Question

Consider an ensemble of thermodynamic systems, each of which is characterized by the same number of particles, pressure and temperature. The thermodynamic function describing the ensemble is

• A. Enthalpy
• B. Helmholtz free energy
• C. Gibbs free energy
• D. Entropy

Hint:

If temperature and pressure are fixed, always choose the Gibbs free energy as the natural thermodynamic potential.

Answer 1

The Correct Option is C

Step 1: Identify ensemble constraints.
The ensemble has fixed: • Number of particles, • Pressure, • Temperature (N, P, T).

Step 2: Connect constraints to thermodynamic potentials.
Each ensemble is described by a thermodynamic potential that is minimised under its natural variables: • Helmholtz free energy $F$ → natural variables $(T, V)$, • Gibbs free energy $G$ → natural variables $(T, P)$, • Enthalpy $H$ → natural variables $(S, P)$.

Step 3: Compare with given ensemble.
Since the ensemble is at fixed $(T,P)$, the appropriate potential is Gibbs free energy $G=H-TS$.

Step 4: Conclusion.
The thermodynamic function describing such an ensemble is the Gibbs free energy.