The temperature and relative humidity of air on a certain day are o 20 C and 80%, respectively. Find the fraction of mass of water vapour that will condense if the temperature falls to 5 ºC. Saturation vapour pressure at o 20 C and o 5 C are 17.5 mmHg and 6.5 mmHg, respectively.

Answer 1

First, we need to calculate the actual vapour pressure of the air at 20ºC using the relative humidity:

Actual Vapour Pressure = Relative Humidity * Saturation Vapour Pressure at 20ºC
Actual Vapour Pressure = 0.80 * 17.5 mmHg
Actual Vapour Pressure = 14 mmHg

Next, we can calculate the maximum amount of water vapour that can be held at 5ºC using the saturation vapour pressure at that temperature:

Maximum Vapour Pressure at 5ºC = 6.5 mmHg

The difference between the actual vapour pressure at 20ºC and the maximum vapour pressure at 5ºC represents the amount of water vapour that will need to condense:

Fraction of mass of water vapour that will condense = (Actual Vapour Pressure at 20ºC - Maximum Vapour Pressure at 5ºC) / Actual Vapour Pressure at 20ºC
Fraction of mass of water vapour that will condense = (14 mmHg - 6.5 mmHg) / 14 mmHg
Fraction of mass of water vapour that will condense = 7.5 mmHg / 14 mmHg
Fraction of mass of water vapour that will condense ≈ 0.536

Therefore, approximately 53.6% of the mass of water vapour will condense when the temperature falls to 5ºC.