# 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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