Question

Two spheres 'S₁' and 'S₂' have radii 'R' and '3R', temperature 'T' K and. `"T"/3` K respectively. If 3 they are coated with a material of same emissivity, rate of radiation of 'S₁'  is E then rate of radiation of ' S₂' is ______.

(spheres are of the same material)

Options

• `"E"/9`

• `"E"/3`

• `"E"/12`

• `"E"/6`

Answer 1

Two spheres 'S₁' and 'S₂' have radii 'R' and '3R', temperature 'T' K and. `"T"/3` K respectively. If 3 they are coated with a material of same emissivity, rate of radiation of 'S₁'  is E then rate of radiation of ' S₂' is `underline( "E"/9)`.

Explanation:

E = `sigma xx 4pi "R"^2 xx "T"^4`

E' = `sigma xx 4pi(3"R")^2 xx ("T"/3)^4`

`therefore ("E'") /"E" = (3)^2/(3)^4 = 9`

`therefore "E'" = 9` E