Question

A black body is heated from ${27}^{\circ }C$ to ${127}^{\circ }C$. The ratio of their energies of raditation emitted will be

Answer 1

From Stefan's law, the total radiant energy emitted per second per unit surface area of a black body is proportional to the fourth power of the absolute temperature of the body
That is, $E=\sigma T^4$
Where $\sigma$ is Stefan's constant.
Given,
Initial temperature $T_1=273+27=300K$
Final temperature $T_2=127+273=400K$
Hence, we have
$\frac{E_1}{E_2}=\frac{T_1^4}{T_2^4}=\frac{(300{)}^4}{(400{)}^4}=\frac{81}{256}$
Therefore, $E_1:E_2=81:256$

Final answer: (a)