A room is maintained at 20°C by a heater of resistance 20 Ω connected to 200 volt mains. The temperature is uniform throughout the room and the heat is transmitted through a glass window of area 1 m²

Question

A room is maintained at 20°C by a heater of resistance 20 Ω connected to 200 volt mains. The temperature is uniform throughout the room and the heat is transmitted through a glass window of area 1 m² and thickness 0.2 cm. Calculate the temperature outside. Thermal conductivity of glass is 0.2 cal m⁻¹ s⁻¹ °C⁻¹ and the mechanical equivalent of heat is 4.2 J cal⁻¹.

TestHub · Accepted Answer

P = R V 2 ​ = 2000 W, all lost through the glass. k = 0.2 × 4.2 = 0.84 W m⁻¹K⁻¹. Δ T = k A P d ​ = 0.84 2000 × 0.002 ​ = 4.76 ∘ C, so outside = 20 − 4.76 = 15.24 ∘ C.

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