Question

Two spheres 'S₁' and 'S₂' have same radii but temperatures T₁ and T₂ respectively. Their emissive power is same and emissivity is in the ratio 1: 4. Theo the ratio of T₁ to T₂ is ______.

Options

• `sqrt(2):1`

• `1:sqrt2`

• 1: 2

• 2: 1

Answer 1

Two spheres 'S₁' and 'S₂' have same radii but temperatures T₁ and T₂ respectively. Their emissive power is same and emissivity is in the ratio 1: 4. Theo the ratio of T₁ to T₂ is `underline(sqrt(2):1)`.

Explanation:

Emissive power P = σe`"T"^4`

`therefore sigma e_1"T"_1^4 = sigma e_2 "T"_2^4`

`"T"_1^4/"T"_2^4` = `"e"_2/"e"_1` = 4

`therefore "T"_1/"T"_2 = sqrt2`