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Q 1. An ideal gas is taken through the cycle {tex} A \rightarrow B \rightarrow C {/tex} {tex} \rightarrow A {/tex} as shown in Fig. If the net heat supplied to the gas in the cycle is {tex} 5\mathrm { J } {/tex} , the work done by the gas in the process {tex} C \rightarrow A {/tex} is
{tex} - 15 \mathrm { J } {/tex}
{tex} - 10 \mathrm { J } {/tex}
{tex} - 5 \mathrm { J } {/tex}
{tex} - 20 \mathrm { J } {/tex}
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Q 2. For an adiabatic expansion process, the quantity {tex} P V {/tex}
decreases.
increases.
remains constant.
depends on adiabatic exponent of the gas.
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Q 3. A gas is confined inside a container having a movable piston. The gas is allowed to expand isobarically. If the initial volume of gas is {tex} V _ { 0 } {/tex} and the speed of sound in the gas is {tex} C _ { 0 } , {/tex} then the speed of sound when the volume of the gas increases to 4{tex} V _ { 0 } {/tex} is
{tex} C_{0} {/tex}
{tex} 2C_{0} {/tex}
{tex} 4C_{0}{/tex}
{tex} C _ { 0 } / 2 {/tex}
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Q 4. An ideal gas is taken through cycle {tex} A \rightarrow B \rightarrow C \rightarrow A {/tex} as shown in Fig. If the net heat supplied to the gas is {tex} \mathrm 10 { J } {/tex} , then the work done by the gas in process {tex} B \rightarrow C {/tex} is
{tex} - 10 J {/tex}
{tex} - 30 J {/tex}
{tex} - 15 J {/tex}
{tex} - 20 J {/tex}
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Q 5. The work of {tex} 146 \mathrm\, { kJ } {/tex} is performed in order to compress {tex}1 kilo\ mole{/tex} of gas adiabatically and in this process, the temperature of the gas increases by {tex} 7 ^ { \circ } \mathrm { C } . {/tex} The gas is {tex}R=(8.3\, J \,mol^{-1} K^{-1}){/tex}
Monoatomic
Diatomic
Triatomic
A mixture of monoatomic and diatomic
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Q 6. If amount of heat given to a system is {tex} 50 \mathrm { J } {/tex} and work done on the system is {tex}15 \mathrm { J } {/tex}, then change in internal energy of the system is
{tex}35 \mathrm J {/tex}
{tex}50 \mathrm { J } {/tex}
{tex} 65 \mathrm { J } {/tex}
{tex} 15\mathrm { J } {/tex}
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Q 7. Which one of the following statements is incorrect?
If positive work is done by a system in a thermodynamic process, its volume must increase.
If heat is added to a system, its temperature must increase.
A body at {tex} 20 ^ { \circ } \mathrm { C } {/tex} radiates in a room, where room temperature is {tex} 30 ^ { \circ } \mathrm { C } {/tex} .
If pressure vs temperature graph of an ideal gas is a straight line, then work done by the gas is zero.
