The temperature and the relative humidity of air are `20^(@)c and 80%` on a certain day. Find the fraction of the mass of water vapour that will condense if the temperature falls to `5^(@)C` .The saturation vapour pressure are `17.5mm`and 6.5mm of mercury at `20^(@)c and 5 degree C respectively.

Explanation

The relative humidity is
(vapour pressure of the air)/(SVPat the same temperature)
Thus, the vapour pressure at `20^(@)C`
`=0.8xx17.5mmof Hg`
`=14mmof Hg.`
Consider a volume V of air, If the vapour pressure is p and the tempreture is T, the mass m of the vapour present is giving by
`pV=(m)/(M)RT`
or, `m=(MV)/(R) (p)/(T). ...(i)`
the mass present at 20^(@)C i
`m_(1)=(MV)/(R) (14mm of Hg)/293K)`
When the air is cooled to `5^(@)C,` some vapour condenses and the air gets saturated with the vapour pressure at 5^(@)C is, therefore, 6.5mm of mercury. The mass pf vapour present at 5^(@)C is, therefore,
`m_(2)=(MV)/(R) (6.5mm of Hg)/(278K).`
THe fraction condensed
`=(m_(1)-m_(2))/(m_(1))=1-(m_(2))/m_(1))`
`=1-(6.5)/(278)xx(293)/(14)=0.51.