QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
HEAT & THERMODYNAMICS PROBLEMS ASKED IN JEE & REE
Q 1.
State whet her True of False : (w (with reason) [ JEE ' 87, 2 + 2 ] (a) (a) At a given given tempe temperat rature ure,, the specif specific ic heat heat of a gas gas at const constant ant press pressure ure is always always greater than its specific heat at constant volumes . (b) The The roo roott mea mean n squ squar aree (rm (rms) s) spee speed d of of oxy oxyge gen n mol molec ecul ules es (O2) at a certain temperature T (degree (degree absolute) absolute) is V . If temperature is doubled and and oxygen oxygen gas dissociates into oxygen atoms, the rms speed is unchanged .
Q 2.
An ideal ideal gas has a spec specific ific heat heat at at cons constan tantt pressu pressure re C p =
5R 2
. The gas is kept in a closed
vessel of volume 0.0083 m 3 at a temperature of 300 ºK & a pressure pressure of 1.6 x 10 6 N/m 2 . An amount of 2.49 x 10 4 Joules of heat energy is supplied to the gas . Calculate the final t em per a t ur e & pr es sur e of t he gas . [ J EE ' 87, 7 ] Q 3.
A containe containerr is divided divided into two two equal equal portions portions . One portio portion n contains contains an ideal ideal gas at pressure P and temperature temperat ure T, T, while the other por tion has a perfect vaccum . If a hole is opened between the two portions, find the change in energy and change in temperature of t h e gas . [ R EE ' 8 7, 3 ]
Q 4.
2 M3 volume of gas at a pressure of 4 x 10 5 Nm−2 is compressed compressed adiabatically so that that the 3 volume becomes 0.5 M . Find the new pressure that would result, if the compression was isothermal . Calculate work done in each process . [ γ = = 1. 4 ] [ R EE ' 8 7, 7 ]
Q 5.
5 Two mol moles es of heli helium um gas γ = are initially at temperature 27º C and occupy a volume 3
of 20 litres . The gas is first expanded at constant pressure unitl the volume is doubled . Then it undergoes an adiabtic change until the temperature returns to its initial value . (i) ske sketch tch the the proc rocess on a p-V dia diagram ram . (ii) what what are are fin final al volu volume me and and pre press ssur uree of of the the gas gas ? (iii) w ha t i s t he w or k don e b y t he gas ? [ J EE ' 88, 6 ] Q 6.
State whet her True or False : (give reasons) [ J EE ' 88, 2 ] 2 spheres of the same material have radii 1 m & 4 m and temperature 4000º K & 2000º K respectively . The energy energy radiated per second by the first sphere is greater than that by the second .
Q 7. 7.
In a cert certain ain regi region on of of space space there there are are only only 5 molec molecule uless per per cm 3 on an average . The temperature there is 3º K . What is the average pressure of this very dilute gas ? [ REE '88, 5 ]
Q 8.
A 50 gm lead bullet, specific heat 0.02 is i nitially at 30º C . It is fired vertically upwards with a speed of 840 m/sec & on returning to the starting level strikes a cake of ice at 0º C. How much ice is melted . Assume that all energy is spent in melting only . [ l at e nt he at of i c e = 80 c al / g m ] [ R EE ' 8 8, 5 ]
Q 9.
