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`