Two thin concentric shells made from copper with radius`r_1 and r_2 (r_2 gt r_1)` have a material of thermal conductivity K filled between them. The inner and outer spheres are maintained at temperatures `T_H and T_C` respectively by keeping a heater of power P at the centre of the two spheres. Find the value of P.

Explanation

Heat flowing per second through each cross-section of the sphere `= P= i`
Thermal resistance of the spherical shell of radius x and thickness dx.
`dR=(dx)/(K.4pi x^2)`
`rArr R= underset(r_1)overset(r^2)int(dx)/(4pix^2. K)=(1)/(4pi K)(1/r_1-1/r_2)`
thermal current

`i=P=(T_H-T_C)/(R )=(4pi K(T_H-T_C)r_1 r_2)/((r_2-r_1))`