Psychrometrics – precise definition of relative humidity Relative humidity (RH) is defined as which ratio under standard psychrometric convention?
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Apartial pressure of the vapor to the saturation vapor pressure at room (ambient) temperature, regardless of gas temperature
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Bpartial pressure of the vapor to the saturation vapor pressure at the gas (air) temperature
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Cactual humidity ratio to saturation humidity ratio at 25°C for all cases
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Dnone of these
Answer
Correct Answer: partial pressure of the vapor to the saturation vapor pressure at the gas (air) temperature
Explanation
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:
State the pressure-based definition: RH = p_v / p_vs at T_air.Note the humidity-ratio equivalence at the same T_air.Emphasize that using a fixed “room temperature” or unrelated temperature gives wrong RH.Therefore, choose the option specifying saturation at the gas temperature.Reject options that fix a temperature irrespective of actual gas conditions.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