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A room at 20^@C is heated by a heater of...

A room at `20^@C` is heated by a heater of resistence 20 ohm connected to 200 V mains. The temperature is uniform throughout the room and the heati s transmitted through a glass window of area `1m^2` and thickness 0.2 cm. Calculate the temperature outside. Thermal conductivity of glass is `0.2 cal//mC^@` s and mechanical equivalent of heat is `4.2 J//cal`.

Text Solution

Verified by Experts

The correct Answer is:
15.24
Power produced by heater = rate of heat flow through window `therefore(V^(2))/(R)=("Tem perature difference")/("Them alresistance")=(20-theta)/((l//KA))thereforetheta=20-(V^(2)l)/(KAR)`
Substituting the values we have, `theta=20-((200)^(2)(0.2xx10^(-2)))/((0.2xx4.2)(1)(20))=15.24^(@)C`
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Knowledge Check

  • A double pan window used for insulating a room thermally from outside consists of two glass sheets each of area 1 m^(2) and thickness 0.01m separated by 0.05 m thick stagnant air space. In the steady state, the room-glass interface and the glass-outdoor interface are at constant temperatures of 27^(@)C and 0^(@)C respectively. The thermal conductivity of glass is 0.8 Wm^(-1)K^(-1) and of air 0.08 Wm^(-1)K^(-1) . Answer the following questions. (a) Calculate the temperature of the inner glass-air interface. (b) Calculate the temperature of the outer glass-air interface. (c) Calculate the rate of flow of heat through the window pane.

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  • A lake surface is exposed to an atmosphere where the temperature is lt 0^(@)C . If the thickness of the ice layer formed on the surface grows form 2cm to 4cm in 1 hour. The atmospheric temperature, T_(a) will be- (Thermal conductivity of ice K = 4 xx 10^(-3) cal//cm//s//.^(@)C , density of ice = 0.9 gm//ice. Latent heat of fustion of ice = 80 cal//m . Neglect the change of density during the state change. Assume that the water below the ice has 0^(@) temperature every where)

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