Question

Which of the following is incorrect thermodynamical relation of Maxwell?

• A. \(\left(\dfrac{\partial T}{\partial V}\right)_S=-\left(\dfrac{\partial P}{\partial S}\right)_V\)
• B. \(\left(\dfrac{\partial T}{\partial P}\right)_S=\left(\dfrac{\partial V}{\partial S}\right)_P\)
• C. \(\left(\dfrac{\partial S}{\partial P}\right)_T=\left(\dfrac{\partial V}{\partial T}\right)_P\)
• D. \(\left(\dfrac{\partial S}{\partial V}\right)_T=\left(\dfrac{\partial P}{\partial T}\right)_V\)

Hint:

Always check the sign carefully in Maxwell relations. The relation \(\left(\frac{\partial S}{\partial P}\right)_T\) contains a negative sign.

Answer 1

The Correct Option is C

Concept:
Maxwell thermodynamic relations are obtained from thermodynamic potentials.

Step 1: Recall the correct relation involving pressure and entropy.
One Maxwell relation is: \[ \left(\frac{\partial S}{\partial P}\right)_T=-\left(\frac{\partial V}{\partial T}\right)_P \]

Step 2: Compare with option (C).
Option (C) gives: \[ \left(\frac{\partial S}{\partial P}\right)_T=\left(\frac{\partial V}{\partial T}\right)_P \] Here, the negative sign is missing.

Step 3: Final answer.
Therefore, option (C) is the incorrect Maxwell relation. \[ \therefore \text{Correct Answer is (C)} \]