$3.$ A $4-$m x $5-$m x $6-$m room is to be heated by an electric resistance heater placed in a short duct in the room. Initially, the room is at $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ and the local atmospheric pressure is $98$ kPa $.$ The room is losing heat steadily to the outside at a rate of $150\backslash (\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$min$\}\backslash ).$ A $\backslash (200-\backslash$mathrm$\{$W$\}\backslash )$ fan circulates the air steadily through the duct and the electric heater at an average mass flow rate of $\backslash (40\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$min$\}\backslash ).$ The duct can be assumed to be adiabatic, and there is no air leaking in or out of the room. If it takes $25$ Min for the room air to reach an average temperature of $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ find $($a$)$ the power rating of the electric heater and $($b$)$ the temperature rise that the air experiences each time it passes through the heater.