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

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 draw any conclusion

Answer

C

Explanation

The energy radiated per second , `P`, by a body of surface area `A`, at temperature `T` Kelvin, is given by
`E = e sigma AT^(4)`
Hence, `E_(1) = e sigma 4 pi(1)^(2) xx (4000)^(4)`
`=e sigma pi xx 1024 xx 10^(12)J`
And `E_(2) = e sigma[4 pi (4)^(2)](2000)^(4)`
`=e sigma pi xx 1024 xx 10^(12)J`
so, `E_(1)=E_(2)`.