$8\mathrm{.}33$ A mixture of acetone vapour and nitrogen gas at $300K$ has a dew point of $283K.$ It enters an evaporator where it picks up acetone vapour. The mixture leaving the evaporator is at $298K$ and has a dew point of $293K.$ The pressure is kept constant at $100$ kPa. Determine the following:

$($a$)$ The absolute humidity of the mixture entering and leaving the evaporator

$($b$)$ The mass of acetone in kilograms evaporated per kilogram of nitrogen entering the evaporator

$($c$)$ The mass of acetone in kilograms evaporated per $100m^3$ of gas entering the evaporator

$($d$)$ The volume of gas leaving the evaporator per $100m^3$ of gas entering the unit The vapour pressure of acetone at $283K$ is $7\mathrm{.}2$kPa and $12\mathrm{.}0$kPa at $293K$

give proper numerical answers with steps for eacu part