On a warm afternoon, the air temperature in a physics laboratory is 30^\circ\text{C}, wher… — JAMB UTME

On a warm afternoon, the air temperature in a physics laboratory is $30^\circ\text{C}$ , where the saturated vapour pressure of water is $32.0\text{ mmHg}$ . When the air is cooled, condensation just begins to form on a metal vessel at $20^\circ\text{C}$ . Given that the saturated vapour pressure of water at $20^\circ\text{C}$ is $17.6\text{ mmHg}$ , what is the relative humidity of the air in percentage?

Answer: 55 %

Answer

The relative humidity of the air is

55\%

The dew point is the temperature at which condensation begins, indicating that the actual water vapour pressure present in the air equals the saturated vapour pressure at

20^\circ\text{C}

, which is

17.6\text{ mmHg}

. Dividing this actual vapour pressure by the saturated vapour pressure at the ambient air temperature of

30^\circ\text{C}

(

32.0\text{ mmHg}

) and multiplying by

100\%

yields

\frac{17.6}{32.0} \times 100\% = 55\%

Step-by-Step Solution

Determine the actual vapour pressure in the air

Actual vapour pressure =

17.6\text{ mmHg}

Condensation starts at the dew point (

20^\circ\text{C}

), meaning the actual vapour pressure in the air equals the saturated vapour pressure at the dew point.

Determine the saturated vapour pressure at the air temperature

Saturated vapour pressure at

30^\circ\text{C}

32.0\text{ mmHg}

This is the maximum vapour pressure the air can exert at its current ambient temperature.

Compute the relative humidity percentage

\text{Relative Humidity} = \frac{17.6}{32.0} \times 100\% = 55\%

Relative humidity is defined as the ratio of actual vapour pressure to saturated vapour pressure at air temperature, expressed as a percentage.

Key Concept

Calculation of relative humidity from saturated vapour pressure at dew point and air temperature

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic