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Q. No.The heat taken by a gas (shown in the graph below) in the process \(a\) to \(b\) is \(6P_{0}V_{0}.\) Match Column I with Column II.
Column I
Column II
\(\mathrm{(A)}\)
Work done in the process \(ab\) \((W_{ab})\)
\(\mathrm{(P)}\)
\(1.5R\)
\(\mathrm{(B)}\)
Change in internal energy in the process \(ab\) \((\Delta U_{ab})\)
\(\mathrm{(Q)}\)
\(\dfrac {3P_0V_0}{2}\)
\(\mathrm{(C)}\)
Molar heat capacity in the given process
\(\mathrm{(R)}\)
\(\dfrac {9P_0V_0}{2}\)
\(\mathrm{(D)}\)
Molar heat capacity at constant volume \((C_{V})\) for the gas
\(\mathrm{(S)}\)
\(2R\)
Codes:
1.
\(\mathrm{A\text-P,B\text-Q,C\text-S,D\text-R}\)
2.
\(\mathrm{A\text-R,B\text-Q,C\text-S,D\text-P}\)
3.
\(\mathrm{A\text-Q,B\text-R,C\text-P,D\text-S}\)
4.
\(\mathrm{A\text- Q,B\text-R,C\text-S,D\text-P}\)
Subtopic: Types of Processes |
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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 |
75%
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The ratio of molar specific heat capacity at constant pressure (\(C_p\)) to that at constant volume (\(C_v\)) varies with temperature (\(T\)) as: (assume temperature is low)
1. \(T^0\)
2. \(T^{\frac{1}{2}}\)
3. \(T^1\)
4. \(T^{\frac{3}{2}}\)
1. \(T^0\)
2. \(T^{\frac{1}{2}}\)
3. \(T^1\)
4. \(T^{\frac{3}{2}}\)
Subtopic: Molar Specific Heat |
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Given below are two statements:
| Assertion (A): | Reversible systems are difficult to find in the real world. |
| Reason (R): | Most processes are dissipative in nature. |
| 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 |
82%
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Given below are two statements:
| Assertion (A): | It is possible that the temperature of a gas may fall even as it is being heated. |
| Reason (R): | The specific heat capacity of a gas changes from process to process. |
| 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: First Law of Thermodynamics |
52%
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Given below are two statements:
| Statement I: | The efficiency of any thermodynamic engine can approach \(100\%\) if friction and all dissipative processes are reduced. |
| Statement II: | The first law of thermodynamics is applicable only to non-living systems. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Second Law of Thermodynamics |
54%
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Given below are two statements:
| Assertion (A): | In an isothermal process, whole of the heat energy supplied to the body is converted into internal energy. |
| Reason (R): | According to the first law of thermodynamics, \(\Delta Q = \Delta U + \Delta W \). |
| 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. | (A) is False but (R) is True. |
Subtopic: Types of Processes |
83%
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We consider a thermodynamic system. If \(\Delta U\) represents the increase in its internal energy and \(W\) the work done by the system, which of the following statements is true?
| 1. | \(\Delta {U}=-{W}\) in an isothermal process. |
| 2. | \(\Delta {U}={W}\) in an isothermal process. |
| 3. | \(\Delta {U}=-{W}\) in an adiabatic process. |
| 4. | \(\Delta {U}={W}\) in an adiabatic process. |
Subtopic: First Law of Thermodynamics |
85%
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AIPMT - 1998
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If a gas changes volume from \(2\) litres to \(10\) litres at a constant temperature of \(300~\text{K}\), then the change in its internal energy will be:
| 1. | \(12~\text{J}\) | 2. | \(24~\text{J}\) |
| 3. | \(36~\text{J}\) | 4. | \(0~\text{J}\) |
Subtopic: Molar Specific Heat |
87%
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AIPMT - 1998
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An ideal gas heat engine operates in a Carnot cycle between 227ºC and 127ºC. It absorbs 6 × 104 cals of heat at higher temperatures.
The amount of heat converted to work will be?
1. 4.8 × 104 cals
2. 2.4 × 104 cals
3. 1.2 × 104 cals
4. 6 × 104 cals
Subtopic: Carnot Engine |
73%
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AIPMT - 2005
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