Question

A blackbody of surface area 1 $c{m}^2$ is placed inside an enclosure. The enclosure has a constant temperature 27${}^{\circ }$ C and the blackbody is maintained at 327 ${}^{\circ }$ C by heating it electrically. What electric power is needed to maintain the temperature?$\sigma =6.0\times {10}^{-8}W/m^2-K^4$.

• A. 0.56 W
• B. 0.37 W
• C. 0.73 W
• D. 0.65 W

Answer 1

The correct option is C

0.73 W

The area of the blackbody is A = ${10}^{-4}{m}^2$, its temperature is $T_1={327}^{\circ }C=600K$ and the temperature of the enclosure is $T_2={27}^{\circ }C=300K$. The blackbody emits radiation at the rate of $A\sigma T_1^4$. The net rate of loss of energy is $A\sigma (T_1^4-T_2^4)$The heater must supply this much of power. Thus, the power needed is $A\sigma (T_1^4-T_2^4)$

=$\left({10}^{-4}{m}^2\right)(6.0\times {10}^{-8}W/m^2-K^4)\left[\right(600K{)}^4-\left(300K{)}^4\right]=0.73W$.