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Q. No.Select the correct option based on statements below.
A Carnot engine works between two thermal reservoirs maintained at absolute temperatures \(T_{\text{high}}\) and \(T_{\text{low}}\).
A Carnot engine works between two thermal reservoirs maintained at absolute temperatures \(T_{\text{high}}\) and \(T_{\text{low}}\).
| Assertion (A): | If the efficiency of the engine is \(\frac1n,\) then the coefficient of performance of the reversed cycle working as a refrigerator is \(n-1\). |
| Reason (R): | The efficiency of Carnot's cycle is \(1-\frac{T_{\text{low}}}{T_{\text{high}}},\) while the coefficient of performance of the reversed cycle is \(\frac{T_{\text{low}}}{T_{\text{high}~-~T_{\text{low}}}}\). |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
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For ideal diatomic gases at normal temperature,
Choose the correct statement(s):
| Statement I: | Molar heat capacity at constant pressure for all diatomic gases is the same. |
| Statement II: | The specific heat capacity at constant pressure of all diatomic ideal gases is the same. |
Choose the correct statement(s):
| 1. | only (I) is correct |
| 2. | only (II) is correct |
| 3. | both (I) and (II) are correct |
| 4. | none of them are correct |
Subtopic: Molar Specific Heat |
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Consider the following two statements.
| Statement I: | If heat is added to a system, its temperature must increase. |
| Statement II: | If positive work is done by a system in a thermodynamic process, its volume must increase. |
| 1. | Both Statement I and Statement II are correct. |
| 2. | Statement I is correct and Statement II is incorrect. |
| 3. | Statement I is incorrect and Statement II is correct. |
| 4. | Both Statement I and Statement II are incorrect. |
Subtopic: Work Done by a Gas |
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The figure shows the \((P\text-V)\) diagram of an ideal gas undergoing a change of state from \(A\) to \(B.\) Four different paths \(\mathrm{I, II, III}\) and \(\mathrm{IV},\) as shown in the figure, may lead to the same change of state.
| (a) | The change in internal energy is the same in cases \(\mathrm{IV}\) and \(\mathrm{III}\) but not in cases \(\mathrm{I}\) and \(\mathrm{II}.\) |
| (b) | The change in internal energy is the same in all four cases. |
| (c) | The work done is maximum in case \(\mathrm{I}.\) |
| (d) | The work done is minimum in case \(\mathrm{II}.\) |
Which of the following options contains only correct statements?
| 1. | (b), (c) and (d) only | 2. | (a) and (d) only |
| 3. | (b) and (c) only | 4. | (a), (c) and (d) only |
Subtopic: Work Done by a Gas |
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Given below are two statements:
| Assertion (A): | It is not possible for a system, unaided by an external agency to transfer heat from a body at a lower temperature to another at a higher temperature. |
| Reason (R): | It is not possible to violate the second law of thermodynamics. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Second Law of Thermodynamics |
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Consider the following statements and select the correct option:
| Statement (A): | Heat is not a state function. |
| Statement (B): | Heat supplied to a system is a path function. |
| 1. | Both statements (A) and (B) are True. |
| 2. | Both statements (A) and (B) are False. |
| 3. | Only statement (A) is True. |
| 4. | Only statement (B) is True. |
Subtopic: Basic Terms |
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The Carnot cycle (reversible) of gas is represented by a pressure-volume curve as shown in the figure. Consider the following statements:
| I. | The area \(ABCD\) = The work done on the gas |
| II. | The area \(ABCD\) = The net heat absorbed |
| III. | The change in the internal energy in the cycle = \(0\) |
Which of the statement(s) given above is/are correct?
| 1. | I only | 2. | II only |
| 3. | II and III | 4. | I, II, and III |
Subtopic: Cyclic Process |
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One mole of a diatomic ideal gas undergoes a cyclic process \(ABC\) as shown in the figure. The process \(BC\) is adiabatic. The temperatures at \(A,\) \(B,\) and \(C\) are \(400\) K, \(800\) K, and \(600\) K respectively. Choose the correct statement:
| 1. | The change in internal energy in the process \(BC\) is \(-500R.\) |
| 2. | The change in internal energy in the whole cyclic process is \(250R.\) |
| 3. | The change in internal energy in the process \(CA\) is \(700R.\) |
| 4. | The change in internal energy in the process \(AB\) is \(-350R.\) |
Subtopic: Cyclic Process |
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One mole of an ideal gas is taken through a cyclic process as shown in the \((V\text-T)\) diagram. Which of the following statements is correct?
| 1. | The magnitude of the work done by the gas is \(RT_{0}\ln 2.\) |
| 2. | The work done by the gas is \(V_{0}T_{0}.\) |
| 3. | The net work done by the gas is zero. |
| 4. | The work done by the gas is \(2RT_{0}\ln2.\) |
Subtopic: Cyclic Process |
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An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric, and isochoric. The curve which represents the adiabatic process among \(1,\) \(2,\) \(3\) and \(4\) is:
| 1. | \(4\) | 2. | \(1\) |
| 3. | \(2\) | 4. | \(3\) |
Subtopic: Types of Processes |
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