GATE 2023 CH – Question 56
Partially saturated air at 1 bar and 50 °C is contacted with water in an adiabatic saturator. The air is cooled and humidified to saturation, and exits at 25 °C with an absolute humidity of 0.02 kg water per kg dry air. Use latent heat of vaporization of water as 2450 kJ kg$^{-1}$, and average specific heat capacity for dry air and water, respectively as 1.01 kJ kg$^{-1}$K$^{-1}$ and 4.18 kJ kg$^{-1}$K$^{-1}$. If the absolute humidity of air entering the adiabatic saturator is $\mathcal{H} \times 10^{-3}$ kg water per kg dry air, the value of $\mathcal{H}$ is __________ (rounded off to two decimal places).
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Correct answer: 9.25 to 9.35
Explanation
The adiabatic saturation balance is $c_s(T - T_s) = \lambda_s(H_s - H)$ with the humid heat $c_s = 1.01 + 4.18H$. Here $(1.01 + 4.18H)(50 - 25) = 2450(0.02 - H)$. So $25.25 + 104.5H = 49 - 2450H$, giving $2554.5H = 23.75$ and $H = 9.297 \times 10^{-3}$ kg/kg. So $\mathcal{H} = 9.30$.