A point source of heat of power P is placed at the centre of a spherical shell of mean radius R. The material of the shell has thermal conductivity K. Calculate the thickness of the shell if temperature difference between the outer and inner surfaces of the shell in steady state is T.

Options

A. `(2piR^(2)kT)/(P)`
B. `(4piR^(2)kT)/(P)`
C. `(piR^(2)kT)/(P)`
D. `(piR^(2)kT)/(4P)`

Answer

B

Explanation

For sphere `kA(-(dT)/(dr)) = P`
`implies kint(-dT) = int(dr.P)/(A) implies -kunderset(0)overset(T)intdT = underset(r_(eta))overset(2)int(dr.P)/(4pir^(2))`
` implies kT = (P)/(4pi)((r_(2)-r_(1))/(r_(1)r_(2))) implies t = (r_(2)-r_(1)) = (kT)/(P)4piR^(2)`