TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
B AS IC A N D
chapter. I - 1 of 12
C ON CE PT S
D E F I N IT I O N S
hermodynamics is the branch of science which treats of various phenomena of energy, and especially of the laws of T hermodynamics transformations of heat into other forms, and vice versa. The science that is devoted to understanding energy in all its forms such as, mechanical, electrical, chemical, and how energy changes forms. Derived from the Greek words, therme, meaning heat and dynamis, meaning strength, particularly applied to motion. In engineering, the science of thermodynamics is conventionally divided into two parts: 1) Chemical Thermodynamics, Thermodynamics, which is devoted largely into reactions and solutions. 2) Thermodynamics concerned with the production and use of work and power Macroscopic and Microscopic Analysis Macroscopic thermodynamics is thermodynamics is the level on which we live in. It is concern on the overall effect of the individual molecular interaction. The measurements are large compared with the measurement of events on the molecular levels, such as distance in meter, time in second, etc. Microscopic thermodynamics thermodynamics look at every molecule and analyze collective molecular action by statistical methods. System, Boundary and Surrounding SYSTEM (thermodynamic system) system) is that portion of the universe, an atom or a galaxy, or some certain quantity of matter, which we specifically wish to study. It is a region enclosed by specified boundaries or by imaginary but definite mental boundaries.
BOUNDARY is an imaginary partition that separates the system from the surrounding environment. SURROUNDING is the region outside the boundary or anything not in the system. In many cases, an analysis is simplified if attention is focused on a particular volume in space into which, or from which, a substance flows. Such volume is a control volume. volume. A pump, a turbine, and an inflating or deflating balloon are examples of control volume. The surface that completely surrounds the control volume is called the control surface. surface. Types of System 1) Closed System is System is a system where matter does not cross the boundaries. -energy can pass through boundaries - examples are piston cylinder assembly, air in a balloon and mercury in a thermometer and pressure cooker 2) Open System System is a system where matter and energy pass across its boundaries - examples are pump, turbine, air conditioner, conditioner, hair blower, etc.
Flow Piston cylinder assembly (Closed System)
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
through a pipe (Open System)
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
3) Isolated System System is a system where neither mass nor energy passed through its boundaries. - example of a partially isolated system is a thermos
Property and State A pure A pure substance is substance is uniform in chemical composition. It may exist in more than one phase in which each phase would have the same composition. The condition when three phases, the solid phase, the liquid phase and the gaseous phase, gaseous phase, coexist is called triple point . PROPERTY is a characteristic quality of the entire system and depends not on how the system changes state but only on the final system state. - are quantities that may be measured or calculated and give meaningful information about the state of the substance but are independent of the path (or method) taken to achieve their values. Therefore properties are point functions.. functions
chapter. I - 2 of 12
Fundamental Units in SI
QUANTITY Base units Length Mass Time Electric current Thermodynamic temperature Amount of substance substance Luminous intensity Supplementary Supplementa ry unit Plane angle Solid angle
NAME
SYMBOL
Meter Kilogram Second Ampere
M Kg S A
Kelvin
K
Mole Candela
Mol Cd
Radians Steradians Steradians
Rad Sr
Common Macroscopic Properties Mass is the absolute quantity of matter in a substance. It is invariant with location: the mass of the body is the same anywhere in the universe. 1 Kgm = 2.2046 lbm 1 slug = 32.174 bm
Two Kinds of Properties Intensive Properties are Properties are properties that are independent of the mass (extent) of the substance - it is also independent of the size of the system; example are temperature and pressure Extensive Property are properties that depend on the size or extent of the system; examples are mass and volume. STATE – It completely described how the substance STATE – exists. Knowing the macroscopic properties, we can determine the state of a substance.
