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)

To calculate the number of kilograms of water required to increase the humidity in the room, we can follow these steps:

Step 1: Calculate the initial amount of water vapor in the room.
Given that the room's volume is 30m³ and the initial humidity is 20%, we can calculate the initial amount of water vapor using the specific humidity formula:

Specific Humidity = Humidity / (100 - Humidity)

Initial Specific Humidity = 20 / (100 - 20) = 0.25

Step 2: Convert the specific humidity to absolute humidity.
The specific humidity gives us the mass of water vapor in a given mass of dry air. We need to convert it to absolute humidity, which is the mass of water vapor per unit volume.

Absolute Humidity = Specific Humidity * Density of Air

The density of air can be approximated to around 1.225 kg/m³.

Initial Absolute Humidity = 0.25 * 1.225 = 0.30625 kg/m³

Step 3: Calculate the final absolute humidity.
We want to increase the humidity from 20% to 85%. Using the same formula and the final humidity, we can calculate the final absolute humidity.

Final Specific Humidity = 85 / (100 - 85) = 5.67

Final Absolute Humidity = Final Specific Humidity * Density of Air = 5.67 * 1.225 = 6.93375 kg/m³

Step 4: Find the difference in absolute humidity.
Now that we have the initial and final absolute humidity values, we need to find the difference in absolute humidity.

Difference in Absolute Humidity = Final Absolute Humidity - Initial Absolute Humidity
= 6.93375 - 0.30625
= 6.6275 kg/m³

Step 5: Calculate the total mass of water required.
To find the mass of water required to achieve the desired humidity, we need to multiply the difference in absolute humidity by the volume of the room.

Total Mass of Water = Difference in Absolute Humidity * Room Volume
= 6.6275 * 30
= 198.825 kg

Therefore, approximately 198.825 kilograms of water must be put into the vaporizer to increase the humidity from 20% to 85%.