Question

An ideal black body emits radiations at the rate of $5.67watt/{cm}^2$. It temperature will be

• A. $10K$
• B. ${10}^{2}K$
• C. ${10}^{3}K$
• D. ${10}^{4}K$

Answer 1

The correct option is C ${10}^{3}K$

For an ideal black body emissive power is
$E=\frac{P}{A}=\sigma \epsilon T^4$
where $A$ is area of black body, $\sigma$ is Stefan-Boltzmann's constant, $\epsilon$ is emissivity and T is temperature
$\sigma =5.67\times {10}^{-8}W{m}^{-2}{K}^{-4}$
for an ideal black body $\epsilon =1$
then
$\frac{P}{A}=\sigma \epsilon T^4$

$⟹5.67\times {10}^4=5.67\times {10}^{-8}\times T^4{T}^4={10}^{12}T={10}^{3}K$
option (C) is the correct answer.