A cube and a sphere of equaledgeand radius ,madeof thesamesubstanceare allowed to cool under identical conditions . Determine whichof the will cool ata faster rate .

A cube and a sphere of equaledgeand radius ,madeof thesamesubstanceare

1.	A cube and a sphere of equaledgeand radius ,madeof thesamesubstanceare allowed to cool under identical conditions . Determine whichof the will cool ata faster rate .
Answer» Solution :The rateof coolingof a bodyis givenby `(-dT)/(dt) = (Ae SIGMA)/( rho Vs) (T^(4) - T_(0)^(4))` Since, SUBSTANCEIS same for bothbodies , so `(E)/(rho s)`= constant. Further , theyare allowed to cool under identicalconditions, so `(T^(4) - T_(0)^(4)) ` = constant`therefore(-dT)/(dt) prop (A)/(V)` Let the edgeof the cubeor radius of the sphere bea, then for the cube`A = 6A^(2)` and `V = a^(3) ` , so A/V = 6/a forthesphere , `A = 4pia^(2)` and `V = (4)/(3) pi a^(3)` , soA/V = 3/a. Evidently , the RATIO A/V is more for cubecoolsat a fasterrate .