During a first-order phase transition such as melting, vaporisation, or sublimation at equilibrium, which specific thermodynamic property remains unchanged for the substance across the coexisting phases?

Introduction / Context:
Phase changes involve latent heat and discontinuities in certain properties. Understanding which property is continuous across coexisting phases is fundamental for phase-equilibrium calculations, Clapeyron relations, and chemical potential concepts.

Given Data / Assumptions:

• Consider a pure substance at equilibrium between two phases (e.g., liquid–vapour) at given T and P.
• Phase change occurs reversibly at these conditions.

Concept / Approach:
At phase equilibrium, the chemical potential of the substance is the same in each phase. For a pure substance, the chemical potential equals the molar Gibbs free energy, g. Thus, g_liquid = g_vapour at the coexistence T and P. In contrast, molar enthalpy (h), internal energy (u), entropy (s), and specific volume (v) undergo finite jumps corresponding to latent heat and volume change.

Step-by-Step Solution:

Verification / Alternative check:
The Clapeyron equation relates discontinuities (Δh, Δv) while enforcing equality of μ or g across phases, reinforcing that g is the continuous potential.

Why Other Options Are Wrong:

• Enthalpy/internal energy/entropy: change by latent heat terms.
• Specific volume: typically changes, often sharply at vaporisation.

Common Pitfalls:
Confusing continuity of Gibbs free energy (equal values across phases) with its derivatives; remember that first derivatives such as entropy and volume are discontinuous in first-order transitions.

Final Answer:
Gibbs free energy (molar)