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Q. No.A diatomic gas (\(\gamma= 1.4\)) does \(400\) J of work when it is expanded isobarically. The heat given to the gas in the process is:
1. \(1000\) J
2. \(1200\) J
3. \(1400\) J
4. \(1600\) J
Subtopic: Molar Specific Heat |
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Given below are two statements:
| Statement I: | When \(\mu\) amount of an ideal gas undergoes adiabatic change from state \(\left({P}_1, {V}_1, {T}_1\right)\) to state \(\left({P}_2, {V}_2, {T}_2\right)\), the work done is \({W}=\dfrac{\mu{R}\left({T}_2-{T}_1\right)}{1-\gamma}\), where \(\gamma=\dfrac{C_P}{C_V}\) and \(R=\) universal gas constant, |
| Statement II: | In the above case, when work is done on the gas, the temperature of the gas would rise. |
| 1. | Both Statement I and Statement II are correct. |
| 2. | Both Statement I and Statement II are incorrect. |
| 3. | Statement I is correct, but statement II is incorrect. |
| 4. | Statement I is incorrect, but statement II is correct. |
Subtopic: Types of Processes |
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A sample of an ideal gas is taken through the cyclic process \(ABCA\) as shown in the figure. It absorbs, \(40~\text{J}\) of heat during part \(AB\), no heat during \(BC\), and rejects \(60~\text{J}\) of heat during \(CA\). A work of \(50~\text{J}\) is done on the gas during part \(BC\). The internal energy of the gas at \(A\) is \(1560~\text{J}\). The work done by the gas during the part \(CA\) is:
1. \(20~\text{J}\)
2. \(30~\text{J}\)
3. \(-30~\text{J}\)
4. \(-60~\text{J}\)
1. \(20~\text{J}\)
2. \(30~\text{J}\)
3. \(-30~\text{J}\)
4. \(-60~\text{J}\)
Subtopic: Cyclic Process |
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In a Carnot engine, the temperature of the reservoir is \(527^\circ \text{C}\) and that of the sink is \(200\) K. If the work done by the engine when it transfers heat from the reservoir to sink is \(12000\) kJ, the quantity of heat absorbed by the engine from the reservoir is:
1. \(12\times10^6\) J
2. \(14\times10^6\) J
3. \(16\times10^6\) J
4. \(18\times10^6\) J
1. \(12\times10^6\) J
2. \(14\times10^6\) J
3. \(16\times10^6\) J
4. \(18\times10^6\) J
Subtopic: Carnot Engine |
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A thermally insulated vessel contains an ideal gas of molecular mass \(M\) and a specific heat ratio of \(1.4.\) The vessel is moving with speed \(v\) and is suddenly brought to rest. Assuming no heat is lost to the surroundings, then the vessel temperature of the gas increases by:
(\(R=\) universal gas constant)
(\(R=\) universal gas constant)
| 1. | \(\dfrac{M v^2}{7 R} \) | 2. | \(\dfrac{M v^2}{5 R} \) |
| 3. | \(\dfrac{2M v^2}{7 R} \) | 4. | \(\dfrac{7M v^2}{5 R} \) |
Subtopic: Molar Specific Heat |
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The efficiency of a Carnot's engine, working between the steam point and ice point, will be:
| 1. | \(26.81\text{%}\) | 2. | \(37.81\text{%}\) |
| 3. | \(47.81\text{%}\) | 4. | \(57.81\text{%}\) |
Subtopic: Carnot Engine |
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A monoatomic gas performs a work of \(\dfrac{ Q} {4}\) where \(Q\) is the heat supplied to it. During this transformation, the molar heat capacity of the gas will be: (\(R\) is the gas constant.)
| 1. | \(R\) | 2. | \(2R\) |
| 3. | \(3R\) | 4. | \(4R\) |
Subtopic: Molar Specific Heat |
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A Carnot engine takes \(5000~\text{kcal}\) of heat from a reservoir at \(727^\circ \text{C}\) and gives heat to a sink at \(127^\circ \text{C}.\) The work done by the engine is:
1. \(3 \times 10^6 ~\text J\)
2. zero
3. \(12.6 \times 10^6 \)
4. \(8.4 \times 10^6 \)
1. \(3 \times 10^6 ~\text J\)
2. zero
3. \(12.6 \times 10^6 \)
4. \(8.4 \times 10^6 \)
Subtopic: Carnot Engine |
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A Carnot engine whose heat sinks at \(27^\circ \text{C},\) has an efficiency of \(25\text{%}.\) By how many degrees should the temperature of the source be changed to increase the efficiency by \(100\text{%}\) of the original efficiency?
1. Increase by \(18^\circ \text{C}\)
2. Increase by \(200^\circ \text{C}\)
3. Increase by \(120^\circ \text{C}\)
4. Increase by \(73^\circ \text{C}\)
1. Increase by \(18^\circ \text{C}\)
2. Increase by \(200^\circ \text{C}\)
3. Increase by \(120^\circ \text{C}\)
4. Increase by \(73^\circ \text{C}\)
Subtopic: Carnot Engine |
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A thermodynamic system is taken from an original state \(D\) to an intermediate state \(E\) by a linear process, as shown in the figure. Its volume is then reduced to the original volume from \(E\) to \(F\) by an isobaric process. The total work done by the gas from \(D\) to \(E\) to \(F\) will be:
| 1. | \(-450 \text{ J} \) | 2. | \(450 \text{ J} \) |
| 3. | \(900 \text{ J} \) | 4. | \(1350 \text{ J} \) |
Subtopic: Work Done by a Gas |
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