THERMODYNAMICS & KINETIC THEORY OF GASES

1. Heat added to a system is equal toa) a change in its internal kinetic energy b) a change in its internal potential energyc) workdone by it d) sum of above all the three.

2. The area inside a closed curve on P-V diagram representsa) the condition of a system b) work done on the systemc) workdone in a cyclic process d) a thermodynamic process

3. In the diagrams (i) to (iv) of figure, variation of volume by changing pressure is shown. A gas is taken along the path ABCD. The change ininternal energy of the gas will be

a) positive in all the cases (i) to (iv) b) positive in cases (i), (ii) and (iii) but zero in case (iv)c) negative in cases (i), (ii) and (iii) but zero in case (iv) d) zero in all the four cases.

4. The second law of thermodynamics impliesa) whole of the heat can be converted into mechanical energy b) no heat engine can be 100% efficientc) every heat engine has an efficiency of 100% d) a refrigerator can reduce the temperature to absolute zero.

5. The maximum amount of heat that can be converted into mechanical energy in any processa) is 100% b) depends upon the temperatures of intake and exhaustc) depends upon the amount of friction present d) is the same for reversible and irreversible cycles.

6. A Carnot engine works between a source and a sink maintained at constant temperatures T1 and T2. For efficiency to be the greatest

a) T1 and T2 should be high b) T1 and T2 should be low

c) T1 should be low and T2 should be high d) T1 should be high and T2 should be low.

7. In a thermodynamic process, pressure of a fixed mass of gas is changed in such a manner that the gas release 20 joule of heat and 8 jouleof work was done on the gas. If the initial internal energy of the gas was 30 joule, then the final internal energy will bea) 2 joule b) 18 joule c) 42 joule d) 58 joule

8. During an adiabatic expansion of 2 moles of a gas, the change in internal energy was found to be equal to -100 J. The workdone during theprocess will be equal toa) zero b) -100 joule c) 200 joule d) 100 joule

9. A Carnot engine working between 300 K and 600 K has a work output of 800 J per cycle. The amount of heat energy supplied to the enginefrom the source in each cycle isa) 800 J b) 1600 J C) 3200 J d) 6400 J

10. The temperature of the sink of a Carnot engine is 27°C. If the efficiency of the engine is 25%, the temperature of the source isa) 227°C b) 327°C c) 127°C d) 27°C

11. The efficiency of a Carnot cycle is 1/6. If in reducing the temperature of sink by 65°K, the efficiency becomes 1/3. The initial and finaltemperatures between which the cycle is working are

a) C13,C52 °−° b) 217°C, 52°C c) 317°C, 52°C d) 17°C, 52°C

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12. The temperature of inside and outside of a refrigerator are 273 K and 303 K respectively. Assuming that the refrigerator cycle is reversible, forevery joule of workdone, the heat delivered to the surrounding will be nearlya) 10 J b) 20 J c) 30 J d) 50 J

13. An ideal non-atomic gas is taken round the cycle ABCDA in the P-V diagram where the coordinates ofthe points are : A ( P1, V1 ) ; B ( 2P1, V1 ) ; C ( 2P1, 2V1 ) and D ( P1, 2V1 ). The work done during thecycle is :

a) P V1 1 b) 2 1 1P V

c) 12 1 1PV d) zero

14. From what minimum height, a block of ice has to be dropped in order that it may melt completely on hitting the ground ? ( L is the latent heatof ice and J is Joule's constant )

a) mgh b) mgh / J c) JL / g d) J/Lg

15. An ideal gas is taken around the cycle ABCA as shown in P-V diagram. The net workdone by the gasduring the cycle is equal to

a) 12 P1 V1 b) 6 P1 V1

c) 3 P1 V1 d) P1 V1

16. When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy suppliedwhich increases the internal energy of the gas isa) 2 / 5 b) 3 / 5 c) 3 / 7 d) 5 / 7

17. A thermodynamical system goes from state (i) P1, V to 2P1, V. Another system goes from state (ii) P1, V to P1, 2V . Then the wokdone in thetwo cases isa) (i) zero (ii) zero b) (i) zero (ii) P1 V c) (i) P1 V (ii) zero d) (i) P1 V (ii) P1 V

18. The pressure exerted by a gas on the walls of a container is given by

a) PMVv=

13

2 b) P VMv=

13

2 c) P M v=13

2 d) P M v= 3 2

19. The absolute temperature of a gas is determinesa) the average momentum of the molecule b) the velocity of sound in thegasc) the number of molecules in the gas d) the mean square velocity ofthe molecules

20. Two vessels having equal volume contains molecular hydrogen at one atmosphere and helium at two atmospheres respectively. If bothsamples are at the same temperature, the mean velocity of hydrogen molecules is

a) equal to that of helium b) twice that of helium c) half that of helium d) 2 times that ofhelium

21. A gas at a pressure P0 is contained in a vessel. If the masses of all the molecules are halved and their velocities doubled, the resultingpressure P would be equal toa) 4 P0 b) 2 P0 c) P0 d) P0/2

