The temperature and humidity of air are 27°C and 50% on a particular day. Calculate the amount of vapour that should be added to 1 cubic metre of air to saturate it. The saturation vapour pressure at 27°C = 3600 Pa.

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Solution

$\begin{array}{l} Here, \\ SVP=3600 Pa \\ T = 273 + 27 = 300K \\ {V = 1m}^{3} \\ M = 18 g for water \\ R H = 50 % \\ \Rightarrow \frac{V P}{S V P} = 0.5 \\ \Rightarrow V P = 0.5 \times 3600 = 1800 \\ {Let m}_{1} be the mass of water present in the 50% humid air. \\ PV = nRT \\ \Rightarrow P V = \frac{m_{1}}{M} R T \\ \Rightarrow 1800 = \frac{m_{1}}{18} \times 8.3 \times 300 \\ \Rightarrow m_{1} = 13 g \\ Required pressure for saturation=3600 Pa \\ {Let m}_{2} be the amount of water required for saturation. \\ \Rightarrow 3600= \frac{m_{2}}{M} R T \\ \Rightarrow m_{2} = \frac{3600 \times 18}{8.3 \times 300} = 26 g \\ {Total excess water vapour that has to be added = m}_{2} - m_{1} \\ = 36 - 13 = 13 g \end{array}$

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