[galpinj]

Hey guys,

Based on my earlier understanding of thermodynamics, adding thermal energy to a system allows the atoms to "vibrate" more and thus move around with more vigor; however, I was recently reading about how the electron sea found in metallic solids is important for the conduction of heat. This makes sense based on prior knowledge (photons can cause electrons to jump to higher energy levels), but doesn't really fit into my picture of how heat influences atoms.

So, does heat increase the velocity of the atom, or does it impact the electrons? Does it do both? Do protons or neutrons have any role in this?

Thank you

[orthoformate]

The atom includes the protons, neutrons, and electrons.

[mjc123]

Thermal conductivity is not the same thing as heat capacity.

[Enthalpy]

In a gas, the valence electrons are bound to one molecule, and even jumping from one molecular orbital to an other uses to need more energy than heat provides (allow for rare exceptions), so the valence electrons don't store nor transport heat.

In a metal, each state available to valence electrons extends to the whole solid, and these states are very close to an other, so heat suffices to put some proportion of the electrons in an energy state that is not minimum. Hence, the electrons can move.

Only a small proportion of all valence electrons of a metal is mobile. The available states extend over few eV energy while room temperature is 26meV, so only the few electrons near the "Fermi level", up to which the states are occupied, can receive enough energy to jump to an available free state. This tells you why the electrons store little heat in a metal too, far less than the vibrations of the crystal do.
https://en.wikipedia.org/wiki/Dulong-Petit_law

But these few electrons near the Fermi level are very mobile. They suffice to let metals conduct electricity very well. And because these few electrons have a speed hence an energy and store heat, they transport heat too in their movements, and do it well because they're so mobile.

One can even find a rule between the conduction of electricity and heat in metals, because a moving electron transports 3kT/2 as well as q. Provided that the crystal's vibrations conduct far less heat than these mobile electrons do, the ratio of both conductivities depends on kT/q but not on the alloy's composition
https://en.wikipedia.org/wiki/Wiedemann-Franz_law
this works nicely for metals around room temperature and is useful with incomplete alloy data. It doesn't work at all for semiconductors and insulators (because their scarce or lacking mobile electrons conduct less heat than the crystal does), nor for superconductors.

----------

You believed to have understood that? Well, this was the standard textbook academic explanation, the one you're expected to answer to get your exams at university. Unfortunately, the Hall effect tells that around one valence electron per atom moves in a metal. Maybe I'm the only human with a problem with that, but I feel this theory is in strong contradiction with the Hall observations. Or maybe I got something wrongly.

[galpinj]

In a gas, the valence electrons are bound to one molecule, and even jumping from one molecular orbital to an other uses to need more energy than heat provides (allow for rare exceptions), so the valence electrons don't store nor transport heat.

In a metal, each state available to valence electrons extends to the whole solid, and these states are very close to an other, so heat suffices to put some proportion of the electrons in an energy state that is not minimum. Hence, the electrons can move.

Only a small proportion of all valence electrons of a metal is mobile. The available states extend over few eV energy while room temperature is 26meV, so only the few electrons near the "Fermi level", up to which the states are occupied, can receive enough energy to jump to an available free state. This tells you why the electrons store little heat in a metal too, far less than the vibrations of the crystal do.
https://en.wikipedia.org/wiki/Dulong-Petit_law

But these few electrons near the Fermi level are very mobile. They suffice to let metals conduct electricity very well. And because these few electrons have a speed hence an energy and store heat, they transport heat too in their movements, and do it well because they're so mobile.

One can even find a rule between the conduction of electricity and heat in metals, because a moving electron transports 3kT/2 as well as q. Provided that the crystal's vibrations conduct far less heat than these mobile electrons do, the ratio of both conductivities depends on kT/q but not on the alloy's composition
https://en.wikipedia.org/wiki/Wiedemann-Franz_law
this works nicely for metals around room temperature and is useful with incomplete alloy data. It doesn't work at all for semiconductors and insulators (because their scarce or lacking mobile electrons conduct less heat than the crystal does), nor for superconductors.

----------

You believed to have understood that? Well, this was the standard textbook academic explanation, the one you're expected to answer to get your exams at university. Unfortunately, the Hall effect tells that around one valence electron per atom moves in a metal. Maybe I'm the only human with a problem with that, but I feel this theory is in strong contradiction with the Hall observations. Or maybe I got something wrongly.

So, in gases, what is storing/transporting heat? How does heat impact the whole atom? It seems strange that, in some instances, heat affects the electrons of an atom, while in other instances its impacting the atom as a whole. What is going on here?