Question

Which one is not correct relationship?

• A. \(G=H-TS\)
• B. \(H=U+PV\)
• C. \(G=H+TS\)
• D. \(A=U-TS\)

Hint:

To remember the signs, think of "Free Energy" as the energy you have after paying the "Entropy Tax" (\(TS\)). Therefore, for both \(G\) and \(A\), the term is always minus \(TS\).

Answer 1

The Correct Option is C

Concept: Thermodynamic potentials are state functions used to describe the internal energy and equilibrium of a system. The four primary potentials are Internal Energy (\(U\)), Enthalpy (\(H\)), Helmholtz Free Energy (\(A\) or \(F\)), and Gibbs Free Energy (\(G\)). They are related via Legendre transformations.

Step 1: Review the standard definitions of thermodynamic potentials.

• Enthalpy (\(H\)): Defined as the total heat content of a system. \[ H = U + PV \]
• Helmholtz Free Energy (\(A\)): The energy available to do work at constant temperature and volume. \[ A = U - TS \]
• Gibbs Free Energy (\(G\)): The energy available to do work at constant temperature and pressure. \[ G = H - TS \]

Step 2: Identify the incorrect relationship.
Comparing the standard definitions to the given options:
• Option (1) \(G=H-TS\) is correct.
• Option (2) \(H=U+PV\) is correct.
• Option (4) \(A=U-TS\) is correct.
• Option (3) states \(G=H+TS\). This is incorrect because Gibbs Free Energy is defined as the difference between enthalpy and the energy unavailable for work (\(TS\)), not their sum.