An apartment has the dimensions 20 m by 10 m by 7 m. The temperature is 25°C, and the relative humidity is 56 percent. What is the total mass (in kg) of water vapor in the air in the apartment?
The total mass of water vapor in the air in the apartment can be calculated using the following equation:
Mass (kg) = Volume (m3) x Density (kg/m3)
Density of water vapor at 25°C and 56% relative humidity is 0.0075 kg/m3.
Therefore, the total mass of water vapor in the air in the apartment is:
Mass (kg) = 20 m x 10 m x 7 m x 0.0075 kg/m3 = 105 kg
It is way lower:
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.
So yeah, about 2kg.