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A blackbody of surface area 1cm^(2) is p...

A blackbody of surface area `1cm^(2)` is placed inside an enclosure. The enclosure has a constant temperature `27(@)C` and the blackbody is maintained at `327(@)C` by heating it electrically. What electric power is needed to maintain the temperature? `sigma=6.0xx10^(-s)Wm^(-2)K(-2)` .

Text Solution

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The area of the blackbody is `A=10^(-4)m^(2)` , its temperature is `T_(1)=327(@)C=600K` . and the temperature of the enclosure is `T_(2)=27(@)C=300K` . The blackbody emits radiation at the rate of `AsigmaT_(1)^(4)` . The radiation falls on it (and gets absorbed) at the rate of `AsigmaT_(2)^(4)` .The net rate of loss of energy is `Asigma( T_(1)^(4)-T_(2)^(4))` . The heater must supply this much of power. thus, the power needed is `Asigma( T_(1)^(4)-T_(2)^(4))` . `=(10^(-4)m^(2)(6.0xx10^(-s)Wm^(-2)K^(-4)^(4)-(300K)^(4)]`. `=0.73W` .
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