Discussion
Air at 70 °C and 0.015 humidity ratio is cooled adiabatically by spraying water. The final temperature of the air is 55 °C. Specific heat capacities of dry air and water vapour are 1.005 and 1.88 kJ kg−1 K−1, respectively and latent heat of vapourization of water at 0 °C is 2501.7 kJ kg−1. The absolute humidity of the outlet air, in kg water vapour per kg dry air is
Answer: C
The outlet humidity is about 0.021 kg/kg dry air.
Adiabatic cooling by spraying water keeps the enthalpy of the moist air essentially constant, with \(h = 1.005\,t + W(2501.7 + 1.88\,t)\) in kJ per kg dry air:
\[ \begin{aligned} h_{1} &= 1.005(70) + 0.015(2501.7 + 131.6) \\ &= 70.35 + 39.50 = 109.85 \\ 109.85 &= 1.005(55) + W_{2}(2501.7 + 103.4) \\ W_{2} &= \frac{109.85 - 55.28}{2605.1} = 0.0209 \end{aligned} \]
The air gains about 0.006 kg of water per kg dry air as it cools by 15 °C. 0.017 and 0.019 add too little moisture to balance the sensible heat given up, and 0.023 adds too much.
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