First slide

Radiation

Question

A black body is at $727^{0} C$ . It emits energy at a rate which is proportional to

Moderate

A

${(727)}^{2}$
B

${(1000)}^{4}$
C

${(1000)}^{2}$
D

${(727)}^{4}$

Solution

Amount of heat energy radiated per second by unit area of a back body is directly proportional to fourth power of absolute temperature.
According to Stefan's law,
$E \propto T^{4}$
or E = ${σT}^{4}$
where $σ$ is a constant of proportionality and called Stefan's constant. Its value is
$5.67 \times 10^{- 8} {Wm}^{- 2} K^{- 4}$
Hence E $\propto {(727 + 273)}^{4}$
E= $\propto {(1000)}^{4}$

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