Feynman Lectures and the Zeroth Law of Thermodynamics

[lugita15]

In Volume 1 of the Feynman Lectures on Physics, Feynman derives the ideal gas law from Newton's laws of motion. But then on page 41-1, he puts a caveat to the derivation he has just completed: "We have perpetually been making a certain important assumption, which is that if a given system is in thermal equilibrium at a given temperature, it will also be in equilibrium with anything else at the same temperature ... This proposition is true and can be proven from the laws of mechanics, but the proof is very complicated and can be established only by using advanced mechanics. It is much easier to prove in quantum mechanics than it is in classical mechanics. It was proved first by Boltzmann, but for now we simply take it to be true."

Does anyone know what Feynman is talking about? Is he referring to the Zeroth Law of Thermodynamics? Can it be proved using Newton's laws of motion, and is the proof really complicated? Where can I find this proof?

Any help would be greatly appreciated.
Thank You in Advance.

 

[lugita15]

I've done some reading about Boltzmann, and I'm thinking that this may have something to do with the equipartition theorem. Is the equipartition theorem in any way connected to the zeroth law?

 

[ogion]

I think you have it right - its the zeroth law of thermodynamics.

The proof of the zeroth law is complicated - because it involves showing that there is a function of the (macroscopic) thermodynamic variables which can be used to define equilibrium (this function is the temperature) starting from microscopic variables (for instance the positions and momenta of all the molecules making up a gas).

 

[lugita15]

I think you have it right - its the zeroth law of thermodynamics.

The proof of the zeroth law is complicated - because it involves showing that there is a function of the (macroscopic) thermodynamic variables which can be used to define equilibrium (this function is the temperature) starting from microscopic variables (for instance the positions and momenta of all the molecules making up a gas).

Where can I find this proof of the zeroth law from Newton's laws? Why does it require "advanced mechanics" (which I assume refers to Lagrangians and Hamiltonians) and why is it easier if you start from quantum mechanics instead?

 

[sardar]

I can shed some light on Feynman's statement and the connection to the Zeroth Law of Thermodynamics. Firstly, the Zeroth Law of Thermodynamics states that if two bodies are each in thermal equilibrium with a third body, then they are in thermal equilibrium with each other. This may seem like a simple and obvious statement, but it is actually a fundamental principle in thermodynamics and has important implications for the behavior of systems in thermal equilibrium.

Feynman is indeed referring to the Zeroth Law in his statement and is essentially saying that the ideal gas law, derived from Newton's laws of motion, assumes that this law holds true. However, proving the Zeroth Law from Newton's laws of motion is a complex and advanced task, and it is much easier to prove using quantum mechanics.

The proof of the Zeroth Law using classical mechanics was first done by Austrian physicist Ludwig Boltzmann in the late 1800s. However, this proof is not as straightforward as one might think and requires a deep understanding of statistical mechanics and thermodynamics. It is not something that can be easily explained in a few sentences and would require a significant amount of study and mathematical rigor to fully understand.

If you are interested in learning more about the proof of the Zeroth Law, I would recommend studying statistical mechanics and thermodynamics, as well as looking into specific textbooks or papers on the subject. While it may be challenging, understanding the proof of the Zeroth Law is essential for a complete understanding of thermodynamics and the behavior of systems in thermal equilibrium.

I hope this helps clarify Feynman's statement and provides some direction for further study. Good luck in your scientific journey!