Question

Match List - I with List - II. List - I (Partial Derivatives) \(and\) List - II (Thermodynamic Quantity)

In the light of the above statements, choose the correct answer from the options given below:

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

Hint:

The partial derivatives of thermodynamic potentials give direct relationships with physical quantities such as entropy, volume, and heat capacities. Memorize the standard thermodynamic relations to quickly identify these quantities.

Answer 1

The Correct Option is C

Analyze each partial derivative and associate it with the correct thermodynamic quantity.

• (A) \( \left( \frac{\partial G}{\partial T} \right)_P \) is related to \( C_p \) because \( \left( \frac{\partial G}{\partial T} \right)_P = -S \), which connects to the entropy change at constant pressure.
• (B) \( \left( \frac{\partial H}{\partial T} \right)_P \) represents the entropy change, \( -S \), according to the thermodynamic relation of enthalpy and entropy.
• (C) \( \left( \frac{\partial G}{\partial P} \right)_T \) is linked to volume, \( V \), via the Gibbs free energy equation \( G = G(P, T) \).
• (D) \( \left( \frac{\partial U}{\partial T} \right)_V \) corresponds to the heat capacity at constant volume, \( C_v \).

The correct associations are: \[ (A) \longrightarrow (II), (B) \longrightarrow (I), (C) \longrightarrow (III), (D) \longrightarrow (IV) \]