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: 81. Then the ratio ‘T₁’ to ‘T₂’ is ______.

Options

• 1 : 1

• 3 : 1

• 9 : 1

• 27 : 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: 81. Then the ratio ‘T₁’ to ‘T₂’ is 3 : 1.

Explanation:

Radiant energy emitted by an ordinary body:

Q = eAσT⁴t   ...(i)

Also, emissive power

`R = Q/(At)`

Given that, r₁ = r₂, R₁ = R₂

∴ A₁ = A₂

∴ `e_1T_1^4 = e_2T_2^4`   ...(ii)

∴ `(T_1^4)/(T_2^4) = e_2/e_1`

`(T_1^4)/(T_2^4) = 81/1`

`T_1/T_2 = 3/1`