NEET Thermodynamics MCQs & PYQs

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.

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).

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.

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) 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.

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).

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.

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).

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.

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.