InterviewSolution
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InterviewSolution
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A cube and a sphere of equal edge and radius, made of the same substance are allowed to cool under identical conditions. Determine which of the two will cool at a faster rate. |
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Answer» From equation, the rate of cooling of a body is given by `(-dT)/(dt)=(Aesigma)/(rhoVs)(T_4-T_0^4)` since, substance is same for both bodies, so `e//rho s=`constant. Finally, thay are allowed to cool under identical conditions so `(T^4-T_0^4)=` constant. `(-dT)/(dt)prop(A)/(V)` Let the edge of the cube or radius of the sphere be a, then for cube, `A=6a^2` and `V=a^3` so `(A)/(V)=6a` For the sphere, `A=4pia^2` and `V=(4//3)pia^3`, so `A//V=3//a` Evidently, the ratio `A//V` is more for cube, so the cube cools at a faster rate. Not the special technique used in this problem. |
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