First slide

Radiation

Question

Two perfectly black spheres A and B having radii 8 cm and 2 cm are maintained at temperatures $127^{o} C$ and $527^{o} C$ respectively. The ratio of the energy radiated by A to that by B is

Easy

A

1 : 2
B

1 : 1
C

2 : 1
D

1 : 4

Solution

Rate of energy radiation $Q = σ A T^{4} = σ (4 π R^{2}) T^{4}$
$∴ \frac{Q_{A}}{Q_{B}} = {(\frac{R_{A}}{R_{B}})}^{2} {(\frac{T_{A}}{T_{B}})}^{4} = {(\frac{8}{2})}^{2} . {(\frac{400}{800})}^{4} = 16 \frac{1}{16} = 1$

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