Question

The energy emitted by a black body at ${727}^{o}C$ is E. If the temperature of the body is increased by ${227}^{o}C$, the emitted energy will become

• A. 13 times
• B. 2.27 times
• C. 1.9 times
• D. 3.9 times

Answer 1

The correct option is B 2.27 times

Here we know that energy emitted by any body is given by $E=\sigma T^4$

So, at temperature $T={727}^{o}C$ energy emitted will be $E$

at temperature $T_1=727+227={954}^{o}C$ energy emitted will be $E_1=\sigma T_1^4$

$\frac{E}{E_1}=\frac{T^4}{T_1^4}$

$E_1=\frac{E\times T_1^4}{T^4}=\frac{E\times {954}^4}{{727}^4}=2.96E$