Answer to Question #222563 in Physics for vsd

Question

An apartment has the dimensions 20 m by 10 m by 7 m. The temperature is 25°C, and the relative humidity is 51 percent. What is the total mass (in kg) of water vapor in the air in the apartment?

Answer 1

Given:

$V=20\times 10\times 7=1400\:\rm m^3$

$\varphi=51\%$

$\rho_{\rm sv}=23\:\rm g/m^3$

The relative humidity

$$\varphi=\frac{\rho}{\rho_{\rm sv}}\times 100\%$$

The density of water vapor in the air

$$\rho=\rho_{\rm sv}*\frac{\varphi}{100\%}=23*\frac{51\%}{100\%}=11.73\:\rm g/m^3$$

The total mass (in kg) of water vapor in the air in the apartment

$$m=\rho*V=11.73*1400=16422\:\rm g=16.422\:\rm kg$$