A black body at a temperature of 227$℃$ radiates heat at the rate of 5 cal${\ cm}^{- 2}s^{- 1}$. At a temperature of 727$℃$ the rate of heat radiated per unit area in cal${\ cm}^{- 2}s^{- 1}$ is

Question

Dr. Abubacker · Accepted Answer

(b) According to Stefan’s law radiant energy emitted by a perfectly black body per unit area per sec ($ie,$ emissive power of black body) is directly proportional to the fourth power of its absolute temperature ie $E \propto T^{4}$
$\Rightarrow$ $\frac{E_{1}}{E_{2}} = \ \frac{T_{1}^{4}}{T_{2}^{4}}$
$\frac{5}{E_{2}} = \ \frac{{(273 + 227)}^{4}}{{(273 + 727)}^{4}}\ $
$E_{2} = 5 	imes \left\lbrack \frac{1000}{500} ightbrack^{4}\ $
=$\ 5 	imes 16 = 80\ cal\ {cm}^{- 2}s^{- 1}$

Q. A black body at a temperature of 227$℃$ radiates heat at the rate of 5 cal${\ cm}^{- 2}s^{- 1}$. At a temperature of 727$℃$ the rate of heat radiated per unit area in cal${\ cm}^{- 2}s^{- 1}$ is

Explanation

Reviewed by Dr. Abubacker

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