indianaronald said:
On an undergrad engineering level of talk, is there any difference between conduction and diffusion ways of heat transfer? Conduction occurs because of the vibrational freedom of atoms. And diffusion is, I think, because of diffusing of atoms?
Heat conduction and heat diffusion are the same thing. On a macroscopic length scale, they both refer to the flow of entropy through the system. There may be some ambiguity when you try to define it in terms of microscopic parameters. When solving thermodynamics problems, one should ignore the atomic scale medium that actually transmits the energy.
Heat conduction is always entropy diffusion, regardless of the actual mechanism of energy transfer. Constraining the atomic scale mechanisms of heat conduction can over determine the mathematical problem.
Heat conduction doesn't have to occur through vibrating atoms (i.e., phonons). Heat conduction can also occur through free electrons vibrating on an atomic scale. This is why metals are such good heat conductors as well as electric conductors. The metals by definition conduct electricity by the flow of free carriers (electrons and holes).
The vibrating free electrons or free holes in a metal pass entropy much faster than vibrating atoms. So most of the heat conduction in a metal is actually carried by vibrating electrons that leave the atoms standing still. In a metal, the heat carried by atomic vibration is far less than the heat carried by free carriers.
In transparent media, entropy can also be carried by electromagnetic waves. Therefore, heat conduction can also occur due to the motion of photons. In meteorology, there are heat balance equations. Much of the "heat" carried upward is through infrared radiation, which is electromagnetic. Depending on context, this can be called heat flow or heat conduction.
The word "heat" can refer to the flow of entropy or a change in internal energy. In the phrases "heat conduction" and "heat conduction", the word heat refers to entropy not internal energy.
These two counter examples should help you understand that heat conduction is not always about vibrating atoms. Vibrating atoms may be a useful picture when analyzing heat flow in opaque insulators. However, the model fails when one is analyzing metals, semimetals or transparent insulators.
Entropy is sometimes referred to as a fluid. Entropy isn't made of loosely packed atoms, like gases. However, it has certain fluid-like properties. It is often useful to analyze the motion of entropy first on a macroscopic level before analyzing the motion on an atomic level. The fluid properties of entropy are not easily analyzed on an atomic level.
Solid state books often have a section on the heat capacity of both electrical insulators and metals. Here is one reference describing heat conductivity in metals:
"Introduction to Solid State Physics" seventh addition, by Charles Kittel (Wiley, 1996) pages 166-169.
Quote from bottom half of page 166:
"Do the electrons or the phonons carry the greater part of heat transport in a metal? In pure metals, the electronic contribution is dominant at all temperatures. In impure metals or in disordered alloys, the electron mean free path is reduced by collisions with impurities, and the phonon contribution may be comparable with the electronic contribution."
BTW: Phonons=Atomic vibrations.