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

Options

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 drawn any conclusion

Answer

C

Explanation

The energy radiated per second E by a sphere of radius R at temperature T kelvin is given by
`E= e sigma AT^(4)`
As both spheres area of the same material, so their emissivities will be equal.
`:. E_(1) = e sigma 4pi (1)^(2) xx (4000)^(4) = e sigma pi xx 1024 xx 10^(12)J//s`
and `E_(2) = e sigma 4pi (4)^(2) (2000)^(4) = e sigma pi xx 1024 xx 10^(12) J//s`
Thus, `E_(1) = E_(2)`