On a winter day, the outside temperature is `0^(@)C` and relative humidity 40%.The air from outside comes into a room and is heated to `20^(@)C. What is the relative humidity in the room? The saturated vapour pressure at `0^(@)C`is 4.6mm of mercury and at `20^(@)C`it is 18mm of mercury.

Explanation

To solve the problem step by step, we will follow the outlined approach in the video transcript:

### Step 1: Gather Given Data
- Outside temperature, \( T_1 = 0^\circ C \)
- Relative humidity outside, \( RH_1 = 40\% \)
- Saturated vapor pressure at \( 0^\circ C \), \( P_{sat, 0} = 4.6 \, \text{mm Hg} \)
- Room temperature, \( T_2 = 20^\circ C \)
- Saturated vapor pressure at \( 20^\circ C \), \( P_{sat, 20} = 18 \, \text{mm Hg} \)
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