A lecture theatre is to be maintained at a temperature of $25\backslash$deg C dry bulb and $18\backslash$deg C wet bulb temperature. The outdoor conditions is assumed to be $33\backslash$deg C dry bulb and $28\backslash$deg C wet bulb. The fresh air accounts for $20\%$ of the total supply air. The sensible heat load is $88$ kW$.$ Air is supplied to the lecture theatre at $13\backslash$deg C with $95\%$ relative humidity. Determine

$($a$)$ the humidity ratio$($w$),$ dry bulb and wet bulb temperatures of the mixing air$($b$)$ the mass flow rate of supply air

$($c$)$ the sensible heat ratio

$($d$)$ the latent heat load