# 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)K
_{B}T=K_{B}T, as (1/2)K_{B}T is PE and (1/2)K_{B}T is KE of the atom.

- In three dimensions average kinetic energy is 3K
_{B}T.

- 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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