The figure shows a system of two concentric spheres of radii r 1 and r 2 and kept at temperatures T 1 and T 2 , respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Step-by-step solution

For conduction from inner sphere to outer one, dQ = - KA dT dr × time dt or dQ dt = - K × 4 π r 2 dT dr ∴ Radial rate of flow d Q d t = P = - 4 π K r 2 dT dr ∴ P ∫ r 1 r 2 dr r 2 = - 4 π K ∫ T 1 T 2 dT or P r 1 - r 2 r 1 r 2 = 4 π K T 2 - T 1 or P = 4 π K T 1 - T 2 r 1 r 2 r 2 - r 1 ∴ d Q d t is proportional to r 1 r 2 r 2 - r 1 .