Question

A spherical black body of radius $r$ radiated power $P$, and its rate of cooling is $R$

• A. $P\propto r$
• B. $P\propto r^2$
• C. $R\propto r^2$
• D. $R\propto \left(1/r\right)$

Answer 1

Answer: (B), (D)

$P\propto r^2$
$R\propto \left(1/r\right)$

$P=\left(4\pi r^2\right)\left(\sigma T^4\right)=ms(-\frac{dT}{dt})=-\frac{4}{3}\pi r^3\rho s\cdot \frac{dT}{dt}$
Here, $R=\frac{dT}{dt}$
$\therefore P\propto r^2$ and $R\propto \frac{1}{r}$.
Hence (B) and (D) are correct.