Answer to Question #144942 in Physics for Johnmak

Question

On a certain day the temperature is 20°c and the dew point is 5.0°C. What is the relative humidity? saturated air at 20°c and 5.0°C contains 17.12 and 6.80 g/m³ of water, respectively.

Answer 1

If the dew point is 5.0°C, this means that at 5.0°C the relative humidity is 100%. Thus, the air contains $\rho = 6.80 g/m³$ of water.

Then, the relative humidity at 20.0°C is:

$$RH = \dfrac{\rho}{\rho_0}\times 100\%$$

Here $\rho_0 = 17.12g/m^3$ is the saturated density of water at 20.0°C. Thus, obtain:

$$RH = \dfrac{6.8}{17.12}\times 100\% \approx 39.7\%$$

Answer. 39.7%.