GATE 2022 CH – Question 57
The dry-bulb temperature of air in a room is 30 °C. The Antoine equation for water is given as $\ln P^{sat} = 12.00 - \frac{4000}{T - 40}$ where $T$ is the temperature in K and $P^{sat}$ is the saturation vapor pressure in bar. The latent heat of vaporization of water is 2000 kJ kg$^{-1}$, the humid heat is 1.0 kJ kg$^{-1}$ K$^{-1}$, and the molecular weights of air and water are 28 kg kmol$^{-1}$ and 18 kg kmol$^{-1}$, respectively. If the absolute humidity of air is $Y'$ kg moisture per kg dry air, then for a wet-bulb depression of 9 °C, $1000 \times Y' = $ _________________ (rounded off to one decimal place).
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Correct answer: 11.14 to 11.26
Explanation
The wet-bulb temperature is $30 - 9 = 21$ °C $= 294.15$ K. Then $\ln P^{sat} = 12 - \frac{4000}{254.15} = -3.738$ and $P^{sat} = 0.02378$ bar (at 1 bar total pressure). The saturation humidity at the wet bulb is $Y_w' = \frac{18}{28} \times \frac{0.02378}{1 - 0.02378} = 0.01566$. The wet-bulb relation is $Y' = Y_w' - \frac{c_s}{\lambda_w}(T - T_w) = 0.01566 - \frac{1.0}{2000} \times 9 = 0.01116$. So $1000Y' = 11.2$.