Psychrometrics – precise definition of relative humidity Relative humidity (RH) is defined as which ratio under standard psychrometric convention?

Introduction / Context:
Relative humidity is a fundamental measure in drying, HVAC, and environmental control. Precision matters: RH must reference saturation properties at the actual gas (air) temperature, not an arbitrary or “room” temperature, to be thermodynamically meaningful and comparable across conditions.

Given Data / Assumptions:

• Ideal-gas behavior for water vapor in air is assumed for typical calculations.
• Saturation vapor pressure depends strongly on temperature.
• Humidity ratio and partial pressure definitions are standard.

Concept / Approach:
Relative humidity RH is defined as RH = p_v / p_vs(T_air), where p_v is the water vapor partial pressure and p_vs(T_air) is the saturation vapor pressure evaluated at the same gas temperature. An equivalent definition uses humidity ratios: RH = (w / w_s) at the gas temperature. Any definition referencing a different temperature than the gas temperature is incorrect because saturation properties change markedly with temperature.

Step-by-Step Solution:

Verification / Alternative check:
Psychrometric charts are constructed at a specified total pressure and evaluate saturation curves at the current air temperature; RH is read as a ratio at that temperature, confirming the definition.

Why Other Options Are Wrong:

• Room-temperature reference: Incorrect when air is not at that exact temperature.
• Fixed 25°C ratio: Arbitrary and wrong for general conditions.
• None of these: Incorrect because a correct definition exists in option (b).

Common Pitfalls:
Confusing RH with absolute humidity or humidity ratio; RH is temperature dependent, so the same moisture content can yield very different RH at different temperatures.

Final Answer:
partial pressure of the vapor to the saturation vapor pressure at the gas (air) temperature