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. `1:1`
B. `16:1`
C. `4:1`
D. `1:9`

Answer

A

Explanation

The power radiated by a sphere of radius R at temperature T is `P = epsilonsigmaT^(4)(4piR^(2))`
Where
`epsilon` = emmissivity of the material of sphere.
`sigma` = Stefan's constant
T = Absolute temperature
R = Radius of the sphere
`implies (P_(1))/(P_(2)) = (T_(1)^(4)R_(1)^(2))/(T_(1)^(4)R_(2)^(2)) = ((4000)/(2000))^(4)((1)/(4))^(2)= (2^(4))xx (1)/(4^(2)) = (16)/(16) = 1`