a$)$ An air$-$conditioning system operates at a total pressure of $1$ atm and consists of a heating section and an evaporative cooler. Air enters the heating section at $15$oC and $55$ percent relative humidity at a rate of $30$ m$3/$min$,$ and it leaves the evaporative cooler at $25$oC and $45$ percent relatively humidity. a$.$Determine $($i$)$ the temperature and relative humidity of the air when it leaves the heating section, $($ii$)$ the rate of heat transfer in the heating section, and $($iii$)$ the rate of water added to air in the evaporative cooler. Draw a schematic representation of the process$($es$)$ on a psychrometric chart. $[12]$

$($b$)$ Explain the factors affecting the thermal comfort of occupants. Briefly mention the indices for thermal comfort.$[4]$