To find the relative humidity (RH) at the new temperature (16°C), we can follow these steps:
-
Find the actual vapor pressure (VP) at 20°C: The relative humidity is given by the formula:
\[ \text{RH} = \frac{\text{VP}}{\text{SVP}} \times 100 \]
Where:
- RH = relative humidity (%)
- VP = actual vapor pressure
- SVP = saturation vapor pressure
Rearranging the formula to find the VP:
\[ \text{VP} = \frac{\text{RH}}{100} \times \text{SVP} \]
Substituting the values for 20°C:
\[ \text{VP} = \frac{36}{100} \times 17.5, \text{mmHg} \]
\[ \text{VP} = 0.36 \times 17.5, \text{mmHg} = 6.3, \text{mmHg} \]
-
Find the new relative humidity at 16°C: Now, we know the actual vapor pressure (VP) remains the same when the air is cooled. We need to find the new relative humidity at 16°C using the saturation vapor pressure at that temperature (13.6 mmHg):
Using the RH formula again:
\[ \text{RH}{16} = \frac{\text{VP}}{\text{SVP}{16}} \times 100 \]
Substituting the values:
\[ \text{RH}_{16} = \frac{6.3, \text{mmHg}}{13.6, \text{mmHg}} \times 100 \]
\[ \text{RH}_{16} = \frac{6.3}{13.6} \times 100 \approx 46.32% \]
Therefore, the relative humidity when the air is cooled to 16°C will be approximately 46.32%.