A room at 20 ° C is heated by a heater of resistance 20 ohm connected to 200 V mains. The temperature is uniform throughout the room and the heat is transmitted through a glass window of area 1 m 2 and thickness 0 .2 cm . Calculate the temperature outside. Thermal conductivity of glass is 0.2 cal / m ° C s and mechanical equivalent of heat is 4 .2 J/cal .

Question

A room at 20 ° C is heated by a heater of resistance 20 ohm connected to 200 V mains. The temperature is uniform throughout the room and the heat is transmitted through a glass window of area 1 m 2 and thickness 0 .2 cm . Calculate the temperature outside. Thermal conductivity of glass is 0.2 cal / m ° C s and mechanical equivalent of heat is 4 .2 J/cal ., 13.69 ° C, 15.24 ° C, 17.85 ° C, 19.96 ° C

MARKS App · Accepted Answer

If θ is the temperature of outside, heat passing per second through the glass window, dQ dt = KA θ 1 - θ 2 L = 0.2 × 1 × 2 0 - θ cal 0.2 × 1 0 - 2 = 1 0 0 2 0 - θ And heat produced per second by the heater in the room P = V 2 R J S = V 2 R c a l s = 2 0 0 × 2 0 0 2 0 × 4.2 = 476.2 cal s Now as the temperature of the room is constant, the heat produced per second by heater must be equal to the heat conducted through the glass window. 1 0 0 2 0 - θ = 476.2 ; θ = 15.24 ∘ C

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