Problem $04\mathrm{.}038-$ Energy balance for an electrical radiator

A $40-$L electrical radiator containing heating oil is placed in a $50-m^3$ room. Both the room and the oil in the radiator are initially at $10C.$ 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 $0\mathrm{.}35k\frac{J}{s}.$ After some time, the average temperature is measured to be $20C$ for the air in the room, and $70\mathrm{.}0C$ for the oil in the radiator. Taking the density and the$-$specific heat of the oil to be $950k\frac{g}{m^3}$ and $2\mathrm{.}2k\frac{J}{k}gC,$ 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$*m^3*kg*K($Table $($:$A-1$