I calculated the contribution of electron in heat capacity of some compounds.Now i want to compare their thermal conductivity which is due to electron contribution.Is there any relation between these quantities?
Here are some links which may be interesting for you:
http://uspas.fnal.gov/materials/10MIT/Lecture_1.2.pdf
http://www.answers.com/Q/Is_there_a_relationship_between_specific_heat_capacity_and_thermal_conductivity
http://arxiv.org/ftp/physics/papers/0404/0404117.pdf
I personally would expect some inter-relation in the case of covalent solids, as both properties are determined by lattice vibrations. In the case of metals where the electronic component is strong I do not expect interrelation..
As the matter of fact, you can correlating both through the thermal diffusivity. The thermal diffusivity is defined as:
α = k/ρCp
where:
α - the thermal diffusivity
k - the thermal conductivity
ρ - density
Cp - the specific heat capacity at constant pressure
Thermal diffusivity is an importnat parameter for transcient heat conducttion analysis (applied to lumped parameer analysis for infinite thermal conductivity and for semi infintie solids),, which is the ratio of thermal conducitivity and thermal storage capacity a product of density and specific heat.. .
As far as a numerical relation, thermal diffusivity (alpha = k*rho*C_P) or effusivity (e = (k*rho*C_P)^(1/2)) is likely what you are looking for. Sometimes one is of more convenient form than the other, if you are trying to fit to experimental data, for example. However, that still gives you at least two unknowns and one equation if you don't know the diffusivity or effusivity.
When talking about the actual heat transfer mechanisms, the significance of electron/phonon contributions depends greatly on the material. At most real-world temperatures, phonons completely dominate heat capacity. In dielectrics, phonons contribute more to thermal conductivity while electrons contribute more in metals due to the free electron population and mobility.
You may be interested in looking into the Wiedemann-Franz-Lorenz law, which relates the electron (only) thermal conductivity to the electrical conductivity of a metal or metal-like (think highly-degenerate semiconductor) material.
After rereading your initial question, you are probably most interested in the kinetic theory derivation of thermal conductivity, which yields:
ki = (1/3)*Ci*vi*λi, where for each energy carrier 'i' (electron, phonon, etc.)
Ci = heat capacity of energy carrier 'i' (J / m^3-K)
vi = velocity of energy carrier 'i' (m / s, order of 10^3 for phonons, 10^6 for electrons)
λi = mean free path of energy carrier 'i' (avg distance traveled between consecutive scattering events, order of a few nm to microns)
This is, in fact, at the heart of the Wiedemann-Franz-Lorenz law, where by assuming the electronic mean free paths contributing to thermal and electrical conduction are approximately the same (not always true), taking the ratio cancels it and removes an unknown.
The thermal diffusivity, α (m^2/s), relates thermal conductivity, k (W/mK), and specific (volume) heat capacity, C (J/m^3K), through the following relationship:
α = k/C = k/ρc
here C= ρc, ρ (Kg/m^3) is the density and c (J/kgK) is the specific heat
(for imcompressible substances, i.e. for most solids, cp = cv =c).
Thermal diffusivity is (1/3)v*λ (see Dunham comment )
https://physics.stackexchange.com/questions/16255/are-specific-heat-and-thermal-conductivity-related
Elsewhere at this forum, I have suggested a mixture rule to estimate the thermal diffusivity for a composite after those of its components: https://www.researchgate.net/post/Why-the-thermal-diffusivity-of-polymer-composites-increases-with-filler-loading
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