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Question
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.
Use R = 8.3 J K-1 mol-1
Solution
Here ,
SVP = 3600 Pa
T = 273 + 27 = 300K
`"V" = 1 "m"^3`
M = 18 g for water
RH = 50%
⇒ `(VP)/(SVP) = 0.5`
⇒ `"VP" = 0.5 xx 3600 = 1800`
Let m1 be the mass of water present in the 50% humid air.
PV = nRT
⇒`PV = m_1/MRT`
⇒ `1800 = "m"_1/18 xx 8.3 xx 300`
⇒ `"m"_1` = 13 g
Required pressure for saturation = 3600 Pa
Let `"m"_2` be the amount of water required for saturation .
⇒ 3600 = `"m"_2/M`RT
⇒ `"m"_2` = `(3600 xx 18)/(8.3 xx 300)` = 26g
Total excess water vapour that has to be added = `"m"_2 - "m"_1`
⇒ 36 - 13 = 13 g
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