22. We have a jar A filled with gas characterised by parameters P, V and T and another jar B filled with a gas with parameters 2P, V/4 and 2T,where the symbols have the usual meanings. The ratio of the number of molecules of jar A to those of jar B isa) 1 : 1 b) 1 : 2 c) 2 : 1 d) 4 : 1

B

A

4P1

P1

V1 3V1

CP

V(O,O)

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23. A gas in a container A is in thermal equilibrium with another gas (having same no.of moles) in container B. If we denote the correspondingpressures and volumes by the suffixes A and B, then which of the following statement is most likely to be true.

a) P P V VA B A B= ≠, b) P P V VA B A B≠ =, c) BBAA VPVP // = d) BBAA VPVP =

24. The speed of sound in a gas is v. The r.m.s velocity of the gas molecules is C. The ratio of v to C is

a) 3 / γ b) γ / 3 c) ( / )3 γ d) ( / )γ 3

25. Two gases are at absolute temperatures 300°K and 350°K respectively. The ratio of average kinetic energy of their molecules isa) 7 : 6 b) 6 : 7 c) 36 : 49 d) 49 : 36

26. A sealed container with negligible thermal coefficient of expansion contains helium (a monatomic gas ). When it is heated from 300 to 600 K,the average kinetic energy of the helium atom is

a) halved b) left unchanged c) doubled d) becomes 2 times.

27. A fixed mass of gas at constant pressure occupies a volume V. The gas undergoes a rise in temperature so that the root mean squarevelocity of its molecules is doubled. The new volume will be

a) V / 2 b) V / 2 c) 2V d) 4V

28. A sample of oxygen gas and a sample of H2 gas both have the same mass, the same volume and the same pressure. The ratio of theirabsolute temperature is

a) 1 : 4 b) 4 : 1 c) 1 : 16 d) 16 : 1

29. If a system is caused to change reversibly from an initial state to a final state by adiabatic means only, thena) the work done is the same for all adiabatic paths connecting the two states.b) the work done is different for different adiabatic paths connecting the two statesc) the total internal energy of the system will change according to different paths.d) there is no work done since there is no transfer of heat energy.

30. When a gas expands adiabaticallya) no energy is required for expansionb) energy is required and it comes from the wall of the container of the gasc) internal energy of the gas is used in doing workd) law of conservation of energy does not hold.

31. During an adiabatic process, the pressure P of a fixed mass of an ideal gas changes by Pδ and its volume V changes by Vδ . The valueof V/Vδ is given by

a) −δP P/ b) −γ δ. /P P c) −1γδ. PP

d) −12γδ. PP

32. The work done in an isothermal expansion of a gas depends upon(a) temperature only b) expansion ratio onlyc) both temperature and expansion ratio d) neither temperature nor expansion ratio.

33. Two samples A and B of a gas initially of the same temperature and pressure are compressed from a volume V to a volume V/2 such thatA is compressed isothermally and B adiabatically. The final pressure ofa) A is greater than that of B b) A is equal to that of Bc) A is less than that of B d) A is twice the pressure of B.

34. A monoatomic ideal gas initially at 17°C is suddenly compressed to one-eight of its original volume. The temperature after compression isa) 17°C b) 136°C c) 887°C d) none of these

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35. Four curves A, B, C and D are drawn in figure for a given amount of gas. The curves which represent adiabatic and isothermal changes are

a) C and D respectively b) D and C respectivelyc) A and B respectively d) B and A respectively

36. If a gas has 'n' degrees of freedom, the ratio of the specific heats of the gas is

a)12+ n

b) 12

+n

c) 1 1+n

d) 12

+n

37. The root mean square speed of a group of n gas molecules, having speed v1 , v2 , v3 , ...., vn is

a)1

1 2 32

nv v v vn( .... )+ + + + b)

112

22

32 2

nv v v vn( .... )+ + + +

c)1

12

22

32 2

nv v v vn( .... )+ + + + d)

( .... )v v v vn

n1 2 32+ + + +L

NMOQP

38. The pressure and density of a diatomic gas )5/7( =γ change adiabatically from ),( ρP to )','( ρP . If 32)/'( =ρρ , then )/'( PPisa) 128 b) 1/128 c) 32 d) none of the above

39. 1/2 mole of helium gas is contained in a container at S.T.P. The heat energy needed to double the pressure of the gas, keeping the volume

constant (heat capacity of the gas 11Kg3J −−= )a) 3276 J b) 1638 J c) 819 J d) 409.5 J

Answers

1. d 2. c 3. d 4. b 5. b 6. d7. b 8. d 9. b 10. c 11. a 12. a13. a 14. c 15. c 16. d 17. b 18. a19. d 20. a 21. b 22. d 23. d 24. d25. b 26. c 27. d 28. d 29. a 30. c31. c 32. c 33. c 34. c 35. c 36. d37. c 38. a 39. b

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