Question

A body radiates energy 5 W at a temperature of ${127}^{\circ }C$. If the temperature is increased to ${927}^{\circ }C$, then it radiates energy at the rate of

• A. 410 W
• B. 81 W
• C. 405 W
• D. 200 W

Answer 1

The correct option is

B

405 W

Rate of energy $\frac{Q}{t}=P=Aϵ\sigma T^4\Rightarrow P\propto T^4$

$\Rightarrow \frac{P_1}{P_2}={\left(\frac{T_1}{T_2}\right)}^4={\left(\frac{927+273}{127+273}\right)}^4\Rightarrow P_1=405W$