$8\mathrm{.}30$ Water is cooled by direct contact with ambient air in cooling towers, In a certain cooling operation, air enters the tower at $300K$ with a partial pressure of water vapour of $670Pa$ and leaves at $294K$ with a partial pressure of water $2\mathrm{.}2$kPa. The total pressure is $100$kPa. Calculate the following:

$($a$)$ The relative humidity of air$-$water vapour at the inlet and exit of the tower

$($b$)$ The percent composition by volume at the inlet and exit of the tower

$($c$)$ The percent humidity of air at the inlet and exit of the tower

$($d$)$ The mass of water vapour in kilograms at the inlet and exit per $100m^3$ of dry air entering the tower

$($e$)$ The mass of water vapour in kilograms at the inlet and exit per $100m^3$ of wet air entering the tower:

The vapour pressure $($in kPa $)$ of water is given by

$ln{P}^5=16\mathrm{.}26205-\frac{3799\mathrm{.}887}{T-46\mathrm{.}854}$