Question

Match List I with List II:

List I	List II
(A) (∂S/∂P)T	(I) (∂P/∂T)V
(B) (∂T/∂V)S	(II) (∂V/∂S)P
(C) (∂T/∂P)S	(III) -(∂V/∂T)P
(D) (∂S/∂V)T	(IV) -(∂P/∂S)V

Choose the correct answer from the options given below:

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

Hint:

These relations come from the equality of mixed second partial derivatives of the thermodynamic potentials (Maxwell’s relations).

Answer 1

The Correct Option is A

Use the well-known Maxwell relations in thermodynamics
$\left( \frac{\partial S}{\partial P} \right)_T = - \left( \frac{\partial V}{\partial T} \right)_P \implies (A) \rightarrow (III), $
$\left( \frac{\partial S}{\partial V} \right)_T =  \left( \frac{\partial P}{\partial T} \right)_V \implies (D) \rightarrow (I), $
$\left( \frac{\partial T}{\partial V} \right)_S = - \left( \frac{\partial P}{\partial S} \right)_V \implies (B) \rightarrow (IV)$, 
$\left( \frac{\partial T}{\partial P} \right)_S = \left( \frac{\partial V}{\partial S} \right)_P \implies (C) \rightarrow (II).$
Thus the correct matches are:
$A \rightarrow III, \quad B \rightarrow IV, \quad C \rightarrow II, \quad D \rightarrow I$