Question

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

• A. $8$ times
• B. $16$ times
• C. $2$ times
• D. $4$ times

Answer 1

The correct option is B $16$ times

For black body radiation
$E=\sigma T^4$
[$E$ is energy radiated per unit time per unit area, $T$ is temperature of the body]
$\frac{E_2}{E_1}={\left(\frac{T_2}{T_1}\right)}^4\Rightarrow \frac{E_2}{E_1}={\left(\frac{273+287}{273+7}\right)}^4$
$={\left(\frac{560}{280}\right)}^4=\frac{16}{1}\Rightarrow E_2=16E_1$