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Q 8. {tex}P-T{/tex}curve of the following process will be
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Q 9. Temperature of source is {tex} 330 ^ { \circ } \mathrm { C } {/tex} . Temperature of sink is changed in order to increase the efficiency of engine from {tex} \frac { 1 } { 5 } {/tex} to {tex} \frac { 1 } { 4 } , {/tex} by
{tex} 30 ^ { \circ } \mathrm { K } {/tex}
{tex} 303 ^ { \circ } \mathrm { K } {/tex}
{tex} 603 ^ { \circ } \mathrm { K } {/tex}
{tex} 60 ^ { \circ } \mathrm { K } {/tex}
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Q 10. {tex}P-V{/tex} diagram of an ideal gas is as shown in Fig. Work done by the gas in the process {tex} A B C D {/tex} is
{tex} 4P _ { 0 } V _ { 0 } {/tex}
{tex}2 P _ { 0 } V _ { 0 } {/tex}
{tex} 3P _ { 0 } V _ { 0 } {/tex}
{tex} P _ { 0 } V _ { 0 } {/tex}
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Q 11. Two rigid boxes containing different ideal gases are placed on a table. Box {tex} A {/tex} contains one mole of nitrogen at temperature {tex} T _ { 0 } {/tex} , while Box {tex} B {/tex} contains one mole of helium at temperature {tex} ( 7 / 3 ) T _ { 0 } . {/tex} The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature. (Ignore the heat capacity of boxes.) Then, the final temperature of the gases, {tex} T _ { f } {/tex}, in terms of {tex} T _ { 0 } {/tex} is
{tex} T _ { f } = \frac { 5 } { 2 } T _ { 0 } {/tex}
{tex} T _ { f } = \frac { 3 } { 7 } T _ { 0 } {/tex}
{tex} T _ { f } = \frac { 7 } { 3 } T _ { 0 } {/tex}
{tex} T _ { f } = \frac { 3 } { 2 } T _ { 0 } {/tex}
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Q 12. A gas is expanded from volume {tex} V _ { 0 } {/tex} to {tex}2 V _ { 0 } {/tex} under three different processes. Process 1 is isobaric process, process 2 is isothermal, and process 3 is adiabatic. Let {tex} \Delta U _ { 1 } , \Delta U _ { 2 } , {/tex} and {tex} \Delta U _ { 3 } {/tex} be the change in internal energy of the gas in these three processes. Then
{tex} \Delta U _ { 1 } > \Delta U _ { 2 } > \Delta U _ { 3 } {/tex}
{tex} \Delta U _ { 1 } < \Delta U _ { 2 } > \Delta U _ { 3 } {/tex}
{tex} \Delta U _ { 2 } < \Delta U _ { 1 } < \Delta U _ { 3 } {/tex}
{tex} \Delta U _ { 2 } > \Delta U _ { 3 } > \Delta U _ { 1 } {/tex}
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Q 13. A cyclic process {tex} A B C D {/tex} is shown in the {tex} P - V {/tex} diagram. Which of the following curves represent the same process?
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Q 14. An ideal gas undergoes four different processes from the same initial state (Fig.). Four processes are adiabatic, isothermal, isobaric, and isochoric. Out of {tex} 1,2,3 , {/tex} and {tex}4{/tex} which one is adiabatic?
{tex}4{/tex}
{tex}3{/tex}
{tex}2{/tex}
{tex}1{/tex}
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Q 15. An ideal gas undergoes cyclic process {tex} A B C D A {/tex} as shown in given {tex} P - V {/tex} diagram. The amount of work done by the gas is.
{tex} 6P _ { 0 } V _ { 0 } {/tex}
{tex} - 2 P _ { 0 } V _ { 0 } {/tex}
{tex} + 2 P _ { 0 } V _ { 0 } {/tex}
{tex} + 4 P _ { 0 } V _ { 0 } {/tex}
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Q 16. An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume {tex} V _ { 1 } {/tex} and contains ideal gas at pressure {tex} P _ { 1 } {/tex} and temperature {tex} T _ { 1 } . {/tex} The other chamber has volume {tex} V _ { 2 } {/tex} and contains ideal gas at pressure {tex} P _ { 2 } {/tex} and temperature {tex} T _ { 2 } . {/tex} If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be:
{tex} \frac { T _ { 1 } T _ { 2 } \left( P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } \right) } { P _ { 1 } V _ { 1 } T _ { 1 } + P _ { 2 } V _ { 2 } T _ { 2 } } {/tex}
{tex} \frac { T _ { 1 } T _ { 2 } \left( P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } \right) } { P _ { 1 } V _ { 1 } T _ { 2 } + P _ { 2 } V _ { 2 } T _ { 1 } } {/tex}
{tex} \frac { P _ { 1 } V _ { 1 } T _ { 1 } + P _ { 2 } V _ { 2 } T _ { 2 } } { P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } } {/tex}
{tex} \frac { P _ { 1 } V _ { 1 } T _ { 2 } + P _ { 2 } V _ { 2 } T _ { 1 } } { P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } } {/tex}
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Q 17. A Carnot engine, whose efficiency is {tex} 40\% {/tex} , takes heat from a source maintained at a temperature of {tex} \mathrm 500\,{ K } {/tex} . It is desired to have an engine of efficiency {tex} 60\% {/tex} . Then, the intake temperature for the same exhaust (sink) temperature must be:
Efficiency of Carnot engine cannot be made larger than {tex}50 \% {/tex}
{tex} 1200\mathrm { K } {/tex}
{tex} 750\mathrm { K } {/tex}
{tex} 600\mathrm { K } {/tex}
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Q 18. One mole of diatomic ideal gas undergoes a cyclic process {tex} A B C {/tex} as shown in Fig. The process {tex} B C {/tex} is adiabatic. The temperatures at {tex} A , B , {/tex} and {tex} C {/tex} are {tex} \mathrm400 { K } {/tex} , {tex} 800 \mathrm { K } , {/tex} and {tex} 600\mathrm { K } {/tex} , respectively. Choose the correct statement.
