Effect of pressure on phase-change points: Which of the following quantities increases when the external pressure on a pure substance is increased?

Introduction:
Designers frequently need to predict how melting and boiling points shift with pressure in separations and materials processing. These dependencies arise from equilibrium thermodynamics and are captured by the Clapeyron and Clausius–Clapeyron relations for phase boundaries.

Given Data / Assumptions:

• Pure, typical substances with positive solid–liquid volume change (most solids are denser than their melts).
• Boiling refers to liquid–vapor equilibrium.
• Wax behaves like a typical solid (melting point increases with pressure).

Concept / Approach:
Boiling point increases with pressure because a higher external pressure requires a higher saturation temperature for the vapor pressure to match it. For melting, most substances contract upon solidification (solid is denser), so increasing pressure favors the solid phase and raises the melting point. Wax follows this normal trend. (Water is a notable exception: it expands upon freezing, hence its melting point decreases with pressure.)

Step-by-Step Solution:
Use Clausius–Clapeyron: ln P_sat increases with 1/T; higher P → higher T for boiling.For melting: dT/dP = T * ΔV / ΔH_fus; with ΔV < 0 (solid denser), dT/dP > 0.Therefore, both melting point (for wax) and boiling point increase with pressure.

Verification / Alternative check:
Phase diagrams for typical organics show positive slopes for solid–liquid lines and rising boiling curves with pressure.

Why Other Options Are Wrong:

• Neither: Contradicted by basic phase-equilibrium relations.
• Only triple-point temperature: Pressure affects the entire coexistence curves, not a single point only.

Common Pitfalls:
Overgeneralizing water’s anomalous behavior to all materials; most behave like wax, not water.

Final Answer:
both (a) and (b)