If temperature of sun were to increase from T to 2T and its radius from R to 2R , then ratio of radi

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10-2.Transmission of Heat

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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

A

$32$

B

$16$

C

$4$

D

$64$

Solution

$\mathrm{E}=\sigma \mathrm{AT}^{4}$

$\mathrm{A} \alpha \mathrm{R}^{2} \quad \therefore \mathrm{E} \alpha \mathrm{R}^{2} \mathrm{T}^{4}$

$\therefore \frac{E_{2}}{E_{1}}=\frac{R_{2}^{2} T_{2}^{4}}{R_{1}^{2} T_{1}^{4}}$

$\text { put } \mathrm{R}_{2}=2 \mathrm{R}, \mathrm{R}_{1}=\mathrm{R}$

$\mathrm{T}_{2}=2 \mathrm{T}, \mathrm{T}_{1}=\mathrm{T}$

$\Rightarrow \frac{E_{2}}{E_{1}}=\frac{(2 R)^{2}(2 T)^{4}}{R^{2} T^{4}}=64$

Standard 11

Physics

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