Assertion (A): Work and heat both can be converted into each other in any condition.
Reason (R): Work and Heat both are different form of energy.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: First Law of Thermodynamics and nature of work/heat. Work and heat are forms of energy transfer, not different forms of energy itself. Their interconversion is governed by thermodynamic laws and not possible under 'any condition'. Both (A) and (R) are false.
Assertion (A): If volume of a gas is increasing but temperature of the gas is decreasing, then heat given to the gas may be positive, negative or zero.
Reason (R): Heat given to a gas is a path function, it is not a state function.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: First Law of Thermodynamics (( Delta U = Q - W )). If volume increases, (W > 0) (work done by gas). If temperature decreases, ( Delta U < 0 ). So, ( Q = Delta U + W ) can be positive, negative, or zero. Heat is indeed a path function. Both (A) and (R) are true, and (R) explains (A).
Assertion (A): The area of entropy versus temperature graph of a cyclic process, is equal to work done.
Reason (R): Change in internal energy of cyclic process is zero.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: T-S diagram and cyclic processes. The area enclosed by a (T-S) diagram for a cyclic process represents the net heat exchanged, ( Q_{net} ), not the work done. For a cyclic process, ( Delta U = 0 ) is true, but Assertion (A) is false. Therefore, both (A) and (R) are false in relation to the explanation.
Assertion (A): On sudden expansion a gas cools.
Reason (R): On sudden expansion, no heat is supplied to system and hence gas does work at the expense of its internal energy.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: Adiabatic expansion and First Law of Thermodynamics. Sudden expansion is a rapid process, approximated as adiabatic (( Q = 0 )). The gas does work ( W > 0 ). By \( \Delta U = Q - W ), ( \Delta U \) becomes negative, leading to a decrease in internal energy and thus cooling. Both (A) and (R) are true, and (R) explains (A).
Assertion (A): Bursting of balloon is not a equilibrium state.
Reason (R): Equilibrium state of a thermodynamic system is completely described by specific values of some macroscopic properties.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: Thermodynamic equilibrium. A bursting balloon is a spontaneous, non-equilibrium process. An equilibrium state is characterized by constant macroscopic properties. Both assertion (A) and reason (R) are true, and (R) correctly explains (A).
Assertion (A): Total entropy change in one cycle of carnot engine is zero.
Reason (R): Entropy is a state function.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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For any reversible cyclic process like a Carnot cycle, the net change in entropy of the working substance is zero. This is because entropy is a state function, meaning its value depends only on the state of the system, not the path taken. Hence, both A and R are true, and R correctly explains A.
Assertion (A): The efficiency of a carnot cycle depends on the nature of the gas used.
Reason (R): Adiabatic process is a part of carnot cycle and work done in adiabatic process does not depend on nature of gas.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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The efficiency of a Carnot engine \(\eta = 1 - \frac{T_c}{T_h}\) depends only on the temperatures of the hot and cold reservoirs, not the nature of the working gas. Work done in an adiabatic process \(W = \frac{nR(T_1 - T_2)}{1 - \gamma}\) depends on \(gamma\) (ratio of specific heats), which is specific to the nature of the gas. Therefore, both Assertion (A) and Reason (R) are false.
Assertion (A): It is not possible for a system, unaided by an external agency to transfer heat from a body at lower temperature to another body a higher temperature.
Reason (R): According to Clausius statement “No process is possible whose sole result is the transfer of heat from a cooled object to a hotter object”.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is the practical implication of the Clausius statement of the second law of thermodynamics: heat does not spontaneously flow from cold to hot. Reason (R) provides the exact wording of the Clausius statement. Thus, both A and R are true, and R is the correct explanation for A.
Assertion (A): Air quickly leaking out of a balloon becomes cooler.
Reason (R): The leaking air undergoes adiabatic expansion.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Air quickly leaking out of a balloon undergoes rapid expansion. This is an adiabatic process where the gas does work, leading to a decrease in internal energy and thus temperature.
Both (A) and (R) are true and (R) is the correct explanation of (A).
Assertion (A): If heat is supplied to an ideal gas in an isothermal process, the internal energy of the gas increases.
Reason (R): When an ideal gas expands adiabatically, it does positive work and its internal energy increases.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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For an ideal gas in an isothermal process, temperature is constant, so internal energy \(Delta U = 0\). Thus (A) is false. In adiabatic expansion, work \(W > 0\) is done by the gas and heat \(Q = 0\), so \(Delta U = -W < 0\), meaning internal energy decreases. Thus (R) is false. Both (A) and (R) are false.