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# 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) $25\%$

Last updated date: 15th Aug 2024
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Hint: The relative humidity on a day is determined by dividing the partial pressure of the water vapour to the vapour pressure of the water. And the answer is multiplied by a hundred, the percentage of the relative humidity on the day is determined.

Useful formula:
The relative humidity on a day is given by,
$R = \dfrac{{{\text{Partial pressure of water vapour}}}}{{{\text{Vapour pressure of water}}}}$
Where, $R$ is the relative humidity of the day.

Complete step by step solution:
Given that,
The partial pressure of the water vapour is, $0.012 \times {10^5}\,Pa$ at $12\,{}^ \circ C$ .
The vapour pressure of the water is $0.016 \times {10^5}\,Pa$ at $12\,{}^ \circ C$ .
Now, the relative humidity is,
The relative humidity on a day is given by,
$R = \dfrac{{{\text{Partial pressure of water vapour}}}}{{{\text{Vapour pressure of water}}}}\,............\left( 1 \right)$
By substituting the given values of the partial pressure of the water vapour and the vapour pressure of the water in the above equation (1), then the above equation (1) is written as,
$R = \dfrac{{0.012 \times {{10}^5}}}{{0.016 \times {{10}^5}}}$
On cancelling the same terms in the numerator and in the denominator in the above equation, then the above equation is written as,
$R = \dfrac{{0.012}}{{0.016}}$
On dividing the above equation, then the above equation is written as,
$R = 0.75\,.................\left( 2 \right)$
To give the solution in the percentage value, so multiply the equation (2) with the hundred. So, the answer in the equation (2) is converted to the percentage.
$R = 0.75 \times 100$
On multiplying the above equation, then the above equation is written as,
$R = 75\%$
Thus, the above equation shows the percentage of the relative humidity on a day.

Note: In equation (2), the relative humidity of the day is not mentioned with the unit because the partial pressure of the water vapour having the unit $Pa$ and the vapour pressure of the water having the unit $Pa$. On dividing these two terms the unit cancels each other. So, the relative humidity has no unit.