Question

If the temperature of the sun is increased 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 $64$

Given $T^{\prime }=2T,r^{\prime }=2r$
Power radiated from an object is given by(Stefan–Boltzmann law)

$P\propto A{T}^4$
$A$ is area of cross section $A\propto r^2$
$T$ is temperature of the body

$\therefore P\propto r^2{T}^4$
$\frac{P^{\prime }}{P}=\left(\frac{r^{\prime }}{r}{)}^2\right(\frac{T^{\prime }}{T}{)}^4=4\times 16$
Hence,
$P^{\prime }=4\times 16P=64P$