At an air temperature of 30^\circ\text{C}, the saturated vapour pressure of water is 32\te… — JAMB UTME

At an air temperature of $30^\circ\text{C}$ , the saturated vapour pressure of water is $32\text{ mmHg}$ . If the dew point of the atmosphere is $15^\circ\text{C}$ and the saturated vapour pressure of water at $15^\circ\text{C}$ is $12\text{ mmHg}$ , what is the relative humidity of the air?

$37.5\%$ Answer
B
$50.0\%$
C
$62.5\%$
D
$75.0\%$

Answer

The relative humidity of the air is

37.5\%

The relative humidity is defined as the ratio of the saturated vapour pressure at the dew point temperature to the saturated vapour pressure at the current air temperature. Substituting the given values gives

\frac{12\text{ mmHg}}{32\text{ mmHg}} \times 100\% = 37.5\%

Step-by-Step Solution

Identify the formula for relative humidity in terms of vapour pressures

\text{Relative Humidity (R.H.)} = \frac{\text{Partial Vapour Pressure of Water at Air Temp}}{\text{Saturated Vapour Pressure at Air Temp}} \times 100\%

By definition, the actual partial vapour pressure of water in unsaturated air equals the saturated vapour pressure at its dew point temperature.

Substitute the given values into the equation

\text{R.H.} = \frac{12\text{ mmHg}}{32\text{ mmHg}} \times 100\%

The SVP at dew point (

15^\circ\text{C}

) is

12\text{ mmHg}

and the SVP at air temperature (

30^\circ\text{C}

) is

32\text{ mmHg}

Calculate the percentage

\text{R.H.} = 0.375 \times 100\% = 37.5\%

Simplifying

\frac{12}{32}

gives

\frac{3}{8}

, which equals

0.375

37.5\%

Key Concept

Relative humidity is the ratio of the actual vapour pressure present in the air (saturated vapour pressure at the dew point) to the maximum saturated vapour pressure the air can hold at its current temperature, expressed as a percentage.

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