First slide

Radiation

Question

Two spheres of the same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. The energy radiated per second by the first sphere is

Moderate

A

greater than that by the second
B

less than that by the second
C

equal in both cases
D

the information is incomplete to draw any conclusion

Solution

The energy radiated per second, P, by a body of surface area A, at temperature T kelvin, is given by
E = ${eσAT}^{4}$
Hence, $E_{1} = eσ 4 π {(1)}^{2} \times {(4000)}^{4}$
= $eσπ \times 1024 \times 10^{12} J$
and $E_{2} = eσ [4 π {(4)}^{2}] {(2000)}^{4}$
= $e σ π \times 1024 \times 10^{12} J$
So, $E_{1} = E_{2}$

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