The figure shows a system of two concentric spheres of radii `r_1 and r_2` are kept at temperature `T_1 and T_2`, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Options

A. `(r_(2) - r_(1))/((r_(1)r_(2))`
B. `ln((r_(2))/(r_(1)))`
C. `(r_(1)r_(2))/((r_(2) - r_(1)))`
D. `(r_(2) - r_(1))`

Answer

C

Explanation

For an elemental spherical sphere shells.
`overset(**)(Q) = K4pir^(2)(-(dT)/(dr)) implies overset(**)(Q)underset(r_(1))overset(r_(2))int (dr)/(r^(2)) = -4piK underset(T_(1))overset(T_(2))intdT`
`implies overset(**)(Q)((r_(2) - r_(1))/(r_(1)r_(2))) = 4piK(T_(1) -T_(2)) implies overset(**)(Q) prop(r_(1)r_(2))/(r_(2)-(r_(1)))`