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Question
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 saturation vapour pressure at 0°C is 4.6 mm of mercury and at 20°C it is 18 mm of mercury.
Solution
Given :
SVP at `0^circC` = 4.6 mm Hg
RH = 40%
⇒`("VP of air" ("P"_1))/"SVP at the same temperature" = 0.4`
⇒ `"P"_1/4.6` = 0.4
⇒ `"P"_1 = 1.84 "mmHg"`
Here , V is constant .
`"T"_1` = 273K
`"T"_2` = 293K
Applying equation of state, we get
`(P_1V)/(T_1) = (P_2V)/(T_2)`
⇒ `P_2 = (P_1T_2)/T_1`
⇒ `P_2 = (1.84 xx 293)/273`
⇒ `P_2` = 1.97
RH inside home = `("VP of air" (P_2))/("SVP at the same temperature") xx 100%`
SVP at the same temperature = 18 mmHg
⇒ RH = `1.97/18 xx 100 = 10.9%`
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