Q. 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 $1/r$
Explanation
(d) Rate of cooling $R_{C} = \frac{d\theta}{dt} = \frac{A\varepsilon\sigma(T^{4} - T_{0}^{4})}{mc}$
$\Rightarrow \frac{d\theta}{dt} \propto \frac{A}{V} \propto \frac{r^{2}}{r^{3}} \Rightarrow \frac{d\theta}{dt} \propto \frac{1}{r}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.