Question

The relative humidity on a day when partial pressure of water vapour is $0.012 \times {10^5}\,Pa$ at ${12^ \circ }\,C$ is
(Take vapour pressure of water at this temperature as $0.016 \times {10^5}\,Pa$ )
(A) $70\%$
(B) $40\%$
(C) $75\%$
(D) $25\%$

Answer 1

To find the relative humidity value, use the formula of the relative humidity given below and substitute the values of the vapour pressure of the water and the partial pressure of the water vapour in it. The simplification of this provides the value for the relative humidity.

Useful formula:
The formula of the relative humidity is given by
$RH = \dfrac{{PP}}{{VP}}$
Where $RH$ is the relative humidity, $PP$ is the partial pressure of the water vapour and $VP$ is the vapor pressure of the water.

Complete step by step solution:
It is given that the
Partial pressure of the water, $PP = 0.125 \times {10^5}\,Pa$
Vapor pressure of the water vapour, $VP = 0.016 \times {10^5}\,Pa$
By using the above formula of the relative humidity of the water vapour,
$RH = \dfrac{{PP}}{{VP}}$
By substituting the values of the partial pressure of the water vapour and the vapour pressure of the water I the above formula, we get
$RH = \dfrac{{0.125 \times {{10}^5}\,Pa}}{{0.016 \times {{10}^5}\,Pa}}$
By performing the basic arithmetic operation, we get
$RH = 0.75$
The above value of the relative humidity can also be written in the form of percentage as,
$RH = 75\%$
Hence the relative humidity of the water is obtained as $75\%$ .

Thus the option (C) is correct.

Note: The value of the relative humidity depends on the temperature and the pressure on that region. The region having the same amount of the vapour pressure and the partial pressure will have the greatest value of relative humidity in cool condition than in warmer condition.