Volume is the amount of space occupied by the mass or matter. 1 m3 = 1000 liters = 35.3147 Ft3 1 gal = 3.7853 liters 3 1 ft = 7.481 gal 1 barrel = 42 gal 1 drum = 50 gal Formula of Volume for Common Solids: Rectangular parallelepiped V A BASE * H Cylinder
V R 2 H
Sphere
V
4 3
R 3
D 2 4 1 6
H
D 3
Fundamental and Derived Units FUNDAMENTAL UNITS are are units that are postulated Length - is the distance between to points in space Time - is the period between two events or during which something happens. DERIVED UNITS are UNITS are units formed from fundamental units. Pressure Pressure - is force per unit area Velocity - distance per unit time
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
Force is defined as the mass times the acceleration. Force is 1N = 2.2046 lb f 1kgf = 9.8066 N 1kgf = 2.2046 lb f otion: Newton’s Second Law of M otion:
“the acceleration of a body is directly proportional to the force acting on it and inversely proportional to its mass. a F
F m ma
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
F
d dt
chapter. I - 3 of 12
dv dm mv m v
dt
dt
but, from classical mechanics mass is invariable with velocity
dm dt
0
F m
dv dt
W V
mg o g cV
g o g c
Specific Gravity / Relative Density is the ratio of the density of a substance to the density of a standard substance. - for liquid the standard substance is water and for gas the standard substance is air at same pressure and temperature.
ma
S .G.
Density of Substance Density of Standard Substance
by introducing a gravitational constant, g c
ma
F
For Solid and Liquid : ratio of the weight of substance to the weight of equal volume of water.
g c
S .G.
W subs. W std . subs.
S .G. but
kg m m
S .G.
9.8066
std . subs.V std . subs.
subs. g o g cV subs. std . subs. g o g cV std . subs.
subs. std . subs.
S .G.
kg f
s N s N lb Ft slug slu g Ft 1 2 32.174 2m s lb f s lb f 2
subs.V subs.
V subs V std . subs.
m Ft ma 1kg m 1 s 2 1 slug 1 s 2 g c F 1 N 1lb f
g c 1
2
S .G.
subs. std . subs.
subs. Water at 4 deg. Celsius
subs. subs kg lb 1000 62.4 m 3 3 m ft Weight in air
Weight in air Weight in water
For Solids (Using Archimedes Principle) Weight is the force due to the gravitational pull of the earth. W
mg o g c
Density is is the mass per unit volume. It is a measure of the size of the molecules and how closely the molecules are spaced in a material.
m V
Specific Volume - volume per unit mass. V 1 v m
W F Specific Weight / Weight Density Density is the weight per unit volume of the material.
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
where: F F’
W BF F '
is the weight of object in air is the weight of object in water
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
subs
S .G.
Water
then the two blocks are said to be in thermal equilibrium and the their temperature are the same.
W V subs W Water V Water .
But, volume of the liquid displaced equals the volume of the object submerged.
V subs V Water S .G.
W
W Water
S .G.
W BF
F W F '
F F F '
Weight in air Weight in air Weight in water
For Ideal Gases (ratio of molecular weight of the gas to the molecular weight of air) P g gas R g T g S .G. air P a RaT a
= P a and T g = T a but, P g = _
Ra
_
R MW a
and R g
R MW g
_
S .G.
Ra R g
R MW a _
S .G.
R MW g
chapter. I - 4 of 12
MW g
Third Law of Thermodynamics The third law of thermodynamics allows the calculation of absolute entropy. The Nearest postulate of the third law is “The absolute entropy of a pure crystalline substance in complete internal equilibrium is zero at zero degrees absolute.” Since temperature is related to the kinetic energy of the fluid, it is evident that the motion of the molecules will increase with increasing temperature. At absolute zero there will be no motion, and the molecules will be completely still. Temperature Scale
K
°C
R
°F
Steam point (Boiling point)
373.15
100
671.67
212
Triple Point of water
273.16
0.01
491.69
32.02
Ice point (Freezing point)
273.15
0
491.67
32
Absolute zero
0
-273.15
0
-459.67
C°) Note:: ΔC = ΔK , ΔF = ΔR and 1ΔC = 1.8ΔF (ΔC = C°) Note
MW a
x FPx
S .G.
MW g
BPx FPx
y FPy BPy FPy
MW a
Pressure is the force exerted by a fluid per unit area. Temperature is the measure of hotness and coldness of Temperature is a body. It is a measure of the average linear kinetic energy of the molecules of the substance, that is, the total kinetic energy of all the molecules divided by the number of molecules. Temperature Scale 1) Absolute Temperature Scale (ex. Scale (ex. Kelvin & Rankine) 2) Arbitrary or Man-made Temperature Scale (ex. Scale (ex. Celsius & Fahrenheit) Zeroth Law of Thermodynamics The zeroth law of thermodynamics state that “when two bodies are in thermal equilibrium with a third body, they are in thermal equilibrium with each other and hence are at the same temperature” . Consider two blocks of material, say, iron; if these two blocks are brought together and there is no change in any observable property,
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
P
F A
P abs P atm P gage
P abs P atm P vacuum
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
Atmospheric pressure Atmospheric pressure is the pressure associated with the atmosphere due to the weight of air. Although this pressure varies according to location and weather patterns, an average value at sea level is 101.325 kPa.
