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
View Answer
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
View Answer
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): 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
View Answer
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
View Answer
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
View Answer
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.
Assertion (A): In adiabatic compression, the temperature of system gets decreased.
Reason (R): Adiabatic compression is a slow process.
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
View Answer
In adiabatic compression, work is done on the gas \(W =0\), leading to an increase in temperature. Thus (A) is false. Adiabatic processes are typically rapid to prevent heat exchange. Thus (R) is false. Both (A) and (R) are false.
Assertion (A): All processes in which P and V are proportional, take place at constant temperature.
Reason (R): Work done in a thermodynamical process is path independent.
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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If \(P propto V\) (i.e., \(P=kV\)), then for an ideal gas \(PV=nRT\) implies \(kV^2=nRT\), so \(T \propto V^2\). Thus, temperature is not constant. (A) is false. Work done \(W = \int PdV\) depends on the path taken on a \(P-V\) diagram, so it is path dependent. (R) is false. Both (A) and (R) are false.
Assertion (A): During adiabatic expansion of an ideal gas, temperature falls but entropy remains constant.
Reason (R): During adiabatic expansion, work is done by the gas using a part of internal energy and no heat exchange takes place the system and the surrounding.
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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During adiabatic expansion, \(Q=0\). The gas does work by using its internal energy, causing temperature to fall. For a reversible adiabatic process, entropy \(\Delta S=0\). (A) is true. (R) correctly explains the energy changes (no heat exchange, internal energy conversion to work) that lead to temperature drop and, for reversible processes, constant entropy. Both are true and (R) is the correct explanation of (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
View Answer
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).