Air is to be dehumidified by condensing the water vapour present in it by cooling at constant pressure. $100m^3$ of air at $100$kPa and $300K$ contains water vapour which exerts a partial pressure of $4$kPa. Keeping the pressure constant, this air is cooled to $275K$ and the condensed water is removed. The partial pressure of water in the air after cooling is found to be $1\mathrm{.}8$kPa. Calculate the following:

$($a$)$ The volume of air after dehumidification in $m^3$

$($b$)$ The mass of water removed in $kg$