Q107 / 200 · NEET 2002 · Physics

For a black body at temperature $727^{\circ} \mathrm{C}$, its radiating power is $60 \mathrm{~W}$ and the temperature of surrounding is $227^{\circ} \mathrm{C}$. If temperature of the black body is changed to $1227^{\circ} \mathrm{C}$, then its radiating power will be:

  • A
    $304 \mathrm{~W}$
  • Correct answer
    B
    $320 \mathrm{~W}$
  • C
    $240 \mathrm{~W}$
  • D
    $120 \mathrm{~W}$

Solution

We can use the formula $\begin{aligned} & P \propto\left(T_4-T_0^4\right) \\ & \therefore \frac{P_2}{P_1}=\frac{(1500)^4-(500)^4}{(1000)^4-(500)^4} \\ & =\frac{500^4\left(3^4-1\right)}{500^4\left(2^4-1\right)} \\ & \therefore \frac{P_2}{60}=\frac{80}{15} \Rightarrow P_2=320 \mathrm{~W} \end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions