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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} .
