The figure shows a system of two concentric spheres of radii r1 and r2 are kept at temperatures T1 and T2, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Consider a shell of thickness (dr) and of radii (r) and the temperature of inner and outer surfaces of this shell be T,(T- dT)dQdt= rate of flow of heat through it =KA[(T-dT)-T]dr=-KAdTdr=-4πKr2dTdr  ∵A=4πr2To measure the radial rate of heat flow, integration technique is used, since the area of the surface through which heat will flow is not constant. Then, dQdt∫r1r21r2dr=-4πK∫T1T2dT dQdt1r1-1r2=-4πKT2-T1 or dQdt=-4πKr1r2T2-T1r2-r1∴  dQdt∝r1r2r2-r1