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

JEE Main · 2004 · 24 Apr 2004 · Offline · Heat & Thermodynamics

If the temperature of the sun were to increase from

T

2 T

and its radius from

R

2 R

, then the ratio of the radiant energy received on earth to what it was previously will be

(A)4
(B)16
(C)32
(D)64✓ Correct

Answer: (D)

Solution

By the Stefan-Boltzmann law the Sun radiates a total power

P = σ (4 π R^{2}) T^{4}

, and the intensity reaching the Earth at distance

d

I = \frac{P}{4 π d ^{2}} \propto R^{2} T^{4}

. Doubling both the radius and the temperature scales this by

(2)^{2} (2)^{4} = 4 \times 16 = 64

, so the energy received grows sixty-four-fold.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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