Question

A black sphere has radius 'R' whose rate of radiation is 'E' at temperature 'T'. If radius is made `R/3`and temperature '3T', the rate of radiation will be ______.

Options

• 9E

• 6E

• 3E

• E

Answer 1

A black sphere has radius 'R' whose rate of radiation is 'E' at temperature 'T'. If radius is made `R/3`and temperature '3T', the rate of radiation will be 9E.

Explanation:

`E_1=sigmaxxpiR_1^2xxT_1^4`

`E_2=sigmaxxpiR_2^2xxT_2^4`

`thereforeE_2/E_1=(R_2/R_1)^2(T_2/T_1)^4=(1/3)^2(3)^4=9`

∴ E₂ = 9E₁ = 9E