A room is heated by a $1\mathrm{.}2-$kW electric resistance heater whose wires have a diameter of $4$ mm and a total length of $3\mathrm{.}4$ m$.$ The air in the room is at $23$ C$,$ and the interior sur faces of the room are at $17$ C$.$ The convection heat transfer coefficient on the surface of the wires is $8$ W$/$ m $2$K$.$ If the rates of heat transfer from the wires to the room by convection and by radiation are equal, the surface temperature of the wire is $($a$)3534$ C $($b$)1778$ C $($c$)1772$ C $($d$)98$ C $($e$)25$ C