Q138 / 160 · TS EAMCET 2021 (06 Aug Shift 2) · Physics
The radiated power of a body at $400 \mathrm{~K}$ is $1000 \mathrm{~W}$. If the temperature is raised to $800 \mathrm{~K}$, what would be the radiated power of the body?
- A12000 W
- B15000 W
- Correct answerC16000 W
- D18000 W
Solution
The radiated power of a body, $P_1=1000 \mathrm{~W}$
Temperature, $T_1=400 \mathrm{~K}$
As, we know that according to Stefan's Boltzmann's law,
Radiated power $\propto$ (Temperature $)^4$
$\therefore$ If the radiated power at temperature $T_2=800 \mathrm{~K}$ is $P_2$, then $\frac{P_2}{P_1}=\left(\frac{T_2}{T_1}\right)^4$
$$
\begin{aligned}
\Rightarrow \quad P_2 & =P_1 \times\left(\frac{T_2}{T_1}\right)^4=1000 \times\left(\frac{800}{400}\right)^4 \\
& =16000 \mathrm{~W}
\end{aligned}
$$
Hence, the correct answer is option: 'C'.