Are there any logical relationship between specific heat capacity and thermal co

Question

Are there any logical relationship between specific heat capacity and thermal conductivity ?

I was wondering about this when I was reading an article on whether to choose cast iron or aluminium vessels for kitchen.

Aluminium has more thermal conductivity and specific heat than iron ( source ).

This must mean more energy is required to raise an unit of aluminium than iron yet aluminium conducts heat better than cast iron.

Does it mean that aluminium also retains heat better ?

How does mass of the vessel affect the heat retention?

Explanation / Answer

There is not really a general answer to your question because both, the specific heat capacity and the thermal conductivity are not due to a single process in the material.

Both are in general terms a "sum" over the individual components in the material that can store thermal energy or transport thermal energy.

For metals at room temperature the most important terms of these sums are the electrons and phonons (vibrations of the lattice). Both can store and transport thermal energy. Their exact values, temperature dependence, etc. is highly material specific.

The specific heat part that is due to the electrons is mainly governed by electrons within a certain energy range (the Fermi energy). Exactly the same electrons transport heat in the material. So more electrons in that range means both, more specific heat and a higher thermal conductivity.

This get complicated if you look at a real material. A little bit of impurities or defects will influence the thermal conductivity quite a bit but the specific heat will not be influenced significantly.

In your concrete case:

Yes, Aluminium will be able to store more thermal energy than Iron (http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html) per mass.
The mass will linearly increase the heat capacity, more mass, higher heat capacity.

(I did not use your term retention, because it is not really defined, but thermal conductivity and heat capacity are easy to understand)

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