hydrogen hydrogen atom in its ground ground state state is excited excited by by means means of a monochr monochromat omatic ic radiatio radiation n of wavelength 970.6 Aº . How many different wavelengths are possible in the resulting emission spectru m ? Find the longest wavelength amongst these . [ REE '89, 7 ]
QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
Q 10. An ideal ideal monoatomi monoatomicc gas is confined confined in a cylinder by a spring loaded piston of cross-section open atmosphere 8 x 10−3 m2 . Initially the gas is at 300 K and occupies t r r d o a volume of 2.4 x 10 −3 m3 and the spring is in its e i t p ← i g p a e r u releaxed (unstretched, uncompressed) state as in h s figure . The gas is heated by a small electric electri c heater until the piston moves out slowly by 0.1 cm . Calculte the final temperature of the gas & the heat supplied (in joules) by the heater . The force constant of spring is 8000 N/m, atmospheric pressure is 1.0 x 10 5 N/m 2 . The cylinder & the piston are thermally insulated . The pistion is massless & there is no friction between the piston & the cylinder . Neglect heat loss through the lead wires of the heater. The heat capacity of the heater coil i s negligible . Assume spring to be massless. [ JEE '89, 8 ] Q 11. Two perfec perfectt gases gases at absolute absolute temperatures temperatures T 1 & T2 are mixed . There Ther e is no loss of energy. en ergy. Find the temperature of the mixture if the masses of the molecules are m 1 & m2 and the number of molecules in the gases are n 1 & n2 re respecti vely . [ R EE ' 8 9, 5 ] Q 12. Hydrogen atom in its ground state is excited by means of a monochromatic monochromatic radiation radiation of wavelength 970.6 Aº . How many different wavelengths are possible in the resulting emis emissi sion on spec spectr trum um ? Find Find the the lon longe gest st wave wavele leng ngth th amon amongs gstt the these se . [ REE REE '89, '89, 3 ] Q 13. An ideal gas gas having initial pressure pressure P, P, volume V and temperature temperature T is allowed allowed to expand expand adiabatically until its volume becomes 5.66 V while its temperature falls to (i) (i) (ii) (ii)
T 2
.
How How man many y deg degre rees es of free freedo dom m do do the the gas gas mol molec ecul ules es have have ? Obtain Obtain the work work done done by by the the gas gas durin during g the the expan expansio sion n as a funct function ion of the the init initial ial pressur e p and volume V . [ J EE ' 90, 7 ]
Q 14. 3 moles moles of an an ideal ideal gas gas at 300º 300º K are isothermally expanded to five times its volume and heated at this constant volume so that the pressure is raised to its initial value before expansion . In the whole process 83.14 kJ heat is required . Calcul ate the ratio gas .
[ l n 5 = 1 .61 ]
Cp Cv
of the
[ R EE ' 9 0, 5 ]
Q 15. A piston divides divides a closed gas cylinder into two parts . Initially the piston piston is kept kept pressed such that one part has a pressure P & volume 5 V and the other other part has pressure 8 P & volume V . The piston is now left free . Find the new pressures & volumes for the adiabtic and and iso isoth ther erma mall pro proce cess sses es . [ for thi thiss gas gas γ = = 1.5 ] [ R EE ' 9 0, 7 ] 7R Q 16. 3 moles moles of an ideal ideal gas gas C p = at pressure P A & temperature TA is isothermally expanded 2
to twice its initial volume . It is then compressed at constant pressure to its ori ginal volume. Finally the gas is compressed at constant volume to its original pressure P A . (a ) Sketch P−V & P−T diagrams for complete process . (b) (b) Calcu Calculat latee the the net net work work done done by by the gas gas and and net net heat heat sup suppli plied ed to to the the gas gas durin during g the c o m p l e t e p r o ce s s . [ J EE ' 91, 8 ] Q 17. 0.014 0.014 kg of of nitrogen nitrogen is is enclose enclosed d in a vessel vessel at a temperatu temperature re of 27º 27º C . How much heat has to be transfered t o the gas to double the r.m.s. velocity of its mol ecules . [ REE '91, 7 ]
QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
Q 18. 10−4 kg oxygen is contained in a non-conducting cylinderical cylinderical vessel of cross sectional − 5 2 − 3 3 area 29.15 x 10 m & volume 10 m . It is closed by a frictionless non-conducting pistion which is free to move in a vertical vertical direction . If the piston is slightly depressed and then released, show that the piston will execute simple harmonic motion . Find its frequency . Ignore atmospheric pressure & take
Cp Cv
= 1.4 for oxygen . [ REE '91, 7 ]
Q 19. A solid copper sphere (density d & specific heat C) of of radius radius r at at an an initial initial temperature 200 K is suspended inside a chamber whose walls are at almost 0 K . The time required for th the t em emperature of th the sphere to drop to 100 K is :______ . [ JE JEE '9 '91, 2 ] Q 20. A piece piece of metal floats floats on mercury . The co-efficients co-efficients of volume volume expansion expansion of the metal and mercury are Y1 & Y2 respectively . If the temperatures of both mercury and the met al are increased by an amount T, the fraction of the volume of the metal submerged in mer cur y chan ges by t h e f act or __ ___ _ . [ J EE ' 91, 2 ] Q 21. A point source source of heat of power P is placed at the centre of a spherical shell of mean radius R . The material of the shell has thermal conductivity K . If the temperature difference between the outer & inner surface of the shell is not to exceed T, T, the thickness of the shell shou l d no t be l e ss t he n ___ ___ . [ J EE ' 91, 2 ] Q 22. Two moles moles of helium gas gas undergo undergo a cyclic process as shown shown in figure . Assuming the gas to be id eal , calculate : (a ) the the ne net cha chan nge in the the hea heat ene energ rgy y. (b) t he n et w or k do ne . (c ) the the ne net ch chang ange in in in intern ternal al energ nergy y.
