Consider an air conditioner operating in a recycle system mode where fresh air taken from the ambient atmosphere is to be cooled and dehumidified and then delivered to a room. Fresh air taker from the ambient atmosphere contains $5$mol$\%$ water. This fresh air stream is then mixed with the recycle stream and the resulting stream contains $2\mathrm{.}3$mol$\%$ water. This stream coming out of the mixer is fed into the air conditioner unit, where a fraction of water present in the air is condensed and removed as liquid, the other stream containing $1\mathrm{.}7$mol$\%$ water is taken out and is fed into a splitter where one stream is taken as the recycle stream and other stream is delivered into the room. The air which is delivered to the room contains $1\mathrm{.}7$mol$\%$ water. Present the following assuming $500$ moles$/$minute of air $($containing $1\mathrm{.}7$mol$\%$ water$)$ is delivered to the room.

$10$ Marks$)$

i$.$ Draw a labeled flowsheet

ii$.$ Present the degree of freedom analysis for the overall system, mixer, air conditioner, and splitter. iii. The molar flow rate of liquid water removed through condensation from the air conditioner. the molar flow rate of the fresh air feed fed into the system, and the molar flow rate of the recycle stream.