A sphere,a cube,and a thin circular plate,all | vedclass

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(A) According to the Stefan-Boltzmann law,the rate of heat loss $dQ/dt$ is proportional to the surface area $A$ of the object,i.e.,$dQ/dt = e \sigma A

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The sphere

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(A) According to the Stefan-Boltzmann law,the rate of heat loss $dQ/dt$ is proportional to the surface area $A$ of the object,i.e.,$dQ/dt = e \sigma A (T^4 - T_0^4)$.Since the rate of cooling $dT/dt$ is given by $(dQ/dt) / (mc)$,and the mass $m$ and specific heat $c$ are the same for all objects,the rate of cooling is directly proportional to the surface area $A$.For a given mass and density,the object with the minimum surface area will have the minimum rate of heat loss.Among a sphere,a cube,and a thin circular plate of the same mass,the sphere has the minimum surface area.Therefore,the sphere will cool the slowest.

$A$ sphere,a cube,and a thin circular plate,all made of the same material,same mass,and same surface finish,are heated to a temperature of $200^{\circ} C$. Which of these objects will cool slowest when left in air at room temperature?

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