Psychrometry — For an unsaturated gas–vapor mixture, what is the value of (wet-bulb temperature − adiabatic saturation temperature)?

Introduction:
Two cornerstone temperatures in psychrometry are the thermodynamic wet-bulb temperature and the adiabatic saturation temperature. They are often treated as interchangeable in engineering calculations, yet their definitions are different. This question probes your understanding of their relationship for unsaturated mixtures under ideal assumptions.

Given Data / Assumptions:

• Ideal (equilibrium) contact between gas and liquid.
• Negligible heat capacity effects of wetted materials; negligible radiation.
• Lewis number close to 1 (typical for air–water), so heat and mass transfer analogies apply.

Concept / Approach:

The adiabatic saturation process brings an unsaturated gas into contact with liquid in an insulated saturator until the outlet gas is saturated and in equilibrium with the outlet liquid. The wet-bulb temperature is the steady temperature reached by a wetted thermometer bulb exposed to the same gas stream with sufficient airflow. Under idealized conditions and Le ≈ 1, energy and mass balances show these temperatures coincide, leading to an essentially zero difference for engineering use.

Step-by-Step Solution:

Verification / Alternative check:

Psychrometric charts for air–water list wet-bulb lines that are nearly coincident with adiabatic saturation lines, confirming the equivalence within typical accuracy requirements.

Why Other Options Are Wrong:

A/B imply a consistent positive or negative bias; in reality, the ideal result is essentially zero. D/E are incorrect because these temperatures are well defined and comparable.

Common Pitfalls:

Confusing thermometer (sling) wet-bulb readings with thermodynamic wet-bulb temperature when ventilation is insufficient; real instruments can deviate from the ideal.

Final Answer:

zero