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. `In((r_(2)))/((r_(1)))`
C. `(r_(1)r_(2))/((r_(2)-r_(1)))`
D. `(r_(2)-r_(1))`

Answer

C

Explanation

`R = overset(r_(2))underset(r_(1)) int (dr)/(k.4pir^(2)) = (1)/(4pik) [(1)/(r_(1))-(1)/(r_(2))] , ((r_(2)-r_(1)))/(4pik.r_(1)r_(2))`
Rate of heat flow `=(T_(2)-T_(1))/(R ) = ((T_(2)-T_(1)))/((r_(2)-r_(1))) .4pikr_(1)r_(2)`
` prop (r_(1)r_(2))/(r_(2)-r_(1))`