A stream of $2m^3/$s of wet air $($on a dry basis$)$ at $4C,1$ atm and with a wet$-$bulb temperature of $2$C$,$ is mixed adiabatically with $6\frac{m^3}{s}$ of air $($on a dry basis$)$ at $25$C and with $50\%$ relative humidity.

$($b$)$ Determine the amount of heat in W that is needed to heat the mixture to $45$C at constant humidity.