In an air$-$conditioning process, $3300$f$($t$^(3))/($m$)$in of outside air at $80\backslash$deg F and $70\%$ relative humidity is

mixed adiabatically with $2100$f$($t$^(3))/($m$)$in of inside air initially at $50\backslash$deg F and $20\%$ relative humidity. The

resultant mixture $($after mixing$)$ then flows through a heating section where heat is added so that the

air is at $70\backslash$deg F as it exits the air$-$conditioning system. The entire process takes place at a pressure of

$16$ psia. Determine the

a$($Bt$($u$)/($m$)$in$).$