`5 m^(3)` of air with a relative humidity of 22% at `15^(@)C and 3 m^(3)` of air with a relative humidity of 46% at `28^(@)C` have been mixed together. The total volume of the mixture is `8m^(3)`. Find the relative humidity of the mixture.

Explanation

Pind first the mass of moisture in each volume of air, i.e. the absolute humidity of the volumes which are mixed. We have in 5 m of air
`m_(1)=f_(1)V_(1)=rho_(1)^("sat")B_(1)V_(1)=12.8xx0.22xx5=14.1g`
In `3m^(2)` of air
`m_(2)=rho_(2)^("sat")B_(2)V_(2)=27.2xx0.46xx3=37.5g`
Next find the absolute humidity of the mixture:
`f=(m_(1)+m_(2))//(V_(1)+V_(2))=6.45g//m^(2)`
To find the relative humidity we must find the temperature of the mixture. Neglecting the vapour mass we may write the equation of heat balance in the form
`rho_(0)V_(1)e_(0)(t-15)=rho_(0)V_(2c_(0))(28-t)`
where the subscripts O show that the density and the specific heat refer to air. We have`t= 20^(@)C`. Now it is easy to compute the rolative bumidity.