Question

A hot metallic sphere of radius r radiates heat. It's rate of cooling is

• A. Independent of r
• B. Proportional to r
• C. Proportional to $r^2$
• D. Proportional to $\frac{1}{r}$

Answer 1

The correct option is D Proportional to $\frac{1}{r}$

Rate of cooling $R_C=\frac{d\theta }{dt}=\frac{A\epsilon \sigma (T^4-T_0^4)}{mc}$
$\Rightarrow \frac{d\theta }{dt}\propto \frac{A}{V}\propto \frac{r^2}{r^3}\Rightarrow \frac{d\theta }{dt}\propto \frac{1}{r}$