A blackened metallic foil kept at a distance d from a spherical heater absorbs power P . What will be the power absorbed by it if temperature of heater and distance are both doubled?

Question

A blackened metallic foil kept at a distance d from a spherical heater absorbs power P . What will be the power absorbed by it if temperature of heater and distance are both doubled? (A) 8P (B) 4P (C) 2P (D) P

Tardigrade Admin · Accepted Answer

Let P be the emissive power, T be the absolute temperature of body and

T_{0}

be the temperature of surroundings.
According to Stefan's-Boltzmann's law, emissive power is

P \propto (T^{4} - T_{0}^{4})

\Rightarrow P \propto T^{4} (∵ T_{0} << T)

.
Also Power of the radiation is inversely proportional to square of distance

P \propto \frac{1}{d ^{2}}

Combining both, we get

\Rightarrow P \propto \frac{T ^{4}}{d ^{2}} \Rightarrow \frac{P _{1}}{P _{2}} = (\frac{T _{1}}{T _{2}})^{4} \times (\frac{d _{2}}{d _{1}})^{2}

\Rightarrow \frac{P}{P _{2}} = (\frac{T}{2 T})^{4} \times (\frac{2 d}{d})^{2} = \frac{1}{4} \Rightarrow P_{2} = 4 P

Q. A blackened metallic foil kept at a distance $d$ from a spherical heater absorbs power $P$ . What will be the power absorbed by it if temperature of heater and distance are both doubled?

$8 P$

$4 P$

$2 P$

$P$

Q. A blackened metallic foil kept at a distance d from a spherical heater absorbs power P . What will be the power absorbed by it if temperature of heater and distance are both doubled?

8P

4P

2P

P

Q. A blackened metallic foil kept at a distance $d$ from a spherical heater absorbs power $P$ . What will be the power absorbed by it if temperature of heater and distance are both doubled?

$8 P$

$4 P$

$2 P$

$P$