m t -
P a
A -----
2
B
→ m t - - - - - a D 1 -
-
30 0 K
-C -
40 0 K
T
[ JEE '92, 8 ] Q 23. How much energy is absorbed by 10 kg kg mole of an ideal gas if it expands expands from an initial pressure of 8 atmosphere to 4 atmosphere at a constant temperature of 27º C ? [ REE '92, 5 ] Q 24. A cylin cylindric drical al block block of leng length th 0.4 0.4 m and area of cross-section 0.04 m 2 is placed co-axially on a thin metal disc of mass 0.4 kg & of the same cross-section . The upper face of the cylinder is mainitained at a constant temperature of 400 K & the initial temperature of the disc is 300 K . If the thermal conductivity conductivity of t he material of cylinder is 10 Watt/m Watt/m−K & the specific heat of the material of the disc is 600 J/kg −K , how long will it take for the temperature of the disc to increase to 350 K ? Assume , for purposes of calculation , the thermal conductivit y of the disc to be very high and the system to be thermally insulat ed exc ept f or t he u ppe r f ac e o f t he cy l i nd er . [ J EE ' 92, 6 ] Q 25. 25. A cont contain ainer er of of volum volumee 1 m3 is divided into equal parts by a partition . One part has an ideal gas at 300 K and the other part is vacuum . The whole system is thermally isolated from the surroundings . When the partition is removed the gas expands to occupy the who l e v ol um e . I t s t em per at ur e wi l l no w b e __ ___ _ . [ J EE ' 93, 1 ] Q 26. One mole mole of mono-ato mono-atomic mic ideal ideal gas is taken taken throug through h the cycle cycle shown in the figure . A → B Ad iabat i c expansion B → C Cooling at co constant vo volume C → D Adiabatic compression D → A H eat i ng at co nst a nt vo l um e .
P
→
A
D
B
→
C
V
QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
The pressure & temper ature at A, B, etc are denoted by P A, TA, PB, TB etc. respectively . Given that TA = 1000 K , PB = (i) (ii) (iii)
2 3
PA & PC =
1 3
PA , calculate the following quantities :
The The work done one by th the gas in the the pro process A → B The The heat heat lost lost by the the gas gas in the the proc proces esss B → C The temperature TD .
[ JE E ' 93, 4 + 4 + 2 ]
Q 27. State whet her True or False : (g ( gi ve r eason ) [ R EE ' 9 3, 2 ] If an ideal gas expands adiabatically, adiabatical ly, it does positive work and its internal energy decreases . Q 28. 28. In an isoba isobaric ric proce process ss , the change in internal energy is dU = n C p dT . Q 29. One mole of a mono-atomic mono-atomic gas is mixed with 3 moles of of a diatomic gas . The The molar spec i f i c he at of t he m i xt ur e at co nst a nt vo l um e i s ___ ___ . [ RE REE '9 '93, 1 ] Q 30. 30. In the figure figure are shown shown three isotherma isothermals ls at temperatu temperatures res T1 = 4000º K , T2 = 2000º K . When 1 gm mole of an ideal monoatomic gas is taken through the paths A → B , B → C , C → D & D → A , find the change change in internal energy U , the work done by the gas W & the heat absorbed by the gas gas Q in each path . Also find these these quantities for the complete cycle ABCDA. Given Given VA = 1 m3 and VB = 2 m3 .
