Thermodynamics 41
19. Three samples of the same gas A, B and C 25. A Carnot engine whose efficiency is 50% has an
exhaust temperature of 500 K. If the efficiency is to
æ 3ö
ç g = ÷ have initially equal volume. Now the be 60% with the same intake temperature, the exhaust
è 2ø temperature must be (in K)
volume of each sample is double. The process is 26. An engine takes in 5 mole of air at 20°C and 1
adiabatic for A, Isobaric for B and isothermal for atm, and compresses it adiabaticaly to 1/10th of
C. If the finanl pressures are equal for all the
the original volume. Assuming air to be a
three samples, the ratio of their initial pressure is
diatomic ideal gas made up of rigid molecules,
(a) 2 2 : 2 :1 (b) 2 2 :1: 2 the change in its internal energy during this
(c) 2 :1: 2 (d) 2 :1: 2 process comes out to be X kJ. The value of X to
20. A Carnot engine whose low temperature reservoir the nearest integer is ________.
is at 7°C has an efficiency of 50%. It is desired to 27. Starting at temperature 300 K, one mole of an
increase the efficiency to 70%. By how many ideal diatomic gas (g = 1.4) is first compressed
degrees should the temperature of the high
temperature reservoir be increased? V1
adiabatically from volume V1 to V2 = . It is
(a) 840 K (b) 280 K 16
(c) 560 K (d) 373 K then allowed to expand isobarically to volume
2V2. If all the processes are the quasi-static then
Numeric Value Answer the final temperature of the gas (in °K) is (to the
21. An ideal gas at 27ºC is compressed adiabatically nearest integer) ______.
8 28. A Carnot engine operates between two
to of its original volume. The rise in
27 reservoirs of temperatures 900 K and 300 K. The
æ 5ö engine performs 1200 J of work per cycle. The
temperature (in °C) is ç g = ÷
è 3ø heat energy (in J) delivered by the engine to the
22. During an adiabatic process of an ideal gas, if P low temperature reser voir, in a cycle, is
1 _______.
is proportional to 1.5 , then the ratio of specific
V 29. Two Carnot engines A and B are operated in
heat capacities at constant pressure to that at series. The first one, A receives heat at T1
constant volume for the gas is (= 600 K) and rejects to a reservoir at
23. During an adiabatic process, the pressure of a temperature T2. The second engine B receives
gas is found to be proportional to the cube of its
heat rejected by the first engine and in turn,
absolute temperature. The ratio CP/CV for the rejects to a heat reservoir at T3 (= 400 K).
gas is Calculate the temperature T2 (in K) if the work
24. A Carnot freezer takes heat from water at 0°C outputs of the two engines are equal.
inside it and rejects it to the room at a temperature 30. A heat engine is involved with exchange of heat
of 27°C. The latent heat of ice is 336 × 103 J kg– of 1915 J, – 40 J, +125 J and – Q J, during one
1. If 5 kg of water at 0°C is converted into ice at cycle achieving an efficiency of 50.0%. The
0°C by the freezer, then the energy consumed value of Q (in J) is :
(in J) by the freezer is close to :
ANSWER KEY
1 (b) 4 (a) 7 (b) 10 (a) 13 (a) 16 (d) 19 (b) 22 (1.5) 25 (400) 28 (600)
2 (a) 5 (c) 8 (d) 11 (a) 14 (a) 17 (b) 20 (d) 23 (1.5) 26 (46) 29 (500)
5
3 (c) 6 (a) 9 (a) 12 (b) 15 (a) 18 (d) 21 (402) 24 (1.67 × 10 ) 27 (1818) 30 (980)
