Question Bank MCQ • 1 Mark Section 5: Thermodynamics & Statistical Physics Thermodynamics & Statistical Physics - Module 4

QB_PH_128: Thermodynamics & Statistical Physics - Module 4

Question Statement

From $dF = -S dT - P dV$, the corresponding Maxwell relation is:
(A) \left(\frac{\partial S}{\partial V}\right)_T = \left(\frac{\partial P}{\partial T}\right)_V
(B) \left(\frac{\partial S}{\partial P}\right)_T = -\left(\frac{\partial V}{\partial T}\right)_P
(C) \left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V
(D) \left(\frac{\partial T}{\partial P}\right)_S = \left(\frac{\partial V}{\partial S}\right)_P
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Mixed partial derivatives of Helmholtz free energy: $\frac{\partial S}{\partial V}\Big|_T = \frac{\partial P}{\partial T}\Big|_V$.
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