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

$\begin{array}{l}\text{Given:}\\ {\text{SVP at 0}}^{o}C\text{= 4}\text{.6 mm Hg}\\ \text{RH =40\%}\\ \Rightarrow \frac{{\text{VP of air (P}}_1\text{)}}{\text{SVP at the same temperature}}=0.4\\ \Rightarrow \frac{P_1}{4.6}=0.4\\ \Rightarrow P_1=1.84\text{mmHg}\\ \mathrm{Here},V\text{is constant.}\\ T_1=273K\\ T_2=293K\\ \text{Applying equationof state, we get}\\ \frac{P_{1}V}{T_1}=\frac{P_{2}V}{T_2}\\ \Rightarrow P_2=\frac{P_1{T}_2}{T_1}\\ \Rightarrow P_2=\frac{1.84\times 293}{273}\\ \Rightarrow P_2=1.97\\ \text{RH inside home=}\frac{{\text{VP of air (P}}_2\text{)}}{\text{SVP at the same temperature}}\times 100\%\\ \text{SVP at the same temperature}=18\text{mmHg}\\ \Rightarrow RH=\frac{1.97}{18}\times 100=10.9\%\end{array}$