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

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Solution

Relative humidity = 40 %

SVP = 4.6 mm of Hg

0.4 = $\frac{V P}{4.6}$

$\Rightarrow V P = 0.4 \times 4.6 = 1.84$

$\frac{P_{1} V}{T_{1}} = \frac{P_{2} V}{T_{2}}$

$\Rightarrow \frac{1.84}{273} = \frac{P^{2}}{293}$

$\Rightarrow P_{2} = \frac{1.84 \times 293}{273}$

Relative humidity at $20^{0}$ C

= $\frac{V P}{S V P} = \frac{1.83 \times 293}{273 \times 18}$

= 0.109 = 10.9 %

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On a winter day, the outside temperature is 00 C and relative humidity 40 %. The air from outside comes into a room and is heated to 200 C. What is the relative humidity in the room ? The saturation vapour pressure at 00 C is 4.6 mm of mercury and at 200 C it is 18 mm of mercury.

Relative humidity = 40 % SVP = 4.6 mm of Hg 0.4 =VP4.6 ⇒VP=0.4×4.6=1.84 P1VT1=P2VT2 ⇒1.84273=P2293 ⇒P2=1.84×293273 Relative humidity at 200 C = VPSVP=1.83×293273×18 = 0.109 = 10.9 %