# Specific Heat of Nano Particles

Specific heat of nano particles is less than bulk specific heat of them. Why?

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$$C_{v-total} = C_{v-electrons} + C_{v-phonons} = (\frac{\partial U}{\partial T}_{v-electrons}) + (\frac{\partial U}{\partial T}_{v-phonons})$$.
Taking into account that energy distributions, we can calculate the specific heat as $$C_{v-total} =\frac{d}{dT}\int E f_{FD}(E)D(E)dE + \frac{d}{dT}\int E f_{BE}(E)D(E)dE$$