Question

Two spherical blackbodies have radii 'r₁' and 'r₂'. Their surface temperature are 'T₁' and 'T₂'. If they radiate same power, then `"r"_2/"r"_1` is ________.

Options

• `"T"_1/"T"_2`

• `"T"_2/"T"_1`

• `("T"_1/"T"_2)^2`

• `("T"_2/"T"_1)^2`

Answer 1

Two spherical blackbodies have radii 'r₁' and 'r₂'. Their surface temperature are 'T₁' and 'T₂'. If they radiate same power, then `"r"_2/"r"_1` is `("T"_1/"T"_2)^2`.

Explanation:

`"For blackbody, P" = "A"epsilonsigma"T"^4`

`"For same power, A" prop 1/"T"^4`

`therefore ("r"_1/"r"_2)^2 = ("T"_2/"T"_1)^4`

`therefore "r"_1/"r"_2 = ("T"_2/"T"_1)^2 "i.e.," "r"_2/"r"_1 = ("T"_1/"T"_2)^2`