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Specific Heat Capacity of Solids





Specific heat Capacity of Solids

  • From law of equipartition of energy we can can also determine specific heats of solids.
  • Consider that atoms in a solid are vibrating about their mean position at some temperature T.
  • Oscillation in one dimension has average energy equals 2(1/2)KBT=KBT, as (1/2)KBT is PE and (1/2)KBT is KE of the atom.
  • In three dimensions average kinetic energy is 3KBT.
  • For one mole of solid total energy is
    $U= 3NK_BT= 3RT$
  • At constant pressure ΔQ =ΔU+PΔV=ΔU since for solids ΔV is negligible hence
    C=ΔQ/ΔT=ΔU/ΔT=3R
  • This is Dulang and Petit law.
  • Here we note that predictions of specific heats of solids on the basis of law of equipartition of energy are independent of temperature.
  • As we go towards low temperatures T→0 there is a pronounced departure from the value of specific heat of solids as calculated.
  • It is seen that specific heats of substance approaches to zero as T→0.
  • This result can further be explained using the principles of quantum mechanics which is beyond our scope.

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