Psychrometrics of unsaturated mixtures: For an unsaturated vapor–gas mixture, the humid volume (mixture volume per unit mass of dry gas) increases with which parameter?

Introduction / Context:
Humid volume is a key psychrometric property defined as the total volume of a vapor–gas mixture per unit mass of dry gas. It influences blower sizing, duct design, and contactor performance in drying, cooling towers, and air-conditioning systems.

Given Data / Assumptions:

• Unsaturated mixture (below dew point of vapor).
• Ideal-gas approximation for mixture properties.
• Comparison at a fixed temperature when evaluating humidity effects.

Concept / Approach:
At a fixed temperature, increasing the mass of vapor (absolute humidity) per unit mass of dry gas adds more moles to the mixture, increasing total specific volume per mass of dry gas. Conversely, at fixed composition and temperature, increasing total pressure compresses the mixture, reducing specific volume (Boyle’s law behavior).

Step-by-Step Solution:
Humid volume v_h ≈ (R * T / P) * (1 + ω * (M_air / M_vapor)) per kg dry air (conceptually).At constant T: raising ω (absolute humidity) raises v_h.At constant T and composition: increasing P lowers v_h.Therefore, v_h increases with absolute humidity, not with total pressure.

Verification / Alternative check:
Psychrometric charts show lines of increasing specific volume with higher humidity ratio at a given dry-bulb temperature, validating the trend.

Why Other Options Are Wrong:
(a) Increasing total pressure decreases specific volume.

(c) and (d) contradict the established relationships; only humidity increase raises humid volume at fixed temperature.

Common Pitfalls:

• Mixing up effects of pressure and humidity on specific volume lines.
• Confusing humid volume per mass of dry gas with specific volume per mass of moist air.

Final Answer:
Absolute humidity at a given temperature