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

Step 1: Understanding the Concept:
This question requires matching fundamental equations and definitions from thermodynamics with their respective names or descriptions.
Step 2: Detailed Explanation:

(A) Clausius-Clapeyron equation: This equation relates the slope of the coexistence curve between two phases of matter on a pressure-temperature (P-T) diagram to the latent heat (L) and the change in volume (V₂ - V₁) during the phase transition. The equation is \( \frac{dP}{dT} = \frac{L}{T(V_2 - V_1)} \). This matches with (IV).

(B) Gibbs Function (G): The Gibbs free energy is a thermodynamic potential defined as \( G = H - TS \). Since Enthalpy \( H = U + PV \), the Gibbs function can be written as \( G = U + PV - TS \). This matches with (III).

(C) Enthalpy (H): Enthalpy is a thermodynamic potential defined as the sum of the internal energy (U) and the product of pressure and volume (PV). The equation is \( H = U + PV \). This matches with (II).

(D) Adiabatic change in Perfect Gas: An adiabatic process is one that occurs without heat or mass transfer. For a perfect gas undergoing a reversible adiabatic process, the relationship between pressure (P) and volume (V) is given by \( PV^\gamma = \text{constant} \), where \( \gamma \) is the heat capacity ratio. This matches with (I).
Step 3: Final Answer:
Based on the analysis, the correct pairings are:
(A) - (IV)
(B) - (III)
(C) - (II)
(D) - (I)
This corresponds to option (A).