A
P
→
B
↓
→ ↑ D
←
VA
C VB
→
T1 T2
T3
V
[ REE '93, 6 ] Q 31. The kinetic kinetic energy energy,, due to translational translational motion, motion, of most most of the molecules of an ideal ideal gas at a bsol ut e t em per a t ur e T i s __ __ __ . [ R EE ' 9 4, 1 ] Q 32. 32. A vesse vessell of volu volume me 2 x 10−2 m3 contains a mixture of hydrogen hydrogen and helium at at 47º C 5 2 − 2 temperature and 4.15 x 10 N/m pressure . The mass of the mi xture is 10 kg . Calculate t he ma sses of hyd r oge n an d h el i u m i n t he g i ven m i xt u r e . [ R EE ' 9 4, 4 ] Q 33. There are are two vessels . Each of them contains one mole of a mono-atomic ideal gas . Initial volume vol ume of the gas in each vessel is 8.3 x 10 −3 m3 at 27º C . Equal amount of heat is supplied to each vessel . In one of the vessel s, the volume of the gas is doubled wi thout change in its internal energy, whereas the volume of the gas is held constant in the second vessel . The vessels are now connected to allow free mixing of the gas . Find the final t em per a t ur e and pr e ssur e of t he com bi n ed g as s yst e m . [ R EE ' 9 4, 6 ] Q 34. An ideal gas with pressure P, P, volume V & temperature T is expanded expanded isothermally to a volume 2 V and a final pressure P i . If the same gas is expanded adiabatical ly to a volume 2 V, the final pressure is P a . The ratio of the specific specific heats for the gas is 1.67 1.67 . The ratio Pa Pi
is is ______ .
[ J EE ' 94, 2 ]
Q 35. An ideal gas is taken through through a cyclic cyclic thermodynamic thermodynamic process process through through four steps . The amounts of heat involved in these steps are Q 1 = 5960 J, Q 2 = − 5585 J, Q 3 = − 2980 J and Q4 = 3645 J respectively . The corresponding works involved are W 1 = 2200 J , W2 = − 825 J , W3 = − 1100 J and W 4 respectively . (i) Find the value of W4 . (ii) W hat i s t h e ef f i ci en cy of t h e cy cl e ? [ JEE '94, 6 ] Q 36. A closed closed containe containerr of volume volume 0.02 0.02 m 3 contains a mixture of neon and argon gases, at a temperature of 27º C & pressure of 1 x 10 5 Nm−2 . The total mass of the mixture is 28 gm.
QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
If the gram molecular weights of neon and argon are 20 & 40 respectively , find the masses of the individual gases in the containe r, assuming them to be ideal . [ Uni ver sa l gas c onst ant R = 8. 314 J / mo l K ] [ J EE ' 94, 6 ] Q 37. A gaseous gaseous mixture enclosed enclosed in a vessel vessel of volume volume V consists of one gram mole of a gas A with τ =
Cp Cv
=
5 3
& another gas B with τ =
7 5
at a certain certain temperature temperature T . The gram
molecular weights of the gases A & B are 4 & 32 respectively . The gases A & B do not react with each other and are assumed to be be ideal ideal . The The gaseous gaseous mixture follows the 19/13 equation ; PV = cont. in adiabatic processes . (A) Find Find the the numbe numberr of gram gram moles moles of the the gas B in the gaseo gaseous us mixtur mixturee . (B) Comput Computee the the speed speed of sou sound nd in the the gaseou gaseouss mixt mixture ure at T = 300 K . ( C) I f T is raised by 1 K from 300 K, find the percentage change in the speed of sound in the gaseous mixture . (D) (D)
The The mix mixtu ture re is comp compre ress ssed ed adia adiaba batic tical ally ly to
1 5
its initial volume V . Find
the change in its adiabatic compressibilit y in terms of the given quantities. [ JEE '95, 1 + 1 + 1 + 10 ] Q 38. At 27º C two moles of an ideal monoatomic gas occupy a volume V . The gas expands adiabatically to a volume 2V . Calculate : ( i ) t h e f i nal t e mp er at u r e of t he ga s , ( i i ) ch ang e i n i t s i nt er nal en er g y & (iii) th t he wo r k don e by t h e ga s d ur i n g t h e p r oce ss . [ J EE ' 96, 5 ] Q 39. The The tem tempe perat rature ure of 100 100 gm of water is to be raised from 24º C to 90º C by adding steam to i t . Ca l cul at e t he m ass o f t he st ea m r eq ui r e d f or t hi s p ur p ose . [ JE JEE '9 '9 6 , 2 ] Q 40. Two metal metal cubes A & B of same size are are arranged arranged as shown shown in figure . The extreme ends of the combination are maintained at the indicated temperatures . The arrangement is thermally insulated . The co-efficients of thermal conductivity of A & B are 300 W/mº C and 200 W/mº C respectively . After steady state is reached the temperature T of the interface will be ______ .
