A 40-L electrical radiator containing heating oil is placed in a 50-m3 room. Both the room and the oil in the radiator are initially at 10°C. The radiator with a rating of 2.4 kW is now turned on. At the same time, heat is lost from the room at an average rate of 0.35 kJ/s. After some time, the average temperature is measured to be 20°C for the air in the room, and 50°C for the oil in the radiator. Taking the density and the specific heat of the oil to be 950 kg/m3 and 2.2 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.

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Chapter1: Units, Trigonometry. And Vectors
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A 40-L electrical radiator containing heating oil is
placed in a 50-m3 room. Both the room and the oil in the radiator
are initially at 10°C. The radiator with a rating of 2.4 kW
is now turned on. At the same time, heat is lost from the room
at an average rate of 0.35 kJ/s. After some time, the average
temperature is measured to be 20°C for the air in the room,
and 50°C for the oil in the radiator. Taking the density and
the specific heat of the oil to be 950 kg/m3 and 2.2 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.

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