chapter. I - 5 of 12
Determine (a) the flow rate in kg/s; (b) the time it takes to fill the tank. Solution: a)
Standard Atmospheric Pressure 1 atm = 101.325 101.325 kPa = 1.01325 Bar = 760 mmHg = 760 mmHg = 14.7 psi = 29.92 in. Hg Gauge pressure Gauge pressure is the amount by which pressure differs from atmospheric pressure. This is measured with a gauge that measures the pressure above (or below) atmospheric pressure. The gauge pressure below atmospheric is called vacuum vacuum.. Absolute pressure Although there is no limit to how high a pressure can be, there is a limit to how low it can be. This point of absolute minimum is the absolute zero pressure (no pressure at all). Absolute pressure is pressure measured above this zero point . Pressure Variation with Liquid Column For a substance of constant density (such as a liquid), the pressure at any vertical position due to the self-weight of the substance above the datum is dependent of the surface area and is given by the equation:
flow rate
m V S .G. Water V
m 1.21000
b)
V
kg L 1m 3 1 min 300 min 1000 L 60 s m 3
V
t
t
V
V
2.1 Two liquids liquids of different densities (ρ 1=1500 kg/m3, ρ2= 500 kg/m3) are poured together into a 100-L tank, filling it. If the resulting density of the mixture is 800 kg/m 3, find the respective amounts of liquids used. Also, find the weight of the mixture; local go=9.675m/s2. Solution :
m V V m V 1 V 2 0.01m3 m m
mm V m
0.01m
800 V 1
kg m
3
V 2 0.01 V 1
m1 m2
100 L
1V 1 2 0.01 V 1
V 1
3
kg m3
1V 1 2V 2 0.01m 3
1V 1 0.01 2 2V 1 0.01m
3
800
m3
3
3
2
1 2
0.01m 0.01m 3
1500 500
m1 1 V 1 1500
3
kg 500 3 m
kg
m2 2 V 2 500
kg 3
m kg m3
0.003 m 3
m3
0.007 m 3
0.003m
4.5 kg
0.007m
3.5 kg
3
3
mm m1 m2 4.5 3.5
8 kg
SAMPLE PROBLEMS
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
kg
0.01m 0.01m
V 2 0.01 V 1 0.01 0.003
1.1 A pump discharges into a 3 m per side cubical tank. The flow rate is 300 liters/min, and the fluid has a density 1.2 times that of water (density of water ρ=1000.0 kg/m3).
s
333m 3 1000 L t 90 min or 1.5 hr L m 3 300 min
800
-h
kg
time to fill the tank
P gage h
+h
6.0
m 8kg 9.675 2 m g s W m m o kg m g c 9.8066 2 s N
7.8926 N
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
fps 2)
1.3 The 1.3 The mass of a given airplane at sea level (g=32.10 is 10 tons. Find its mass in lb m, slugs and kg and its gravitational weight in lb f and and in N when it is travelling at a 50,000 ft. elevation. The acceleration of gravity (g) decreases by 3.33 × 10 -6 fps2 for each foot of elevation. Solution : a) Mass in lbm, slugs and kg lb f lb ft 32.174 2m 10tons 2000 tons s lb f Wg c m g o
32.10
ft
s 2
1kg m
F W
a g O
W
W
5 g O g O
m 80kg m 9.8066 2 s F 6 kg m m 1 2 s N
6W 6
W
mg O g C
4707.168 N
1.5 Make 1.5 Make a conversion formula from Fahrenheit scale to Celsius scale and vice versa. Solution : C 0C
m 20,046.106 lbm
9,092.854 kg m
m 20,046.106lbm
chapter. I - 6 of 12
2.2046lbm
slu g 623.05 3 slu g 32.174lb
F 32 F C F 32 100 C 0 C 212 32 F 100 180 5 9 and C F 32 F C 32 5 9
m 20,046.106lb
b)
1.6 At 1.6 At what temp is the Fahrenheit and Celsius scale has the same reading? Solution : (F = C = A)
Weight lbf and N
W
mg o g c
ft
623.053 slug 32.10 3.33 x10 6 50,000
slug ft 1 2 s lb f
s 2
W 19,896.263lb f
1kg f 9.8066 N W 19,896.263 lb f 2.2046lb f 1kg f W 88.503.444 N 1.4 1.4 During take-off in a space ship, an 80 kg astronaut is subjected to an acceleration equal to 5 times the pull of earth’s standard gravity. If the take -off is vertical, what force does he exert on the seat? Solution:
C 0C 100C 0C C 100
F 32 F 212 32 F
F 32 180
A
100
C 100
F 32 180
A 32 180
A 40 C or F 1.7 At 1.7 At what temperature will the Fahrenheit scale be 64° more that the Celsius scale? Solution : F = 64 + C 64 C 32 C 0 F 32 F C 100C 0C 212 32 F 100 180 C C 32 5
