The temperature in a room is kept at a constant 20 °C but the humidity is only 20%. If the room has a volume of 30m³, and the room’s door and windows closed, how many kilograms of water must be put into the vaporizer to increase the humidity from 20% to 85% ( the molecular weight of water is 18)
You must be referring to the relative humidty (R.H.), not the absolute humidity.
You need to know the saturation pressure of water at 20 C. It is easy to look up. From that, you can calculate how much water vapor the room would contain at 100% relative humidity. You will need to use the ideal gas law.
Then calculate the water mass difference between 85% R.H. and 20% R.H. cases.
Thanks for your guidance
To find the number of kilograms of water needed to increase the humidity in the room, we need to calculate the difference in absolute humidity between the initial and final states of the room.
First, let's calculate the absolute humidity (in kg/m³) for both the initial and final conditions:
Initial absolute humidity (AH1) = Relative humidity (RH1) * saturation vapor pressure at 20°C (SVP1)
Final absolute humidity (AH2) = Relative humidity (RH2) * saturation vapor pressure at 20°C (SVP2)
The saturation vapor pressure at 20°C can be looked up in a steam table or calculated using an empirical formula. For this example, let's use the approximate value of 0.0231 kg/m³.
Initial absolute humidity (AH1) = 0.20 * 0.0231 kg/m³
Final absolute humidity (AH2) = 0.85 * 0.0231 kg/m³
To find the difference in absolute humidity (ΔAH), we subtract the initial absolute humidity from the final:
ΔAH = AH2 - AH1
Now, we can calculate the total amount of water needed to increase the humidity by multiplying the difference in absolute humidity by the volume of the room:
Total water needed = ΔAH * room volume
Total water needed = ΔAH * 30 m³
Finally, we need to convert the result into kilograms:
Total water needed (in kg) = (ΔAH * 30) / 1000
Note that we divide by 1000 to convert from grams to kilograms.
Therefore, to find the number of kilograms of water needed to increase the humidity in the room, you can follow these steps:
1. Calculate initial absolute humidity (AH1): AH1 = 0.20 * 0.0231 kg/m³
2. Calculate final absolute humidity (AH2): AH2 = 0.85 * 0.0231 kg/m³
3. Calculate the difference in absolute humidity (ΔAH): ΔAH = AH2 - AH1
4. Calculate the total water needed (in kg): Total water needed = (ΔAH * 30) / 1000
By plugging in the appropriate values, you can find the number of kilograms of water required to increase the humidity in the room.