# 30 degrees outside, air humidity 50%. Will drops appear on the glasses of a bespectacled man

30 degrees outside, air humidity 50%. Will drops appear on the glasses of a bespectacled man when the sun sets behind the mountain and the temperature is 20. Calculate through which formula to prove?

According to the table “Density of saturated water vapor”, we determine the density of saturated vapor at 30 ° С ρн:

ρн = 30.3 g / m ^ 3.

Relative air density φ is the ratio of water vapor density ρ to saturated vapor density ρн:

φ = (ρ / ρн) * 100%;

50% = (ρ / (30.3 g / m ^ 3)) * 100%;

1 = (ρ / (30.3 g / m ^ 3)) * 2.

We find the density of vapor in air at a humidity of 50%:

ρ = (30.3 g / m ^ 3) / 2 = 15.15 g / m ^ 3.

The same will be the vapor density at 20 ° C.

According to the same table, we find that the density of saturated vapor at 20 ° C is 17.3 g / m ^ 3, that is, at a density of 15.15 g / m ^ 3, water vapor will not be saturated, therefore, water droplets on glasses will not will appear.