C 40 C
9
or
F 104 F
1.8 A 1.8 A water manometer is connected to the inlet manifold of an engine and records a height of 300 mm. Convert this to gage pressure in kilopascal and absolute pressure in psi if barometer reading is 13.95 psi. Solution : P gage h 1000
From Newton’s 3rd Law of Motion : Action and Reaction R
Fv 0
kg m 1kN 9.8066 2 0.3m 3 m s 1000 N
P gage 2.942 kPa
Wa g O
Fup Fdown F R W
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
14.7 psi 101.325kPa
P abs P atm P gage 13.95 psi 2.942kPa P abs 14.3768 psia
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
1.9 Compute 1.9 Compute for the value of h based on the figure.
chapter. I - 7 of 12
EXERCISES (01) A tank contains a mixture of 20 kg of nitrogen and 20 kg of carbon dioxide. The total tank volume is 20 m 3. Determine the density and specific volume of the mixture. (02) A spring scale is used used to measure force and to determine the mass of a sample of moon rocks on the moon’s surface. The springs were calibrated calibrate d for the earth’s gravitational acceleration of 9.8 m/s 2. The scale reads 4.5 kg, and the moon’s gravitational attraction is 1.8 m/s 2. Determine the samples mass. What would the reading be on a beam balance scale? (Ans. 24.5 kg)
Solution : P 1 h P 2 3
lb 1 ft 3.2 0.93 62.4 3 h 2 5.32in ft 12in 2.13 h 1.1615in 8.2lb
1.10 For the situation sketched above, the following information is known : density of water 1000 kg/m3 density of mercury 13590.0 kg/m3 pressure at point I 500 kPa local gravity 9.8 m/s2 Determine the pressure at point I I
(03) Someone proposes a new absolute temperature scale in in which the boiling and freezing points of water at atmospheric pressure are 500°X and 100°X, respectively. Develop a relation to convert this scale to degree Celsius. (04) A vertical column of water will be supported to what height by standard atmospheric pressure? (05) A diver descends 100 100 m to a sunken ship. A container is found with a pressure gage reading 100 kPa (gage). Atmospheric pressure is 100 kPa. What is the absolute pressure of the gas in the container? (Ans. 1180.66 kPaa) (06) Containers A, B and C contains contains three different liquids with specific gravities of 1.2, 1.6 and 2.0 respectively. If the liquids in containers A and B are mixed, the resulting specific gravity is 1.36. When liquids in containers B and C are mixed the resulting specific gravity is 1.8. Mixing liquids in containers A and C result to a specific gravity of 1.52. Determine the resulting specific gravity when the three liquids in the containers A, B and C are mixed together. (07) The readings t A & t B of two centigrade thermometer A & B
Solution :
agree at the ice point (0 C) and steam point (100 C) and are 2 related by a equation t A = l + mt B + nt B B between these two points, where l, m, n are constant. When both are immersed in
P II 0.4m water 0.5m Hg 2m water 500kPa g P II 0.4m water 0.5m Hg 2m water o 500kPa g c m 9.8 kg kg s 2 1kN 0.5m13590 P II 2.4m1000 m 3 m 3 1 kg m 1000 N s 2 N 500kP a
P II 456.929 kPa
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
a well stirred oil bath, thermometer A registers 51 C while B
registers 50 C. Determine the reading on the thermometer A
when B reads 25 C. (Ans.25.75°C)
(08) A beer barrel has a mass of 10 kg and a volume volume of 20 liters. Assuming the density of beer is 1000kg/m 3, determine
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
chapter. I - 8 of 12
the total mass and weight of the barrel when it is filled with beer. (Ans.294N) (09) A certain thermometer is calibrated using using ice and steam points as fixed points designating them as being temperature 0 C & 100 C respectively, then the thermodynamic function chosen to establish the scale is t = alnx + b ; instead of the line scale t=ax+b. (a) Determine the constant a & b and (b) Developed a relation to express t = f (x,x ,x ). i s )
