Answer to Question #86010 in Molecular Physics | Thermodynamics for Beast

Question

Outdoor air temperature is 0 ° C and relative humidity 90%. The air is blown into the house
and heated to 20 ° C. What is the new relative humidity?

Answer 1

Solution:

Relative humidity is the ratio of vapor density to saturation vapor density.

Relative humidity of the air at $0^\circ C:$

$$\phi_1=\frac{\rho} {\rho_{01}}100\%$$

Relative humidity of the air at $20^\circ C:$

$$\phi_2=\frac{\rho} {\rho_{02}}100\%$$

$\rho_{01}=4.84 g/m^3,\: \rho_{02}=17.2 g/m^3$ are saturation vapor densities at $0^\circ C\:and\:20^\circ C$ respectively.

From first equation:

$$\rho=\frac{\phi_1 \rho_{01}} {100\%}$$

Therefore:

$$\phi_2=\frac{\phi_1 \rho_{01}100\%} {\rho_{02}100\%}=\frac{\phi_1 \rho_{01}} {\rho_{02}}=\frac{90\%\cdot 4.84} {17.2}=25\%$$

Answer:

$$\phi_2=25\%$$