthalpy of the steam in kJ/kg. a. 2,400.12 kJ/kg b. 20,432.10 kJ/kg c. 28,124.20 kJ/kg d. 30,101.15 kJ/kg BP2-95. Steam enters a throttling calorimeter at a pressure of 1.03 MPa. The calorimeter downstream pressure and temperature are respect ively ively 0.100 MPa and 125 oC. What is i s the percentage moisture of the supply steam? (Steam properties properties h, kJ/kg, s, k J/kg-K: @1.03 MPa, hfg hfg = 2010.7, hg = 2779.25; @ 0.1 MP a & 125oC, 125oC, h=2726.6) a. 1.98 b. 2.62 c.3.15 d. 5.21 BP2-97. Steam expands adiabatically in a turbine from 2 MPa, 400 oC to 400 kPa, 250 oC. What is the effe effect ct iveness iveness of o the process process in percent ass uming an atmospheric atmospheric temperature temperature of 15 C. Neglect changes in kinetic and potential energy. (Steam properties h, k J/kg, s, kJ/kg-K: kJ/kg -K: @ 2.0 MPa and 400oC; 400oC; h = 3247.6 s = 7.1271; @ 400 kPa & 250oC, 250oC, h= 2964.2, s= 7.3789) a. 79.62 b. 84.52 c. 82.45 d. 74.57 BP2-93.. A drum c ontaining s team with BP2-93 with 2.5 m in diameter diameter is i s 7.5 m long. long. Of the total volume, volume, 1/3 contains saturated s team at 800 kPa and the other 2/3 contains saturated water. If this tank should explode, how much water would evaporate? Consider the process to be of constant enthalpy. (Steam proper properties ties h, kJ/kg, v, v, m3/kg m 3/kg @0.8 MPa, hf = 721.11, 721.11, hg = 2769.1, vf= vf= 0.0011148, vg=0.2404; @ 0.101325 MPa & 100oC, hf=419.04, hg= 2676.1, vf=0.0010435, vf=0.0010435, vg=2769.1) a. 2,123.76 kg b. 2,424.62 kg c. 2,651.24 kg d. 2,948.11 kg
BP2-92. A Batangas base industrial c ompany operates BP2-92. operates a steam power power plant with reheat reheat and regene regeneration. ration. The The s team enters a turbine turbine at 300 bar bar and 900 K and expands to 1 bar. bar. Steam leaves leaves the first stage at 30 bar an d part part of it entering a closed heater while t he rest reheated to 800K. B oth section of of the turbine have have adiabatic efficiency efficiency of 93%. A condensate pump exist s between the main condenser condenser and the heater. heater. Another A nother pump li es between between the heater heater and condensate outl et line from from the heater heater (condensed extracted st eam). Compute Compute for for the extracted fracti fraction on of the total mass flow to the heater. a. 0.234 b. 0.543 c. 0.765 d. 0.485
1. A furnace urn ace burns bur ns natural gas with the the volumet v olumetric ric analysis analy sis as follows:CH ows:CH 4 = 85% ; C 2H6 =12% ; C 3H8 = 3 3%The gas flow rate is o.37 m /sec and 25% 2 5% excess air is required for complete complete combustion. combustion. Air and fuel fuel enters the furnace at 25 C and 101.325 KPa. Determine Determine a. The actual air-fuel ratio b. The volumetric volumetric analysis analy sis of the the products pr oducts c. The orsat analysis d. The dew point temper temperature ature of the the products pr oducts 2. A steam steam generator gene rator bur ns fuel fuel with 20% excess air. The fuel uel oil o il may may be repr esented by C 14H30. The flue gases leave the preheater prehe ater at 310 KPa. Find the the minimum nimum stack stack temper temperatur aturee to avoid condensation. 3. A gas turbine power plant receives an unknown type of hydrocarbon fuel. The fuel is burned with air yielding the following Orsat analysis of the products of combustion.CO 2 = 10.5% 10.5% ; O2 = 5.3% 5.3% ; N2 = 84.2% . Determine the percent per cent excess air. 4. For a fuel oil with this ultimat ultimatee analysis: C = 83.7% ; H 2 = 12.7% ; O2 =1.2% ; N 2 = 1.7% ; S = 0.7% ; Assume Assume combust combustion ion air to to have a dry dr y bulb temperature temperature of 27 C and a wet bulb temper temperature ature of 21C with 30% excess air for complete complete combustion. combustion. Determine the total total combustion combustion gas volume per kg fuel fuel at 205C and 101 KPa. 5. A circular circular oil o il tank tank 10 1 0 m long and 1.5 m diameter diameter is used for for fuel fuel oil stora storage. ge. Calculate the number of days day s oil supply the tank can hold for for continuous operation oper ation at the the following conditions: ons: Steam flow - 1050 kg/hr Steam dr y and satura saturated ted at 1.4 MPa Feedwater temperature temperature - 110C Boiler effi efficiency ciency - 75% Fuel oil - 34 API 6. There Ther e are 20 kg of flue gases formed per pe r kg of fuel fuel burne bu rnedd in the combustion combustion of a fuel oil C 12H26. What is the excess air in percent? 7. A fuel has the following following volumetric analysis: CH 4 = 68% C 2H6 = 32% 32% Assume Assume complet completee combust combustion ion with with 15% excess ex cess air at 101.325 KPa, 21 C What is the partial pressure of the water vapor vap or in Kpa and the the dew point temperature of the the products pro ducts.. 8. A gravimet gra vimetric ric analysis a nalysis of a typical automotive automotive gasoline gives 86% C and 14% H 2. What What average ave rage chemi che mical cal formula in the for form m of C nHm, approximates appr oximates this fuel. 9. A gaseous fuel fuel that is derived der ived from from coal coa l has the following v olumetric olumetric analysis: analy sis: H 2, 47.9%; CH 4, 33.9%; C2H4,5.2%; CO, 6.1%; CO2 2.6% 2.6% ; N2, 3.7% 3.7% ; and O2, 0.6% . It is burn with with 110% theoretical theoretical air. Determine the volume flow rate of air required per unit volume of the gas when both are measured at the same P and T. the dew point temper temperature ature of the the combustion combustion products pro ducts,, if the the total total pressure pre ssure is 2 atmospher atmospheree 10. The ultim ultimate ate analysis analy sis of a fuel oil is 85% Carbon Car bon and 15% Hydr ogen. If this this fuel is burned burne d in an intern internal al combustion combustion engine and requires require s 15% excess air for complete complete combustion, combustion, determine a. the the combustion combustion equation b. the the actual air fuel fuel ratio c. the kg of CO 2 formed per kg of fuel d. the Orsat analysis of the products e. the the molecular weight and a nd gas constant constant of o f the he products pr oducts f. the the Specific heats Cp C p and Cv of the pr oducts