(10) If the total length of the tube containing mercury is 1.5m, what should be the value of height x so that the difference in pressure between points 1 and 2 is 78.743kPag? Assume the following specific gravity: for water=1.0, mercury=13.59 and oil = 0.80. (Ans. 0.5 m)
(13) A pressure cooker cooker operates by cooking cooking food at a higher pressure and temperature that is possible at atmospheric conditions. Steam is contained in the sealed pot, with a small vent hole in the middle of the cover, allowing steam to escape. The pressure is regulated by covering the vent hole with a small weight, which is displaced slightly by th e escaping steam. Atmospheric pressure is 100 kPa, the vent hole area is 7 mm 2, and the pressure inside should be 250 kPa. What is the mass of the weight? (Ans. 0.107kg) (14) Steam is held in two compartments compartments (A and B) separated separated 3 by a membrane. The total volume is 777 ft , and the volume of compartment B is 280 ft3. The specific volume of the steam in B is 9.5 ft3/lbm. The membrane breaks, and the resulting specific volume is 12.75 ft 3/min. Determine the original specific volume in compartment A. (15) A tank has a vacuum gage attached to it indicating 25 in Hg (vacuum) where atmospheric pressure is 14.5 psia. Determine the tank. (Ans. 2.22 psia)
(11) Find the area of the piston on which the the 45 kN force act. (16) A hiker is carrying a barometer that measures 29.92inHg 29.92inHg absolute at the base of the mountain. The barometer reads 25.5inHg absolute at the top of the mountain. mountain. The average air air density is 0.076 lb m/ft3, the gravitational acceleration remains constant at 32.174 ft /s 2. What is the mountain’s height? (Ans. 4114.6 ft)
(12) The vertical vertical frictionless piston-cylinder shown below contains a gas at an unknown pressure. The piston has a mass of 10 kg and a cross-sectional area of 75cm 2. The spring exerts a downward force of 100 N on the piston, and atmospheric pressure is 100 kPa. Determine the pressure of the gas. (126.4 kPa)
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
(17) An inhabitant of another planet weighs 50 lb on a spring spring type of scale in the planet atmosphere, where the local gravity acceleration is g = 6.0 fps 2. This inhabitant appears in St. Michael, Alaska, where the local gravity acceleration is g=32.22 fps2. For this outer-space being, determine (a) his mass in lb in slugs on his native planet, (b) his mass in lb and slugs on earth (c) his weight as indicated by a spring type scale on earth. (Ans. a. 268lb, b. 8.33 slugs, c. 268.4 lb)
(18) A Fahrenheit and a centigrade thermometer are both immersed in a fluid. The Fahrenheit numerical reading is twice
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
that of the centigrade reading. What is the temperature of the fluid in Rankine and Kelvin scale? (Ans. 433)
(19) A 3 kg plastic plastic tank has a volume volume of 0.2m3 is filled with liquid water. Assuming the density of water is 1000kg/m 3. Determine the weight of the combined system. (20) What is the net force acting acting on the car cruising at constant velocity of 70 km/hr (a) on a level road and (b) on an uphill road? (21) Determine the mass and weight of air contained contained in a room whose dimensions are 6m x 6m x 8m. Assume the density of air is 1.16kg/m 3. (Ans. 334.1 kg, 3277N) (22) A manometer containing containing water (density (density = 62.1 lb/ft3) and mercury (specific gravity = 13.55) connects two pressure regions A and B as shown in the figure. The local gravity acceleration is g = 32 fps2. If the pressure at point B is 50 psig, find the pressure in A.
