Please Explain Your Answer

Classical Mechanics Level 3

A solid sphere of copper of radius $R$ and hollow sphere of the same material of inner radius $r$ and outer radius $R$ are heated to the same temperature and allowed to cool in same environment.

Which of the following is correct?

none of these both start cooling at the same rate hollow sphere starts cooling faster solid sphere starts cooling faster

1 solution

Neelesh Vij
Oct 4, 2016

Assuming all heat is lost due to radiation.

By stephan-bolzmann's law:

$\displaystyle \dfrac{dQ}{dt} = AeT^4 = mc \dfrac{dT}{dt}$ : where $e$ is the emmisivity of material

Mass can be written as $\text{volume} \times {density}$ . As crosssection area and density for both sphere is same so:

$\displaystyle \dfrac{dT}{dt} = \dfrac{e \times T^4}{c \times \text{volume of material}}$

For hollow sphere the volume is less so the initial rate of cooling will be higher for hollow sphere !

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