Question

Which one of the following does not change during a phase change such as melting, vaporization and sublimation?

• A. Specific internal energy
• B. Specific enthalpy
• C. Specific entropy
• D. Specific Gibbs Free energy

Hint:

In first-order phase transitions, the primary thermodynamic properties ($u, h, s, v$) change discontinuously, but the specific Gibbs free energy $g$ remains continuous across the phase boundary.

Answer 1

The Correct Option is D

Concept: During a phase change of a pure substance occurring at constant temperature ($T$) and pressure ($P$), the two phases coexist in thermodynamic equilibrium. Let us examine how the different thermodynamic properties behave during a phase transition like boiling water to steam:

• Specific Internal Energy ($u$) & Specific Enthalpy ($h$): Heat (latent heat) must be added or removed to break intermolecular bonds during a phase transition. This causes a discontinuous jump in internal energy and enthalpy ($\Delta h = \Delta h_{\text{latent}} \neq 0$).

• Specific Entropy ($s$): Because heat is transferred, the molecular disorder changes ($\Delta s = \frac{\Delta h_{\text{latent}}}{T} \neq 0$).

• Specific Gibbs Free Energy ($g$): The criterion for phase equilibrium at constant $T$ and $P$ requires the chemical potential ($\mu$) of both coexisting phases to be equal. For a pure component, the chemical potential is identical to the specific Gibbs free energy: \[ g_{\text{phase 1}} = g_{\text{phase 2}} \implies \Delta g = 0 \]

Step 1: Apply the fundamental property relation for Gibbs Free Energy.
The fundamental differential equation for $g$ is: \[ dg = v \, dP - s \, dT \] During a phase transition, both temperature and pressure are fixed, so $dP = 0$ and $dT = 0$. This confirms that $dg = 0$, meaning the specific Gibbs free energy remains continuous and unchanging as a molecule transitions from one phase to another.