Question

The total radiative power emitted by spherical blackbody with radius $R$ and temperature $T$ is $P$. If the radius is doubled and the temperature is halved then the radiative power will be.

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

Answer 1

The correct option is A $P/4$

Radiative power emitted $P=\sigma eA{T}^4$

where $A=4\pi r^2$ is the surface area of the body, $\sigma$ is Stefan's constant, $T$ is the temperature and $e$ is emmissivity of black body.

$⟹$ $P\propto r^2{T}^4$

Given : $r^{\prime }=2r$ and $T^{\prime }=\frac{T}{2}$

$\therefore$ $\frac{P^{\prime }}{P}=\frac{(r^{\prime }{)}^2}{r^2}\frac{(T^{\prime }{)}^4}{T^4}$

Or $\frac{P^{\prime }}{P}=\frac{(2r{)}^2}{r^2}\frac{(T/2{)}^4}{T^4}$

$⟹$ $P^{\prime }=\frac{P}{4}$