Electronic and magnetic heat capacity

4 Heat capacity contributions of electronic origin Electronic and magnetic heat capacity 

Using this simple argument, the electronic heat capacity, CE, of a free electron gas is 

An exact derivation that takes into account the variation of the Fermi level with temperature gives basically the same result  

The electronic heat capacity thus varies linearly with temperature and is often represented as 

Since the lattice contribution to the heat capacity varies with T3, the total heat capacity at low temperatures (typically T 10 K or lower) to a first approximation is given by 

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