# The heat taken by the gas in process $$a$$ to $$b$$ is $$6P_{0}V_{0}.$$ Match Column I with Column II.                            Column I Column II A. $$W_{ab}$$ P. $$1.5R$$ B.  $$\Delta U_{ab}$$ Q. $$\dfrac {3P_0V_0}{2}$$ C. molar heat capacity in the given process R. $$\dfrac {9P_0V_0}{2}$$ D. $$C_{v}$$ for the gas S. $$2R$$ Choose the correct option: 1. A → P, B → Q, C → S, D → R  2. A → R, B → Q, C → S, D → P 3. A → Q, B → R, C → P, D → S 4. A → Q, B → R, C → S, D → 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 $$\left(\mathrm{P}_1, \mathrm{~V}_1, \mathrm{~T}_1\right)$$ to state $$\left(\mathrm{P}_2, \mathrm{~V}_2, \mathrm{~T}_2 \right)$$, the work done is,  $$\mathrm{W}=\frac{\mu{R}\left(\mathrm{T}_2-\mathrm{T}_1\right)}{1-\gamma}$$, where $$\gamma=\frac{C_P}{C_v}$$ 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 true. 2 Both statement-I and statement-II are false. 3 Statement-I is true but statement-II is false. 4 Statement-I is false but statement-II is true.
Subtopic:  Types of Processes |
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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. $$T^{\frac{3}{2}}$$
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 |
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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 |
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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 |
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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 |
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We consider a thermodynamic system. If ∆U represents the increase in its internal energy and W the work done by the system, which of the following statements is true?

 1 $$\Delta \mathrm{U}=-\mathrm{W}$$  in an isothermal process 2 $$\Delta \mathrm{U}=\mathrm{W}$$ in an isothermal process 3 $$\Delta \mathrm{U}=-\mathrm{W}$$ in an adiabatic process 4 $$\Delta \mathrm{U}=\mathrm{W}$$  in an adiabatic process
Subtopic:  First Law of Thermodynamics |
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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 300K, then the change in its internal energy will be:

 1 12 J 2 24 J 3 36 J 4 0 J
Subtopic:  Molar Specific Heat |
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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 |
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AIPMT - 2005
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