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_(1)r_(2))/((r_(1)-r_(2)))`
B. `(r_(2)-r_(1))`
C. `(r_(2)-r_(1))(r_(1)r_(2))`
D. `I n((r_(2))/(r_(1)))`

Answer

A

Explanation

Consider a concentric spherical shell of radius r and thickness dr as shown in the The radial rate of flow of heat through this shell in steady state will be
`H = (dQ)/(dt) = - KA (dT)/(dr) = -K (4pir^(2))(dT)/(dr)`
`rArrunderset(r_(1))overset(r_(2))int(dr)/(r^(2))=-(4piK)/(H)underset(T_(1))overset(T_(2))intdT`
Which on integration and simplifiction gives
`H=(dQ)/(dt) = (4piKr_(1)r_(2)(T_(1)-T_(2)))/(r_(2)-r_(1))`
`rArr(dQ)/(dt)prop(r_(1)r_(2))/((r_(2)-r_(1)))`
.