On a winter day, the outside temperature is `0^(@)C` and relative humidity 40%.The air from outside comes into a room and is heated to `20^(@)C. What is the relative humidity in the room? The saturated vapour pressure at `0^(@)C`is 4.6mm of mercury and at `20^(@)C`it is 18mm of mercury.

Explanation

Relative humidity = 40%
SVP = 4.6 mm of Hg
0.4 = VP/ 4.6
` rArr VP = 0.4 xx 4.6 = 1.84`
`((P_1)V/T_1) = ((P_2)V/ (T_2))`
` rArr 1.84/273 = (P_2 / 293)`
` rArr (P_2) = (1.84 xx 293 / 273)`
` Relative humidity at 20^@C. `
` = VP/SVP = ((1.83 xx 293)/(273 xx 18))`
` 0.109 = 10.9% ` .