Question

If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be ______.

Options

• 32

• 16

• 4

• 64

Answer 1

If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on Earth to what it was previously will be 64.

Explanation:

From Stefan's law, energy radiated by the sun per second,

E = σAT⁴;

∴ A ∝ R²

∴ E ∝ R²T⁴

∴ `E_2/E_1 = (R_2^2T_2^4)/(R_1^2T_1^4)`

put R₂ = 2R, R₁ = R; T₂ = 2T, T₁ = T

⇒ `E_2/E_1 = ((2R)^2(2T)^4)/(R^2T^4) = 64`