A $40-$L electrical radiator containing heating oil is placed in a $50$ m$3$m$3$ room. Both the room and the oil in the radiator are initially at $10$C$.$ The radiator with a rating of $2\mathrm{.}4$ kW is now turned on$.$ At the same time, heat is lost from the room at an average rate of $0\mathrm{.}35$ kJ$/$s$.$ After some time, the average temperature is measured to be $20$C for the air in the room, and $45\mathrm{.}0$C for the oil in the radiator. Taking the density and the specific heat of the oil to be$950$kg$/$m$3950$kg$/$m$3$ and $2\mathrm{.}2$ kJ$/$kg$$C$,$ respectively, determine how long the heater is kept on$.$ Assume the room is well sealed so that there are no air leaks. The gas constant of air is R$=0\mathrm{.}287$kPa$$m$3/$kg$$KR$=0\mathrm{.}287$kPa$$m$3/$kg$$K $($Table A$-1).$ Also, c $=0\mathrm{.}718$ kJ$/$kg$$K for air at room temperature $($Table A$-2).$ Oil properties are given to be$$ $=950$kg$/$m$3$$=950$kg$/$m$3$ and$$ cp$=2\mathrm{.}2$kJ$/$kg$$Ccp$=2\mathrm{.}2$kJ$/$kg$$C $($Round the final answer to three decimal places.$)$

The temperature of the air in the room is $10$ degrees Celsius. Heat, Q$,$ flows out of the room.

The heater is kept on for min.