GATE 2016 ME (ME2) – Question 57

Thermal Engineering Applications · Psychrometry and air-conditioning · 2 marks · Numerical answer

A moist-air sample has relative humidity 70%, water-vapour partial pressure 1.6 kPa and total pressure 101.325 kPa. Treat it as an ideal mixture of water vapour and dry air. Saturation pressure and temperature obey $\ln(p_s/p_0)=14.317-5304/T_s$, with $p_0=101.325$ kPa and $T_s$ in K. The sample dry-bulb temperature is ______ °C.

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Correct answer: 19.5 to 19.9

Explanation

Relative humidity is pv/ps, giving ps=1.6/0.70=2.285714kPa. Rearrange ln(ps/101.325)=14.317−5304/Ts to obtain Ts=5304/[14.317−ln(2.285714/101.325)]=292.8986K. The air dry-bulb temperature is therefore **19.7486°C** using273.15K offset.