$1.($a$)$ What is the lowest temperature that air can attain in an evaporative cooler if it enters at $\backslash (1\backslash$mathrm$\{$~atm$\},302\backslash$mathrm$\{$~K$\}\backslash )$ and $40$ percent relative humidity? Show the process in psychrometry chart.

$($b$)$ Air at $\backslash (10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ dry bulb temperature and $\backslash (90\backslash \%\backslash )$ relative humidity is to be heated and humidified to $\backslash (35^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ dry bulb temperature and $\backslash (22\mathrm{.}5^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ wet butb temperature. The air is pre$-$heated sensibly before passing to the air washer in which water is recirculated. The relative humidity of the air coming out of the air washer is $\backslash (90\backslash \%\backslash ).$ This air is again reheated sensibly to obtain the final desire condition. Find by using psychrometry chart: $($i$)$ the temperature to which the air should be preheated, $($ii$)$ the total heating required, $($iii$)$ the makeup water required in the air washer, and $($iv$)$ the humidifying efficiency of the air washer.

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$|5+15=20|$

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