A room measuring $5$m x $8$m x $2\mathrm{.}5$ m height is going to be heated with an electrical planar heater transferring heat by natural convection $($hnc $=25$ W$/$m$2.$C$).$ The temperature of the planar heater is maintained at $60$ C$.$ The desired room temperature is $21$ C$,$ whereas the external temperature is $5$ C$.$ The global heat transfer coefficient U between the room and the exterior is $1\mathrm{.}0$ W$/$m$2.$C$.$

Determine:

$($a$)$ The area of planar heater needed $($m$2)$

$($b$)$ Heat loss to the exterior $($W$)$

$($c$)$ Cost per day of the heat loss $($cost of electricity $0\mathrm{.}07$ $$/$kWh$)$