C º 0 0 1
A
B C º 0
T
[ JEE '96, 2 ] Q 41. There There is a soap bubble bubble of radiu radiuss 2.4 2.4 x 10−4 m in air air cylinder which which is originally originally at the pressure of 10 5 Nm−2 . The air i n the cylinder is now compressed isothermally until the radius of the bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film fi lm is 0.08 Nm −1 . [ R EE ' 9 6, 5 ] Q 42. A vertical vertical hollow hollow cylinder cylinder contains contains an ideal ideal gas . The gas gas is enclosed by a 5kg movable movable −3 2 piston with an area of cross-section cross-section 5 x 10 m . Now, the gas is heated from 300 K to 350 K and the piston rises by 0.1 m . The piston is now clamped at this position and the gas is cooled back to 300 K . Find the difference between the heat energy added during heating process & energy lost during the cooling process . [1 atm pressure = 10 5 N m−2] [ REE '96, 5 ] Q 43. A double-pan double-panee window window used for insulati insulating ng a room thermally thermally from from outside outside consists consists of two glass sheets each of area 1 m2 & thickness 0.01 m separated by a 0.05 m thick stagnant air space . In the steady state, the room-glass interface and the glass-outdoor interface are at constant temperatures of 27º C & 0º C respectively . Calculate the rate of heat heat flow through
QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
the window pane . Also find the temperatures of other interfaces . Given, thermal conductivities of glass and air as 0.8 & 0.08 Wm −1 K−1 re respectiv tively . [ JE JEE '97 '97, 5 ] Q 44. A sample sample of 2 kg of of monoatomic monoatomic Helium (assumed (assumed ideal) ideal) is taken P (10 N/m ) through the process ABC and another sample of 2 kg of the B C same gas is taken through the proc ess ADC as in figure . Given, 10 - - - - - - molecular mass of Helium = 4 . 5 - - - - - - (i) (i) what what is the the temp temper erat atur uree of of Hel Heliu ium m in in eac each h of of the the stat states es -D A A, B, C & D ? -V (m ) (ii) Is the there re any any way way of tel telli ling ng afte afterw rwar ards ds whic which h sam sampl plee of of 10 20 Helium went through the process ABC and which went through the t he process ADC ? Write Writ e Yes or No . (iii (iii)) How How much much is the the heat heat invo involve lved d in each each of of the proc proces esse sess ABC ABC & ADC ADC . [ JEE '97, 5 ] 4
2
3
Q 45. A gas thermometer is used as a standard thermometer thermometer for measurement of temperature . When the gas container container of of the thermometer is immersed immersed in water at its triple point 273.16 K, the pressure in the gas thermometer thermometer reads 3 x 10 4 N/m 2 . When the gas container of the same thermometer is immersed in another system, the gas pressure reads 3.5 x 10 4 N/m 2 . The temperature of this system system is therefore therefore ______ ______ ºC . [ JEE ,97, 2 ] Q 46. The average average translational translational kinetic kinetic energy of a molecule molecule in a gas becomes equal to 1 eV at a t em pe r at ur e __ ___ _ . [ R EE ' 9 7, 1 ] Q 47. Two moles of an an ideal monoatomic monoatomic gas are are confined within a cylinder cylinder by a massless massless & frictionless spring loaded loaded piston of cross-sectiona cross-sectionall area 4 x 10 −3 m 2 . The spring is, initially in its relaxed state state . Now the gas is heated heated by an electric electric heated, placed placed inside the cylinder, for some time . During this time, the gas expands and does 50 J of work in moving the piston piston through a distance 0.10 0.10 m . The temperature temperature of the gas increases increases by 50 K . Calcula Calculate te the spring spring const constant ant & the the heat heat supplied supplied by by the heater heater . [ REE '97, 5 ] Q 48. Two vessels vessels A & B, thermally insulated, contain an ideal monoatomic gas . A small tube fitted with a valve connects these vessels . Initially Initial ly the vessel A has 2 litres of gas at 300 K and 2 x 105 N m−2 pressure while vessel B has 4 litres of gas at at 350 K & 5 − 2 4 x 10 N m pressure . The valve is now opened and the system reaches equilibri um in pressu pressure re & temp tempera eratur turee . Calcu Calculat latee the the new new pressu pressure re & tempe temperat rature ure . [ REE '97, '97, 5 ] Q 49. One mole mole of a diato diatomic mic ideal ideal gas gas (γ º = 1.4) is taken through a cyclic process starting from point A . The process A → B is an adiabatic compression . B → C is isobaric expansion. C
→ D an adiabatic expansion & D → A is isochoric . The volume ratios are
and
VC VB
VA VB
= 16
= 2 & the temperature at A is TA = 300º K . Calculate the temperature of the gas
at t h e p oi n t s B & D and f i n d t h e ef f i ci e ncy of t he cyc l e .
