Which Will Have The Higher Temperature?

Classical Mechanics Level 5

Consider two identical homogeneous spheres made of the same material. Each of the spheres is of mass \(m\) and radius \(r\). Both have the same initial temperature. One of them rests on a thermally insulating horizontal plane and the other hangs from an insulating thread. Now equal amount of heat \(Q\) is given to each of the spheres as a result of which their temperature rises.

Find the absolute value of the difference in the final temperatures of the spheres in Kelvins rounded off to the nearest integer.

Details and Assumptions:

  • All kinds of heat losses are negligible.
  • \(m=1\mbox{ kg}\)
  • \(r=1\mbox{ m}\)
  • \(g=10\mbox{ m/s}^{2}\)
  • \(Q=100\mbox{ J}\)
  • Coefficient of linear expansion of the material (\(\alpha\))=\(10^{-6} \mbox{ K}^{-1}\)
  • Specific heat capacity of the material of the spheres\((C) \) = \( 2\times10^{-2} \mbox{ J K}^{-1} \mbox{ kg}^{-1}\)

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