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Q. No.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
Which of the following options contains only correct statements?
Subtopic: Work Done by a Gas |
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Match the thermodynamic processes taking place in a system with the correct conditions. In the table, \(\Delta Q\) is the heat supplied, \(\Delta W\) is the work done and \(\Delta U\) is the change in internal energy of the system.
| Process | Condition | ||
| (I) | Adiabatic | (A) | \(\Delta W=0\) |
| (II) | Isothermal | (B) | \(\Delta Q=0\) |
| (III) | Isochoric | (C) | \(\Delta U\neq0, \Delta W\neq0,\Delta Q\neq0\) |
| (IV) | Isobaric | (D) | \(\Delta U=0\) |
Codes:
| 1. | (I) – (B), (II) – (A), (III) – (D), (IV) – (C) |
| 2. | (I) – (A), (II) – (A), (III) – (B), (IV) – (C) |
| 3. | (I) – (A), (II) – (B), (III) – (D), (IV) – (D) |
| 4. | (I) – (B), (II) – (D), (III) – (A), (IV) – (C) |
Subtopic: Types of Processes |
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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 |
57%
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Figure shows P-T diagram for given mass of an ideal gas for the process A→B. During this process, density of the gas is
1. Decreasing
2. Increasing
3. Constant
4. First decreasing then increasing
Subtopic: Types of Processes |
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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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An ideal gas is taken reversibly around the cycle \(a\text-b\text-c\text-d\text-a\) as shown on the temperature \((T)\) - entropy \((S)\) diagram.
The most appropriate representation of the above cycle on an internal energy \((U)\) - volume \((V)\) diagram is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
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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 |
73%
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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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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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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 |
77%
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