[ J EE ' 97, 5 ]
Q 50. The appar apparatus atus shown shown in in the figure figure consis consists ts of four four glass glass columns connected by horizontal sections . The height of two central columns B & C are 49 cm each . The two A B C D outer columns colum ns A & D are open to the atmos phere . A & C 9 5º 5º 95º 5º are maintained at a temperature of 95º C while the columns B & D are maintained at 5º C . The height of the liquid in A & D measured from the base line are 52.8 cm & 51 cm respectively . Determine the coef f i ci ent of t h er mal expan si on of th e l i q ui d . [ J EE ' 97, 5 ]
QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
Q 51. Earth Earth receiv receives es 1400 1400 W/m2 of solar power . If all the solar energy falling on a lens of area 0.2 m 2 is 25 X focussed on to a block of ice of mass 280 grams, the time taken to melt the ice will be ______ minutes . (latent heat of fusion of ice = 3.3 x 10 5 J/kg) [ JEE '97, 2 ]
ANSWER SHEET Q 1. (i) T (ii) F
WAd = −14.8 x 10 5 J Q 6. False
Q 5. (ii) V = 113.14 litres , P = 0.440 atm
Q 8. 52.875 gm
Q 14. V = 1.42
For isothermal , P =
Q 10. (i) 800 K
13 6
P , V1 =
30 13
V ; V2 =
Q 18. 0.318 per sec
Q 21. 4 πR2 KT/P
Q 22 (a) 1153 J
Q 24 t = 2 min. 46.3 sec. 3 2
KT
Q 41. 8.08 x 10 5 P a
48 13
V
(b) 1153 J
Q 25. 300 K
V ; V2 =
8 3
Q 49. TB = 909.3 K , T D = 791.09 K , Q 51. 5.5 min
PV
Q 23. Q = 1.728 x 10 7 J
(iii) 0
Q 35. (i) 765 J 1 6
;
(ii) 10.83 %
− 0.0248
Q 39. 12 gm
Q 43. 41.5 W ,
∆ QABC = 3.25 x 10 6 J ; ∆ QADC = 2.75 x 10 6 J
Q 47. K = 2000 N/m , dQ = 1295 J
4
V &
V T
Q 40. 60º C
θ1 = 26.48º C , θ2 = 0.52º C
Q 44. (i) TA = 120.33 K , T B = 240.66 K , T C = 481.32 K , T D = 240.66 K (iii)
5
Q 26. (i) 1869.75 J (ii) 5297.6 J (iii) 500 K
(iii) 2767.23 J
Q 42. 55 J
3
Q 13. (i) 5 (ii)
Q 16. (B) , W = 0.58 RT RTA ,
Q 37. (d) nB = 2 ; 401 ms −1 ;
− 2767.23 J
10
(iii) 124450 J
7 Crd 1 Q 19. t = where d is density 72 σ 10 6
Q 33. 96.3º C , 2.462 x 10 6 atm
Q 36. 23.928 g ; 4.072 g Q 38. (i) 189 K (ii)
(ii) 720 J
Q 15. For adiabatic , P = 1.84 P, P, V 1 =
Q = 0.58 RT A
Q 31.
Q 4. 4 . WiSo = −1.10 9 x 10 6 J ;
Q 2. 2 . T = 675 K , P = 3.6 x 10 6
Q 45. 45.536º C
(ii) No
Q 46. 7730 K
Q 48. P = 3.3 x 10 5 N/m 2 , T = 338.71 K
η = 61.4 %
Q 50. 5.46 x 10−5 /º C