chapter. I - 9 of 12
man would experience in an aircraft whose acceleration is 6 g’s. (26) Consider a 70 kg woman who has a total foot imprint area of 400cm2. She wishes to walk in the snow, but the snow cannot withstand pressure greater than 0.5 kPa. Determine the minimum size of the snow shoes needed (imprint area per shoe) to enable her to walk on the snow without sinking. (27) The gage pressure in a liquid at a depth depth of 3m is read to be 28 kPa. Determine the gage pressure in the same liquid at depth of 12m. (28) The absolute temperature in water at a depth of 5m is read to be 145 kPa. Determine (a) the local atmospheric pressure, and (b) the absolute pressure at a depth of 5m in a liquid whose specific gravity is 0.85 at the same location. (29) A vacuum gage connected connected to a tank reads 30 kPa at a location where the barometric reading is 755 mmHg. Determine the absolute pressure in the tank. Take ρHg=13,590kg/m3. (Ans. 70.6 kPa) (30) A pressure gage connected connected to a tank reads 50 psi at a location where the barometric reading is 29.1 inHg. Determine the absolute pressure in the tank. Take ρHg=848.4 lb/ft3. (Ans. 64.29 psi) (31) The barometer of a mountain hiker reads 930 mbars at the beginning of a hiking trip and 780 mbars at the end. Neglecting the effect of altitude on the local gravitational acceleration, determine the vertical distance climbed. Assume an average air density of 1.20 kg/m3. (Ans. 1274m)
(23) At 24° latitude, the gravitational acceleration acceleration as a function of elevation z above sea level is given by g=a-bz, where a=9.807 m/s2 and b=3.32x10 -6 s-2. Determine the height above sea where the weight of an object will decrease by 1 percent. (Ans. 29,539m) (24) A 150 lbm astronaut took his bathroom scale (a spring scale) and a beam scale (compares masses) to the moon where the local gravity is g=5.48 ft/s 2. Determine how much he will weigh (a) on the spring scale and (b) on the beam scale. (Ans. 25.5 lb, 150 lb) (25) The acceleration acceleration of high-speed high-speed aircraft is is sometimes expressed in g’s (in multiples multi ples of the standard acceleration of gravity). Determine the net upward force, in N that a 90 kg
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
(32) Determine the pressure pressure exerted on a diver at 30m below below the free surface of the sea. Assume a barometric pressure of 101 kPa and a specific gravity of 1.03 for seawater. (Ans. 404.0 KPa) (33) Determine the force necessary necessary to accelerate a mass of of 20 2 lbm at a rate of 60 ft/s vertically upward. (Ans.53.3 lb )f (34) The weight of a10 lb mass i s measured at a location where g=32.1 ft/s2 on a spring scale originally calibrated in a region where g=32.3 ft/s2. What will be the reading? (35) A gas is contained in a vertical, frictionless frictionless piston cylinder device. The piston has a mass of 4 kg and a cross sectional area of 35 cm 2. A compresses spring above the piston exerts a
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
force of 60 N on the piston. If the atmospheric pressure is 95 kPa, determine the pressure inside the cylinder.
chapter. I - 10 of 12
(41) A 20 ft3 tank of air separated by a membrane into section A with an initial specific volume of 0.80ft 3/lbm and section B with a mass of 12.0 lb m. The membrane is broken, and the resulting density is 1.350lb m/ft3. Find the initial specific volume in section B. in ft3/lbm. (Ans. 0.667)
(42) A horizontal 2m diameter gate is located in the bottom of a water tank. Determine the force required to just open the gate.
