First slide

Radiation

Question

A spherical black body with a radius of 12 cm radiates 450 W power of 500 K. If the radius were half and temperature doubled, the power radiated in watt would be

Easy

A

225
B

450
C

900
D

1800

Solution

We know that power radiated is given by
$P = {σT}^{4} (4 {πT}^{2}) \propto T^{4} r^{2}$
$∴ \frac{P_{2}}{P_{1}} = {(\frac{T_{2}}{T_{1}})}^{4} {(\frac{r_{2}}{r_{1}})}^{2} = (2)^{4} \times {(\frac{1}{2})}^{2} = 4$
or $P_{2} = 4 P_{1} = 4 \times 450 = 1800 watt$

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