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.

Answer 1

The relative humidity in the room is 10.9%

Explanation:

Given data in the question

Saturated vapour pressure at $=4.6 \mathrm{mm} \mathrm{Hg}$  

RH (Relative humidity) $=40 \% |$  

$\frac{\text { vapour pressure of air (p1) }}{\text { Saturated vapour pressure at the same temperature }}=0.4$

$\frac{p_{1}}{4.6}=0.4$

$P_{1}=1.84 \mathrm{mm} \mathrm{Hg}$

V = constant.  

$T_{1}=273 K$

$T_{2}=293 K$

Applying state equation, we get

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

$\begin{aligned}&P_{2}=\frac{P_{2} T_{2}}{T 1}\\&P 2=1.84 \times \frac{293}{273}\\&P 2=1.97\end{aligned}$

RH (Relative humidity) inside home=

( vapour pressureof air (P2))/(Saturated vapour pressure at the same temperature)*100%

Saturated pressure of the vapour at the same temperature=18 mm Hg

$\mathrm{RH} \text { (Relative humidity) }=\frac{1.97}{18} \times 100=0.109 \times 100=10.9 \%$