Question

If the temperature of a black body increases from $7^{\circ }C$ to ${287}^{\circ }C$, the rate of energy radiation increases by

• A. ${\left(\frac{287}{7}\right)}^4$
• B. 16
• C. 4
• D. 2

Answer 1

The correct option is B

16

From Stefan's law, $E=\sigma T^4$
$\therefore E_1=\sigma (273+7{)}^4={280}^4$.....(1)
and $E_2=\sigma (273+287{)}^4={560}^4$.....(2)
From (1) and (2), $\frac{E_2}{E_1}={\left(\frac{560}{280}\right)}^4=16$
Hence, the correct choice is (b).