GATE 2017 ME (ME1) – Question 45
Moist air is an ideal-gas mixture of water vapour and dry air, with molecular weights 18 and 28.84 respectively. At 100 kPa, 30°C and 55% relative humidity, with saturation vapour pressure 4246 Pa at 30°C, find grams of water vapour per kg of dry air.
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Correct answer: 14.7 to 15.1
Explanation
Vapour partial pressure is $p_v=0.55(4246)=2335.3$ Pa, leaving dry-air pressure $p_a=100000-2335.3=97664.7$ Pa. The ideal-gas mass ratio is $w=(M_v/M_a)(p_v/p_a)=(18/28.84)(2335.3/97664.7)=0.014924$ kg/kg. Converting to grams gives 14.92 g of vapour per kg of dry air.