A black body is heated from $7^0\mathrm{C} \mathrm{to} {287}^0\mathrm{C}$. The ratio of radiation emitted is

Given: Initial temperature, ${\mathrm{T}}_1 = 7^0\mathrm{C} = 280 \mathrm{K}$

Final temperature, ${\mathrm{T}}_2= {287}^0\mathrm{C} = 560 \mathrm{K}$

According to Stefan's law the radiated energy is given y

E $\propto {\mathrm{T}}^4$

Hence $\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2} = \frac{{{\mathrm{T}}_1}^4}{{{\mathrm{T}}_2}^4} = {\left(\frac{280}{560}\right)}^4= \frac{1}{16}$

    ${\mathrm{E}}_1 : {\mathrm{E}}_2 = 1 : 16$