A thick spherical shell of inner and outer radii r and R respectively has thermal conductivity `k = (rho)/(x^(n))` , where `rho` is a constant and x is distance from the centre of the shell. The inner and outer walls are maintained at temperature `T_(1)` and `T_(2) (lt T_(1))`
(a) Find the value of number n (call it `n_(0)`) for which the temperature gradient remains constant throughout the thickness of the shell.
(b) For `n=n_(0)`, find the value of x at which the temperature is `(T_(1)+T_(2))/(2)`
(c) For `n = n_(0)`, calculate the rate of flow of heat through the shell.

Answer

(a) `n_(0)=2` (b) `(r+R)/(2)`