Question

If the temperature of the sum 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. 4
• B. 16
• C. 32
• D. 64

Answer 1

The correct option is D 64

from stefan's law the energy radiated by sun is:

$P=\sigma eA{T}^4$

1st case $P_1=\sigma e\times 4\pi R^2{T}^4$

2nd case $P_2=\sigma e\times 4\pi \left(2R{)}^2\right(2T{)}^4=\sigma e4\pi R^{2}T64\times 64$

$P_{=}{P}_1\times 64$

$\frac{P_2}{P_1}=64$