A closed vessel contains moist air at o 20 C, the relative humidity being 30%. What should be the relative humidity if the vessel

were cooled to o 10 C? Saturation vapour pressure of water at o 20 C is 17.5 mmHg and at o 10 C is 9.2 mmHg.

1 answer

To solve this problem, we can use the formula for relative humidity:

Relative Humidity (RH) = (Actual Vapour Pressure / Saturation Vapour Pressure) x 100

First, let's calculate the actual vapor pressure at 20 C using the given relative humidity of 30%:

RH = 30%
Saturation Vapour Pressure at 20 C = 17.5 mmHg

Actual Vapour Pressure at 20 C = RH / 100 x Saturation Vapour Pressure
Actual Vapour Pressure at 20 C = 0.30 x 17.5 = 5.25 mmHg

Now, let's calculate the actual vapor pressure at 10 C using the given saturation vapor pressure at 10 C:

Saturation Vapour Pressure at 10 C = 9.2 mmHg

Relative Humidity at 10 C = (Actual Vapour Pressure at 10 C / Saturation Vapour Pressure at 10 C) x 100

Since the amount of water vapor remains constant, the actual vapor pressure at both temperatures remains the same. Therefore, the actual Vapour Pressure at 10 C = 5.25 mmHg

Relative Humidity at 10 C = (5.25 / 9.2) x 100 =~ 57.1%

Therefore, the relative humidity should be approximately 57.1% if the vessel were cooled to 10 C.