(36) A cubic meter of water at room temperature has a weight of 9800 N at a location where g=9.8m/s 2. What is its specific weight and its density at a location where g=9.77m/s2? (37) The acceleration of gravity is given as a function of g=9.81elevation above sea level by the relation -6 3.32x10 h, with h measured in meters. What is the weight of an airplane at 10km elevation when its weight at sea level is 40 kN? (Ans. 39.86kN) (38) The force of attraction between two masses m1 and m2, having dimensions that are small compared with their separation distance R, is given by Newton’s third law, F=Gm1m2 /R /R2, where G=6.67259x10-11 N-m2 /kg 2. What is the total gravitational force that the sun (1.97x10 30 kg) and the earth (5.95x1024 kg) exert on the moon (7.37x10 22 kg) at an instant when the earth, moon, and sun form a 90° angle? The earth-moon and sun-moon distances are 380x10 3 km and) 150x106 km, respectively (39) A bell jar 250mm in diameter sits on a plate and is evacuated until a vacuum of 700mmHg exits. The local barometer reads 760mmHg. Find the absolute pressure inside the jar, and determine the force required to lift the jar off the plate. Neglect the weight of the bell jar. (Ans. 8005 Pa, 4584 N) (40) Assume the acceleration of gravity on a celestial body to be given as a function of altitude by the expression g=4-1.6x10 – 6 h m/s2, where h is in meters above the surface of the planet. A space probe weighed 100 kN on the earth sea level. Determine (a) the mass of the probe. (b) Its weight on the surface of the planet (c) Its weight at an elevation of 200 km above the surface of the planet. (Ans. 10197.2141 kg, 40.79 kN, 37.53 kN)
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
5m
F
Hinge
(43) A vertical storage tank initially contains water (ρ=1000kg/m3) at a depth of 4m. Immiscible oil with a specific gravity of 0.88 is added until the total liquid height is 10m. If the barometer pressure is 97.2kPa and g=9.80m/s2, determine the absolute pressure at the bottom of the water, in kPa and bars. (Ans. 188.1, 1.88) (44) The gage pressure of a gas inside a tank is 25kPa. Determine the vertical height, in meters, of liquid within a manometer attached to the system if the fluid at room temperature is (a) water, (b) mercury (ρ=13,600kg/m 3), and (c) an oil with a specific gravity of 0.88 and g=9.75 m/s 2. (45) A pilot notices that the barometer pressure outside his aircraft is 800 mbars. The airport below the plane reports a barometric pressure of 1020 mbar. If the air density averages 1.15 kg/m3 and the local gravity is 9.70 m/s 2, determine the height of the aircraft above the ground, in meters. (Ans. 128, 188) (46) A submarine is cruising at a depth of 280 m in seawater with a specific gravity of 1.03. If the inside of the submarine is pressurized to standard atmospheric, determine the pressure difference across the hull in (a) kPa, (b) bars. The average local gravity is 9.70m/s2. (2700, 28) (47) If the atmosphere is assumed to be isothermal at 60°F and follows the relationship Pv=RT (an ideal gas), compute the pressure, in psia, and density, in lb m/ft3, at (a) 5000ft and (b) 2000 ft above sea level. The pressure and density at sea level are taken to be 14.7psia and 0.077lb m/ft3, respectively.
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
(48) A constant volume gas thermometer is brought into contact with a system of unknown temperature T and then into contact with the triple state of water. The mercury column attached to the thermometer has readings of 14.6 and -2.6 in, respectively. The barometer pressure is 29.80 in Hg, and the specific gravity of mercury is 13.6. Find the value of the unknown temperature in degrees Rankine. (49) The average atmospheric pressure on earth is approximated as a function of altitude by the relation
P atm 101.325 1 0.02256z
5.256
where Patm is the atmospheric pressure in kPa and z is the altitude in km with z=0 at sea level. Determine the approximate atmospheric pressure at Atlanta ( z = 306m ). At what height above a bove the sea level will the barometer read 14 psia?
