Does the heat capacity change for a metallic system?

[girlinphysics]

In class we derived the relationship between temperature and heat capacity for the Debye model. We found that in 3D the heat capacity is proportional to temperature cubed. My question is, would this relationship change in a metallic system?

 

[nasu]

The Debye model is applied to the heat capacity of the lattice. This contribution applies to metals too.
In metals there is another contribution from the free electrons but it is quite small and it shows up only at very low temperatures.
So yes, there is a range of temperatures in metals where the cubic law applies quite well.
See this illustration, for example:
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/imgheat/silisph.gif

 

[girlinphysics]

The Debye model is applied to the heat capacity of the lattice. This contribution applies to metals too.
In metals there is another contribution from the free electrons but it is quite small and it shows up only at very low temperatures.
So yes, there is a range of temperatures in metals where the cubic law applies quite well.
See this illustration, for example:
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/imgheat/silisph.gif

This explains a lot, thank you very much for your answer!