Question

Suppose the relative humidity of air was 96% on a cold morning when the temperature was 20 degree Celsius . In the afternoon, the air temperature has risen to 35 degree Celsius , but the actual amount of water vapor in air is the same as it was in the morning. The barometric pressure is also the same as it was in the morning. What is the approximate relative humidity in the afternoon?

Answer 1

Therelative humidity, temperature and dew point are approximately related by:

$T_{dp}=T-\frac{100-RH}{5}$

Plugging the values for the temperature and relative humidity given we have that:

$\begin{gathered} T_{dp}=20-\frac{100-96}{5} \\ T_{dp}=20-\frac{4}{5} \\ T_{dp}=20-0.8 \\ T_{dp}=19.2 \end{gathered}$

Once we know the dew point we can plug it in the equation with the afternoon temperature to find the relative humidity:

$\begin{gathered} 19.2=35-\frac{100-RH}{5} \\ \frac{100-RH}{5}=35-19.2 \\ 100-RH=5(15.8) \\ 100-RH=79 \\ RH=100-79 \\ RH=21 \end{gathered}$

Therefore, the relative humidity is 21%