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. If the temperature difference between the outer and inner surface of the shell in not to exceed T, the thickness of the shell should not be less than .......

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)`