Question

Match List-I with List-II

\[ \begin{array}{|l|l|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; \text{Classius Clapeyron equation} & (I) \; PV^\gamma = \text{constant} \\ (B) \; \text{Gibbs Function} & (II) \; U + PV \\ (C) \; \text{Enthalpy} & (III) \; U - TS + PV \\ (D) \; \text{Adiabatic change in Perfect Gas} & (IV) \; \dfrac{dP}{dT} = \dfrac{L}{T (V_2 - V_1)} \\ \hline \end{array} \]
Choose the correct answer from the options given below:

• (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
• (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
• (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
• (A) - (II), (B) - (I), (C) - (IV), (D) - (III)

Hint:

Remember the four main thermodynamic potentials:
Internal Energy: U
Enthalpy: H = U + PV
Helmholtz Free Energy: F = U - TS
Gibbs Free Energy: G = H - TS = U + PV - TS
Knowing these definitions by heart is crucial for thermodynamics questions.

Answer 1

The Correct Option is A

Objective: Match thermodynamic equations and definitions with their names.

Analysis:

(A) Clausius-Clapeyron equation: Describes the slope of the coexistence curve on a P-T diagram, relating it to latent heat (L) and volume change (V₂ - V₁) as \( \frac{dP}{dT} = \frac{L}{T(V_2 - V_1)} \). This corresponds to (IV).

(B) Gibbs Function (G): Defined as \( G = H - TS \). Substituting \( H = U + PV \), it becomes \( G = U + PV - TS \). This corresponds to (III).

(C) Enthalpy (H): Defined as \( H = U + PV \), representing the sum of internal energy and the product of pressure and volume. This corresponds to (II).

(D) Adiabatic change in Perfect Gas: For a reversible adiabatic process, the relationship is \( PV^\gamma = \text{constant} \), where \( \gamma \) is the heat capacity ratio. This corresponds to (I).

Conclusion: The correct pairings are (A)-(IV), (B)-(III), (C)-(II), and (D)-(I). This aligns with option (A).