Question

Which of the following equation is not correct?

• A. $dG = Vdp - SdT$
• B. $dA = -pdV + SdT$
• C. $dH = TdS + Vdp$
• D. $dU = TdS - pdV$

Hint:

Use the mnemonic "Good Physicists Have Studied Under Very Able Teachers" to remember the positions of $G, P, H, S, U, V, A, T$ in the thermodynamic square.

Answer 1

The Correct Option is B

Step 1: Concept The fundamental thermodynamic equations relate the change in internal energy ($U$), enthalpy ($H$), Gibbs free energy ($G$), and Helmholtz free energy ($A$) to changes in entropy ($S$), temperature ($T$), pressure ($p$), and volume ($V$).

Step 2: Meaning Helmholtz free energy is defined as $A = U - TS$. Taking the differential gives $dA = dU - TdS - SdT$.

Step 3: Analysis Substituting the first law expression $dU = TdS - pdV$ into the differential for $A$: $dA = (TdS - pdV) - TdS - SdT$, which simplifies to $dA = -pdV - SdT$.

Step 4: Conclusion Comparing this to the options, option (B) incorrectly uses a positive sign for the $SdT$ term. All other Maxwell relations provided are correct. Final Answer: (B)