Re: [Phys-L] the historical determination of absolute zero

[John Denker <jsd@av8n.com>]

On 10/17/24 11:36 AM, Prof. Keith S. Taber via Phys−l wrote:
> I was very surprised to read that absolute zero had been found from
> studies of Brownian motion

Your skepticism is very well founded.

The Kelvin temperature scale was proposed in 1848 by some guy named Kelvin, and there had been various more−or−less accurate estimates of absolute zero even before then. Good brief discussion here:
  https://www.nist.gov/si−redefinition/kelvin−history

This was many decades before Einstein gave a thermodynamic explanation for Brownian motion.

The history of absolute zero is the history of thermometry, and indeed the history of the concept of temperature.

There are lots of things you would expect to be proportional to absolute temperature, and you can measure any of them and extrapolate to zero. Most of them poop out at some point; for example, at low temperatures your ideal gas becomes non−ideal. Even so, you can cross check different methods in the regime where they agree and extrapolate that.

Kelvin spent a few words discussing that, then pointed out that there's one thing that is independent of any particular material, namely Carnot efficiency. Whatever refrigerator you're using to produce low temperatures can serve as its own thermometer. Inject a known amount of energy (via an electrical heater or whatever) and measure how efficiently the refrigerator deals with it. (Been there, done that.)

https://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html


Here's the modern approach: Start with the expression
              ∂E            ∂E
        dE = −−−−−−−− dS − −−−−−−−− dV
              ∂S | V        ∂V | S

which is not even physics; it's just math. It's the chain rule for partial derivatives, subject to mild conditions.

Identify that with the intuitive expression:
        dE = T dS − P dV

and we have, implicitly, the definition of temperature. The only possibility is
             ∂E
        T = −−−−−−−−
             ∂S | V

You can rather easily prove that T, defined this way, behaves the way it should, in accordance with your intuitive notions of temperature, including ideal gases, Brownian motion, Carnot efficiency, zero-point motion, et cetera.


On 10/17/24 2:23 PM, Paul Nord via Phys-l wrote:

> Motion does not cease at 0ºK.

Very true.

> But we can say nothing about what the motion is.

I wouldn't go that far. There's quite a lot we can
say, some of it quite interesting.


>  It does not interact with other matter since a collection of
> particles at this temperature has no energy to give up in an interaction
> with other particles.

That's what Einstein thought. That's what everybody thought
for the longest time, but it's just not true.

Consider very cold resistor A connected to very cold resistor
B by a long wire. A radiates zero-point noise toward B and
vice versa. They exchange equal-and-opposite amounts of
energy per unit time, so they remain in thermal equilibrium
at zero Kelvin (just like any other temperature).

You can actually measure the zero-point radiation, but you
have to use a voltmeter (not a photon counter). And it has
to be a really fancy voltmeter, because the voltage is tiny.
The experiment has been done.
  https://www.sciencedirect.com/science/article/abs/pii/0378436381909785