Question

If the radius of a star is $R$ and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is $Q ?$ ($\sigma$ stands for Stefan's constant)

• A. $\frac{Q}{ 4 \pi R^2 \sigma}$
• B. $\bigg(\frac{Q}{ 4 \pi R^2 \sigma} \bigg) ^{-1/2}$
• C. $\bigg(\frac{4 \pi R^2 Q}{ \sigma} \bigg)^{1/4}$
• D. $\bigg(\frac{Q}{ 4 \pi R^2 \sigma} \bigg)^{1/4}$

Answer 1

Answer: (D)

$\bigg(\frac{Q}{ 4 \pi R^2 \sigma} \bigg)^{1/4}$

Answer 2

According to Stefan's law, $Q=\sigma A T^{4}$
or $T=\left(\frac{Q}{\sigma A}\right)^{1 / 4}$
$=\left(\frac{Q}{\sigma 4 \pi R^{2}}\right)^{1 / 4}$