Question

Which of the following relations is (are) true for thermodynamic variables?

• A. $TdS = C_V dT + T\left(\dfrac{\partial P}{\partial T}\right)_V dV$
• B. $TdS = C_P dT - T\left(\dfrac{\partial V}{\partial T}\right)_P dP$
• C. $dF = -S dT + P dV$
• D. $dG = -S dT + V dP$

Hint:

Remember: $dF = -S dT - P dV$ and $dG = -S dT + V dP$ are fundamental exact thermodynamic identities.

Answer 1

The Correct Option is A, B, D

Step 1: Use Maxwell relations.
Thermodynamic identities: $dF = -S\,dT - P\,dV$ (not +P dV) → (C) is false. $dG = -S\,dT + V\,dP$ → (D) correct.

Step 2: Entropy differential identities.
Using exact relations for $S(T,V)$: $TdS = C_V dT + T\left(\frac{\partial P}{\partial T}\right)_V dV$ → (A) correct. $TdS = C_P dT - T\left(\frac{\partial V}{\partial T}\right)_P dP$ → (B) is incorrect sign.

Step 3: Conclusion.
Correct statements are (A) and (D).