Question

A perfect black body of surface area $1{\text{cm}}^2$ is heated to a temperature $1000\text{K}$. The amount of energy radiated by the body in $1\text{s}$ is (Stefan’s constant $\sigma =5.67\times {10}^{-8}W{m}^{-2}{K}^{-4}$)

• A. $5.67\text{J}$
• B. $0.567\text{J}$
• C. $56.7\text{J}$
• D. $567\text{J}$

Answer 1

The correct option is A $5.67\text{J}$

$P=ϵA\sigma T^4$
$=1\times {10}^{-4}\times 5.67\times {10}^{-8}\times (1000{)}^4$
$={10}^{-4}\times 5.67\times {10}^{-8}\times {10}^{12}$

$p=5.67W$

$\frac{E}{\Delta t}=5.67W$

$E=5\cdot 67\times \Delta t$

$E=5\cdot 67\times 1=5.67J$