$(30$ marks$)$

i$.)$ A dehumidifier is used to extract excess moisture from the air inside a

room with dimensions $863m^3.$ The room was initially at a dry bulb

temperature of $30C,70\%$ relative humidity and ends up at a wet bulb

temperature of $11C,100\%$ relative humidity. If the dry air density is $1\mathrm{.}2$

$k\frac{g}{m^3},$ what mass of water vapour $(kg)$ has been removed by the

dehumidifier?

$(10$ Marks$).$

ii$.)$ A dehumidifier has been operating in a damp student flat for several

hours. The dehumidifier is turned off once the air in the room has

reached a relative humidity of $70\%$ and a dry bulb temperature of $16$

$C.$ It is found that $450$ grams of water has been collected in the

dehumidifier tray. If the dry air mass is $90kg$ and the dry bulb

temperature in the room was $19C$ when the dehumidifier was turned

on$,$ what was the initial relative humidity?

$(10$ Marks$).$

iii.$)$ On a hot humid day, when the dry bulb temperature is $28C$ and the

relative humidity is $100\%,$ Bill takes an empty $1$ litre bottle that has

been left open to the air, seals the bottle by putting on its lid, and puts

the bottle in his fridge which is at a temperature of $5C.$ The density of

the dry air in the bottle can be taken to be $1\mathrm{.}2k\frac{g}{m^3},$ and the density of

water to be $1000kg*m^{-3}.$ What volume of condensation will form in the

bottle in $l(l={10}^{-9}{m}^3)$