Project ForgeThermodynamics
First Law of Thermodynamics
GATE 2016
Hard
The partial pressure of water vapour in a moist air sample of relative humidity 70% is 1.6 kPa, the total pressure being 101.325 kPa. The relation between saturation temperature (Ts in K) and saturation pressure (ps in kPa) for water is ln(ps/po)=14.317-5304/Ts, where po=101.325 kPa. The dry bulb temperature of the moist air sample (in °C) is __________.
19.7 °C(± 0.3 accepted)
Explanation
RH = pv/ps(Tdb), so ps(Tdb) = pv/RH = 1.6/0.7 ≈ 2.286 kPa. Using ln(ps/po)=14.317-5304/Ts: ln(2.286/101.325)=-3.792=14.317-5304/Ts → 5304/Ts=18.109 → Ts≈292.9 K ≈ 19.7°C.
Source: GATE ME 2016 Set-2 (2016)
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