chapter. I - 11 of 12
where T atm atm is the temperature of the atmosphere in Kelvin and z is the altitude in kilometer with z = 0 at at sea level. Determine the average temperature of the atmosphere outside an airplane that is cruising at an altitude of 11,000 m. (52) Two liquid streams are pouring in a container, 8 in. diameter and 15in. high. The mass flow rate of stream A is 1.2 lb/sec and the volume flow rate of B is 0.035 ft 3/s. If the specific gravities of A and B are 1.1 and 0.9, respectively, in how many seconds will the container be filled? What is the gage and absolute pressure at the bottom of the filled tank in psia. (Ans. 8.31s, 15.22 psia) (53) Assume the acceleration of gravity on a celestial body to be given as a function of altitude by the expression g=4-1.6x10 – 6 h m/s2 , where h is in meters above the surface of the planet. A space probe weighed 100 kN on the earth sea level. Determine (a) the mass of the probe. (b) Its weight on the surface of the planet (c) Its weight at an elevation of 200 km above the surface of the planet. planet . (Ans. 10197.2141 kg, 40.79 kN, 37.53 kN (54) A bell jar 250mm in diameter sits on a plate and is evacuated until a vacuum of 700mmHg exists. The local barometer reads 760mmHg. Find the absolute pressure inside the jar, and determine the force required to lift the jar off the plate. Neglect the weight of the bell jar . jar . (Ans. 8005 Pa, 4584 N)
(50) A pressure cooker cooks a lot faster than an ordinary pan by maintaining a higher pressure and temperature inside. The lid of of a pressure cooker is well sealed, and steam can escape only through an opening in the middle of the lid. A separate piece of certain mass, the petcock, sits on top of this opening and prevents steam from escaping until the pressure force overcomes the weight of the petcock. The periodic escape of the steam in this manner prevents any potentially dangerous pressure buildup and keeps the pressure inside at a constant value. Determine the height (H) and diameter (D) of the petcock of a pressure cooker whose operating pressure is 105 kPa gage and has an opening cross-sectional area of 4.5 mm 2 (steam opening for pressure relief). Assume an atmospheric pressure of 101 kPa and the density of the metal used is 4625 kg/m 3. (51) The average temperature of the atmosphere in the world is approximated as a function of altitude by the relation
T atm 288.15 6.5 z
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
(55) The resistance-temperature relationship for a thermistor can be described by an equation of the form R=Ke /t where R is the resistance at temperature t , with K, and being constant. Test results from calibration are: Resistance in k Ω Trials Temperature in °C 1 3
210 90
27 39
Approximate (a) the temperature when the resistance is 190 Ω. (b) the resistance of the thermistor at 40°C . (Ans. a. 28.02°C and b. 85.81) (56) A small experimental rocket which has a mass of 70 kg is accelerated at a rate of 6.0 m/s 2. What total force is required, in Newton, is (a) the rocket is moving horizontally and without friction and (b) the rocket is moving vertically upward and without friction at a location where local gravity is 9.45 m/s 2. ( Ans. Ans. 420, 1082 ) (57) A 7 lbm piece of steel is subjected to a vertical force of 8 lbf . The local gravity is 31.1 ft/s2, and frictional effects are
TH E RM ODYN AM I CS-I : Basic Basic Conce Concep pts and and Definition Definitionss
neglected. Determine the acceleration of the mass if the external vertical force is (a) downward, (b) upward in ft/s 2. ( Ans. Ans. 67.9, 5.65 ) 9-m3 tank
(58) An of nitrogen is separated by a membrane into two sections. sections. Section A has an initial initial density of 1.667 3 kg/m and section B has a mass of 6 kg. After the membrane is broken, the density is found to be 1.778kg/m 3. Find the initial density of the gas in section B in kg/m 3. ( Ans. Ans. 0.667 ) (59) A vertical piston-cylinder device has a piston diameter of 11 cm and piston mass of 40 kg. the atmospheric pressure is 0.10Mpa and the local gravity is 9.79 m/s 2. Determine the absolute pressure of the gas within the device. (60) A vertical storage tank initially contains water (density = 1000kg/m3) at a depth of 4 m. immiscible oil with a specific gravity of 0.88 is added until the total height is 10 m. If the barometric pressure is 97.2 kPa and local gravity is 9.80 m/s2, determine the absolute pressure at the bottom of the water, in kPa and bars. ( Ans. Ans. 188.1, 1.88 ) (61) Convert a chromel-alumel thermocouple measurement of 3.100 millivolts (mV) to degress Celsius. For a chromelalumel type K thermocouple, 3.100 mV is between the
School of Mech Mecha anical nical E nginee ngineeri ng MI T - Schoo
chapter. I - 12 of 12
entries of 2.667 (at 150°F) and 3.819 (at 200°F). Assume a linear relation between the two. (62) Determine the pressure at point A for the inclined manometer shown in the figure below.
Open to atmosphere
Air
A Reservoir
5"
B Mercury (SG=13.59)
30°
(63) Two gaseous streams enter a combining tube and leave as a single mixture. These data apply at the entrance sections: For one gas, A1 = 70 in 2, v1 = 500 fps, v 1 = 10 ft3/lb; for the other gas, A2 = 60 in2, ρ 2 = 0.120 lb/ft 3 and a mass flow rate of 60,000 pounds per hour. At the exit, v3 = 350 fps, v 3 = 7 ft 3/lb. Find (a) the velocity at section 2 (b) the flow rate, area at the exit section.
