Question

A black body is heated from ${27}^{o}C$ to ${927}^{o}C$. The ratio of radiation emitted will be:

• A. $1:4$
• B. $1:8$
• C. $1:16$
• D. $1:256$

Answer 1

The correct option is D $1:256$

Energy radiated depends on the temperature of the body.
Stefan's law states that the total amount of energy radiated per second per unit area of a perfect black body is directly proportional to the fourth power of the absolute temperature of the surface of the body,ie,
$E\propto T^4$
or $E=\sigma T^4$
where $\sigma$ is Stefan's constant. It's value is $5.67\times {10}^{-8}W{m}^{-2}{K}^{-4}$
Here, $T_1=27+273=300K$
$T_2=927+273=1200K$
$\therefore \frac{E_1}{E_2}={\left(\frac{300}{1200}\right)}^4=1:256$