Does the Kinetic Theory of Gases have an analog for solids?

[yrjosmiel]

And if I can extend this further, for liquids?

 

[mjc123]

No. Kinetic theory of gases, in its simplest form, assumes there are no intermolecular forces, and treats molecules as hard spheres. Solids and liquids only exist at all because of intermolecular forces, and to understand them you have to appreciate the nature of the forces, their strength, directionality etc. Unfortunately there cannot be anything as simple as the kinetic theory of gases for condensed phases.​

 

[Lord Jestocost]

Within the framework of the "Sommerfeld Theory of Metals", one speaks of the "Electron Gas".

 

[vanhees71]

This "electron gas" describes only a part of the solid, namely the conduction electrons, and it provides a good description for certain quantities related with them (like heat and electric conductivity).

In fact, it's one very successful trick to figure out, whether for some aspect you are interested in about a condensed-matter (many-body) system you can find an apropriate quasi-particle description. These are collective (quantized) modes that have narrow spectral functions in energy. An example are the conduction electrons and phonons (i.e., quantized collective vibrations of the crystal lattice) in a metal.

 

[yrjosmiel]

Then, if temperature means the average kinetic energy per particle for gases, what does it mean for solids and liquids?

 

[DrClaude]

Then, if temperature means the average kinetic energy per particle for gases, what does it mean for solids and liquids?

Who says that temperature means that? Temperature is well defined thermodynamically:
$$
\frac{1}{T} = \frac{\partial S}{\partial E}
$$

 

[yrjosmiel]

Who says that temperature means that? Temperature is well defined thermodynamically:
$$
\frac{1}{T} = \frac{\partial S}{\partial E}
$$

Based on the historical development of the kinetic theory of gases, a simplified description of fluid matter, temperature is proportional to the average kinetic energy of the random microscopic motions of the constituent microscopic particles, such as electrons, atoms, and molecules, but rigorous descriptions must include all quantum states of matter.
-Wikipedia

I got it from here.

Also, if possible, can you explain to me what that equation means?

 

[jbriggs444]

Also, if possible, can you explain to me what that equation means?

The equation in question being $\frac{1}{T}= \frac{\partial S}{\partial E}$
That same equation (in somewhat altered form) can be found in equation (10) at https://en.wikipedia.org/wiki/Temperature#Definition_from_statistical_mechanics

It says that the partial derivative of Entropy with respect to Energy is equal to the inverse of temperature. In somewhat simpler terms, $\frac{\partial S}{\partial E}$ tells you how much entropy will increase if you add a little energy to a particular system.

If entropy increases a lot when you add energy, that means that inverse temperature is high. So temperature is low. That's a cold system.
If entropy increases a little when you add energy, that means that inverse temperature is low. So temperature is high. That's a hot system.

Second law of thermodynamics: Entropy always increases.

If you put a "hot" system in contact with a "cold" system, heat must flow so as to increase entropy. Some heat will flow into the "cold" system (where a little energy increase results in a lot of entropy increase). It will flow out of the "hot" system (where a little energy decrease results in only a little entropy decrease).

[I've never taken a thermo course -- @DrClaude certainly knows this stuff far better than I]

A nice thing about this formulation is that it still works when the kinetic energy formulation fails. It even works in exotic environments where an increase in energy results in a decrease in entropy. In those environments, one can have a negative temperatures -- which turn out to be hotter than any positive temperature. That feature is one reason for expressing the above equation in terms of $\frac{1}{T}$. Inverse temperatures do not have that annoying jump between positive and negative.

 

[yrjosmiel]

However, can I still say that temperature is related with the movement of the particles? Or is that an understatement to what temperature really is?

 

[jbriggs444]

However, can I still say that temperature is related with the movement of the particles? Or is that an understatement to what temperature really is?

Over a reasonable variety of conditions, kinetic energy per degree of freedom is a good measure of temperature.