Subtopic: Psychrometry – properties of air-water vapour mixture
Question Statement:
If absolute humidity at saturation and percentage humidity of air are 0.075 kg water vapour (kg dry air)⁻¹ and 60% respectively, the relative humidity of air is
Options:
(A) 57.4%
(B) 60.0%
(C) 62.7%
(D) 74.5%
Official Answer Key:
C
Step-by-Step Solution & Explanation
Percentage humidity μ = W/Ws, so humidity ratio W = μ·Ws = 0.60×0.075 = 0.045 kg/kg. Relating percentage humidity to relative humidity (φ) via the psychrometric relation μ = φ / [1 − (1−φ)(Ws/(0.622+Ws))], solving iteratively for φ with Ws=0.075: φ = μ / [1 − (1−μ)(Ws/(0.622+Ws))] = 0.60/[1 − 0.40×(0.075/0.697)] = 0.60/[1−0.0430] = 0.60/0.957 = 0.627 = 62.7%, matching option (C). (Percentage humidity and relative humidity are numerically close but not identical — option (B) 60.0% is the value obtained if the two terms are wrongly treated as equal.)
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