Assertion (A): Absolute zero temperature is not the zero energy temperature.
Reason (R): At absolute zero temperature the gas may possess potential 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: Absolute zero and molecular energy. At absolute zero 0 K, the average kinetic energy of molecules is at its minimum (or zero for an ideal gas classically). However, molecules can still possess potential energy due to intermolecular forces or external fields. Hence, total energy is not necessarily zero. Both (A) and (R) are true, and (R) correctly explains (A).
Assertion (A): For gas molecules absolute zero temperature is not the temperature of zero energy.
Reason (R): Only the kinetic energy of the molecules is represented by temperature.
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: Temperature and molecular energy. Temperature is a direct measure of the average translational kinetic energy of molecules. While kinetic energy is minimal at 0 K, gas molecules can still have potential energy from intermolecular interactions. Thus,0 K is not zero total energy. Both (A) and (R) are true, and (R) explains (A).
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): 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): 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.
Assertion (A): In adiabatic expansion of monoatomic ideal gas, if volume increases by 12%, then pressure decreases by 20%.
Reason (R): In adiabatic process \(PV^{5/3} = \text{constant}\).
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 a monoatomic ideal gas, \(\gamma = 5/3\), so \(PV^{5/3} = \text{constant}\). (R) is true. If volume increases by 12%, \(V_2 = V_1(1+0.12)\). Using \(P_1V_1^{\gamma} = P_2V_2^{\gamma}\), we get \(P_2 = P_1(1+0.12)^{-5/3}\). Using approximation \((1+x)^n approx 1+nx\) for small \(x\), \(P_2 \approx P_1(1 - (5/3)(0.12)) = P_1(1-0.20) = 0.8P_1\). Thus, pressure decreases by 20%. (A) is true. (R) correctly explains (A).
Assertion (A): In an isochoric process, work done by the gas is zero.
Reason (R): In a process, if initial volume is equal to the final volume, work done by the gas 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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In an isochoric process, volume is constant, so \(Delta V = 0\). Work done \(W = PDelta V = 0\). So (A) is true. However, in a cyclic process, initial and final volumes are equal, but net work done is generally non-zero (area of the cycle on \(P-V\) diagram). So (R) is false.
Assertion (A): The specific heat of a gas in an adiabatic process is zero but it is infinite in an isothermal process.
Reason (R): Specific heat of a gas is directly proportional to heat exchanged with the system and inversely proportional to change in temperature.
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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Specific heat \(C = Q/(n\Delta T)\). For adiabatic process, \(Q=0\), so \(C=0\). For isothermal process, \(\Delta T=0\) (with \(Q \ne 0\)), so \(C=\infty\). Both (A) and (R) are true and (R) correctly explains (A) as it defines specific heat.