What is the mass of water in a closed room 5.2m x 6.3m x 2.5m when the temperature is 24 degrees celsius and the relative humidity is 65%?
To find the mass of water in the closed room, we will need to calculate the volume of water in the air and then multiply it by the density of water.
Step 1: Calculate the volume of the closed room.
Volume = Length x Width x Height
= 5.2m x 6.3m x 2.5m
= 82.02 cubic meters
Step 2: Calculate the volume of water in the air.
To calculate the volume of water vapor in a given volume of air, we need to consider the relative humidity and the maximum amount of moisture the air can hold at that temperature, known as the saturation vapor pressure.
First, we need to find the saturation vapor pressure at 24 degrees Celsius. We can use a table or an equation for this purpose. Let's assume the saturation vapor pressure at 24 degrees Celsius is 24.3 millibars.
The actual vapor pressure can be found by multiplying the saturation vapor pressure by the relative humidity:
Actual vapor pressure = Saturation vapor pressure x (Relative humidity/100)
= 24.3 mb x (65/100)
≈ 15.8 mb
Using the ideal gas law, we can equate the pressure and find the number of moles of water vapor (n). Since the number of moles (n) is directly proportional to the volume (V), we can write:
P x V = n x R x T
Where:
P = Pressure of the water vapor (15.8 mb)
V = Volume of the water vapor (unknown)
n = Number of moles of water vapor (unknown)
R = Gas constant (8.314 J/mol K)
T = Temperature in Kelvin (24 degrees Celsius + 273.15 = 297.15 K)
Simplifying the equation, we get:
V = (n x R x T) / P
Step 3: Convert the volume of water vapor to mass.
Since we have the volume of water vapor, we can now calculate the mass using the density of water. The density of water at room temperature and atmospheric pressure is approximately 1000 kg/m³.
Mass of water vapor = Volume of water vapor x Density of water
Finally, we have the mass of water in the closed room.
Note: This calculation assumes the water vapor is in equilibrium with the liquid water in the room and neglects other factors like air exchange and condensation on surfaces.