Clausius–Clapeyron, humidity measures, and saturation:\nWhich statement about vapor–liquid equilibrium and humidity definitions is incorrect under standard thermodynamic conventions?

Introduction / Context:
Thermodynamic relations such as the Clapeyron and Clausius–Clapeyron equations describe how saturation pressure changes with temperature and how latent heat is embedded in the slope of the vapor-pressure curve. In gas–vapor mixtures (e.g., air–water), engineers also use measures like relative humidity and percentage saturation. Knowing exactly what each term means prevents design and operating errors in drying, humidification, and distillation systems.

Given Data / Assumptions:

• Definitions follow standard chemical engineering/psychrometric conventions.
• Unsaturated mixture means partial pressure of vapor is less than the saturation pressure at the same temperature.
• Absolute humidity is mass of vapor per mass of dry carrier gas.

Concept / Approach:
Relative humidity is defined as p_v / p_sat(T). Percentage saturation also compares actual and saturation humidities but includes the ratio of total pressures and non-idealities; for ideal mixtures it is always less than relative humidity unless the system is at saturation. Therefore, equating the two for unsaturated mixtures is incorrect. The Clapeyron form dP/dT = λ / [T * (V_G − V_L)] and its integrated Clausius–Clapeyron approximation are standard. At the boiling point (where the carrier gas vanishes), absolute humidity (kg vapor/kg dry gas) diverges, effectively “infinite.”

Step-by-Step Solution:

Verification / Alternative check:
Psychrometric charts and derivations show percentage saturation equals relative humidity only at saturation; otherwise percentage saturation is lower.

Why Other Options Are Wrong (or Right):

• (a) Correct relation between latent heat and vapor-pressure slope.
• (b) Correct: as dry gas fraction → 0 at boiling, absolute humidity → ∞.
• (c) Incorrect: the two measures are not numerically equal for unsaturated mixtures.
• (d) Correct general Clapeyron equation.

Common Pitfalls:
Confusing relative humidity with percentage saturation; mixing sign conventions in Clapeyron/Clausius–Clapeyron; forgetting limiting behavior at boiling where dry gas basis collapses.

Final Answer:
For an unsaturated vapor–gas mixture, percentage saturation equals relative saturation numerically.