What is the total mass (in kg) of water vapor in the air in the apartment?

Question

An apartment has the dimensions 15 m by 8 m by 5 m. The temperature is 25°C, and the relative humidity is 57 percent. What is the total mass (in kg) of water vapor in the air in the apartment?

Answer 1

To find the mass of water at a given temperature and relative humidity, you have to know the mass of water vapor in a cubic meter of air when the air is saturated at the temperature.

First calculate the volume of the room in m³. Multiply the 3 dimensions together. Volume = 15*8*5 = 600 m³.

I found data for the vapor density of saturated water vapor at 20 C and 30 C which is 0.017 and 0.03 kg/m³.

Linearly interpolate to get the value at 25 C to get 0.0065 kg/m³. This is an approximation as the curve is not linear.

The total mass of water in the room at saturation is 600 m³ x 0.0065 kg/m³ = 3.9 kg. As the relative humidity is 57%, the actual mass of water vapor is 0.57 x 3.9 kg = 2 kg approximately.