First slide

Radiation

Question

A spherical black body with a radius of 12 cm radiates 440 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be

Moderate

A

225
B

450
C

900
D

1600

Solution

Radiated power by blackbody P = $\frac{Q}{t} = {AσT}^{4}$
$\Rightarrow P \propto {AT}^{4} \propto r^{2} T^{4} \Rightarrow \frac{P_{1}}{P_{2}} = {(\frac{r_{1}}{r_{2}})}^{2} {(\frac{T_{1}}{T_{2}})}^{4}$
$\Rightarrow \frac{400}{P_{2}} = {(\frac{12}{6})}^{2} {(\frac{500}{1000})}^{4}$
$\Rightarrow P_{2} = 1600 W$

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