Question

Match List - I with List - II.

Choose the correct answer from the options given below :

• A. ( A ) − ( I I ) , ( B ) − ( I ) , ( C ) − ( I I I ) , ( D ) − ( I V )
• B. ( A ) − ( I ) , ( B ) − ( I I ) , ( C ) − ( I V ) , ( D ) − ( I I I )
• C. ( A ) − ( I I ) , ( B ) − ( I ) , ( C ) − ( I V ) , ( D ) − ( I I I )
• D. ( A ) − ( I I ) , ( B ) − ( I I I ) , ( C ) − ( I ) , ( D ) − ( I V )

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

The task involves correlating partial derivatives of thermodynamic quantities with their physical interpretations or symbols. Let's analyze each derivative:

1. Partial Derivative \( \left( \dfrac{\partial G}{\partial T} \right)_P \): This represents the variation of Gibbs free energy \( G \) with temperature \( T \) at constant pressure \( P \). In thermodynamics, this is directly related to entropy \( S \) by the equation \(S = - \left( \dfrac{\partial G}{\partial T} \right)_P\). Therefore, it corresponds to \(-S\) (II).
2. Partial Derivative \( \left( \dfrac{\partial H}{\partial T} \right)_P \): This derivative signifies the change in enthalpy \( H \) with respect to temperature \( T \) at constant pressure \( P \). It is equivalent to the heat capacity at constant pressure, \( C_P \). Consequently, it matches with \( C_P \) (I).
3. Partial Derivative \( \left( \dfrac{\partial C}{\partial P} \right)_T \): While typically examined in the context of compressibility and expansivity, in this specific representation, it relates to volume \( V \), which is a more intuitive conceptual match. Thus, it corresponds to volume \( V \) (IV).
4. Partial Derivative \( \left( \dfrac{\partial U}{\partial V} \right)_V \): This derivative describes the change in internal energy \( U \) with volume \( V \) at constant volume. It is crucial for characterizing \( C_V \) under specific conditions or during particular transformations. Hence, it matches with \( C_V \) (III).

The resulting correct matches are: ( A ) − ( I I ) , ( B ) − ( I ) , ( C ) − ( I V ) , ( D ) − ( I I I ).