Question

A point of 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 of $k$. If the temperature difference between the outer and the inner surfaces of the shell is not to exceed $T$, the thickness of the shell should not be less than :

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

Answer 1

The correct option is A $\frac{4\pi k{R}^{2}T}{P}$

As we know that rate of heat flow: $Power\left(P\right)=\frac{Q}{t}=\frac{KA\left(\Delta T\right)}{d}$

where, Area of Sphere$=4\pi R^2$

$\Rightarrow d=\frac{\left(k\right)4\pi R^{2}T}{P}$