Question

Two spherical black bodies of radius r₁ and r₂ with surface temperature T₁ and T₂ respectively, radiate same power, then r₁ : r₂ is ______.

Options

• `("T"_2/"T"_1)^4`

• `("T"_2/"T"_1)^2`

• `("T"_1/"T"_2)^2`

• `("T"_1/"T"_2)^4`

Answer 1

Two spherical black bodies of radius r₁ and r₂ with surface temperature T₁ and T₂ respectively, radiate same power, then r₁ : r₂ is `underline(("T"_2/"T"_1)^2)`.

Explanation:

The power radiated by the black body,

E = εσAT⁴

It is given that, both spherical bodies radiate same power.

∴ E₁ = E₂

`"T"_1^4 "r"_1^2 = "T"_2^4 "r"_2^2` (for spherical body, A = 4πr²)

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

OR

`4pi_1^2"T"_1^4 = 4pi"r"_2^2"T"_2^4`

`"R"_1^2/"r"_2^2 = "T"_2^4/"T"_1^4`

`"r"_1/"r"_2 = "T"_2^2/"T"_1^2`