Question

A point source of heat of power P is placed at the center of a spherical shell of mean radius R. The material of the shell has thermal conductivity k. If the temperature difference between the outer and the inner surface of the shell is not to exceed T, then the thickness of the shell should not be less than

• A. $\frac{2\pi R^{2}kT}{P}$
• B. $\frac{4\pi R^{2}kT}{P}$
• C. $\frac{\pi R^{2}kT}{P}$
• D. $\frac{\pi R^{2}kT}{4P}$

Answer 1

The correct option is B $\frac{4\pi R^{2}kT}{P}$

According to given question,
Rate of a generation of heat $=$ rate of heat transfer.

Rate of flow of heat $=P=\frac{kA△\theta }{△x}=\frac{k\times 4\pi R^{2}T}{△x}$

$\Rightarrow$ Thickness of shell; $△x=\frac{4\pi R^{2}kT}{P}$