Question

A blackened metallic foil is dept at a distance $d$ from a spherical heater. The power absorbed by the foil is $P$, the temperature of heater and distance both are doubled, then the power absorbed by the foil will be:

• A. $8P$
• B. $4P$
• C. $2P$
• D. $P$

Answer 1

The correct option is B $4P$

Power $P\alpha \left(T^4-{T_0}^4\right)$

implies that $P\alpha T^4\left(\therefore T_0<<T\right)$

Energy received per second $\left(P\right)\alpha \frac{1}{d^2}$

Inverse square law $P\alpha \frac{T^4}{T^4}$

therefore

$\frac{P_1}{P_2}={\left(\frac{T_1}{T_2}\right)}^4\times {\left(\frac{d_2}{d_1}\right)}^2$

implies that $\frac{P_1}{P_2}={\left(\frac{T}{2T}\right)}^2\times {\left(\frac{2d}{d}\right)}^2=\frac{1}{4}$

implies that $P_2=4P$

Hence option $B$ is the correct answer