The change in internal energy in whole cyclic process is {tex}250 { R } {/tex} .
The change in internal energy in the process {tex} C A {/tex} is {tex} \mathrm 700 \,{ R } {/tex} .
The change in internal energy in the process {tex} A B {/tex} is {tex} - 350 { R } {/tex} .
The change in internal energy in the process {tex} B C {/tex} is {tex} - 500 { R } {/tex} .
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Q 19. The work of {tex} 146 \mathrm { kJ } {/tex} is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by {tex} 7 ^ { \circ } \mathrm { C } {/tex}. The gas is {tex} \left( R = 8.3 \mathrm { J } \mathrm { mol } ^ { - 1 } \mathrm { K } ^ { - 1 } \right) {/tex}
monoatomic
diatomic
triatomic
a mixture of monoatomic and diatomic.
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Q 20. One mole of ideal monoatomic gas {tex} ( \gamma = 5 / 3 ) {/tex} is mixed with one mole of diatomic gas {tex} ( \gamma = 7 / 5 ) {/tex}. What is {tex} \gamma {/tex} for the mixture? {tex} \gamma {/tex} denotes the ratio of specific heat at constant pressure, to that at constant volume.
{tex} 3 / 2 {/tex}
{tex} 23 / 15 {/tex}
{tex} 35 / 23 {/tex}
{tex} 4 / 3 {/tex}
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Q 21. Two thermally insulated vessels {tex}1{/tex} and {tex}2{/tex} are filled with air at temperatures {tex} \left( T _ { 1 } , T _ { 2 } \right) , {/tex} volume {tex} \left( V _ { 1 } , V _ { 2 } \right) {/tex} and pressure {tex} \left( P _ { 1 } , P _ { 2 } \right) {/tex} respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
{tex} T _ { 1 } + T _ { 2 } {/tex}
{tex} \left( T _ { 1 } + T _ { 2 } \right) / 2 {/tex}
{tex} \frac { T _ { 1 } T _ { 2 } \left( P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } \right) } { P _ { 1 } V _ { 1 } T _ { 2 } + P _ { 2 } V _ { 2 } T _ { 1 } } {/tex}
{tex} \frac { T _ { 1 } T _ { 2 } \left( P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } \right) } { P _ { 1 } V _ { 1 } T _ { 1 } + P _ { 2 } V _ { 2 } T _ { 2 } } {/tex}
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Q 22. Which of the following is incorrect regarding the first law of thermodynamics?
It introduces the concept of the internal energy
It introduces the concept of entropy
It is not applicable to any cyclic process
It is a restatement of the principle of conservation of energy
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Q 23. When a system is taken from state {tex} i {/tex} to state {tex} f {/tex} along the path {tex} iaf, {/tex} it is found that {tex} Q = 50 {/tex} cal and {tex} W = 20 {/tex} cal. Along the path {tex} ibf \ Q = 36 {/tex} cal. W along the path {tex}ibf{/tex} is 
{tex}14 \mathrm {\ cal} {/tex}
{tex} 6 \mathrm {\ cal } {/tex}
{tex} 16 \mathrm {\ cal } {/tex}
{tex}66 \mathrm {\ cal}{/tex}
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Q 24. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio {tex} C _ { P } / C _ { V } {/tex} for the gas is
{tex} 4 / 3 {/tex}
{tex}2{/tex}
{tex} 5 / 3 {/tex}
{tex} 3 / 2 {/tex}
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Q 25. Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will
increase
decrease
remain same
decrease for some, while increase for others.
