# Motion and Heat

Discussion in 'Physics & Math' started by SimonsCat, Jan 21, 2017.

1. ### SimonsCatRegistered Member

Messages:
213
Ugh, I can't actually stand the man. But behind his skeletal, Marfan like features, the basic concept of motion and heat is hopefully not lost and hopefully can explain it in simpler terms so that [some] posters will learn the theory of kinetic heat.

Last edited: Jan 21, 2017

3. ### exchemistValued Senior Member

Messages:
6,923
What makes you think that this will teach anybody here anything? This is for 9 year olds.

Q-reeus likes this.

5. ### exchemistValued Senior Member

Messages:
6,923
I listened to you, but I decided I agreed with Q-reeus rather than with you, and said so.

I explained reasonably clearly what I think the correct interpretation of zero point energy is, as far as temperature is concerned. I laid out my argument - demonstrating as I did so that I know at least a decent amount of the relevant physics, and I cited sources in support of my interpretation. What is more, I was able to do so in a civil manner.

This video, as you well know, says nothing at all about what we were discussing and is clearly aimed at children. Your comment that you think it is appropriate "to get through to " me can therefore be nothing but mere abuse.

If you can manage to write a civil and properly reasoned critique of my argument, I will do my best to respond in a thoughtful and civil way.

7. ### exchemistValued Senior Member

Messages:
6,923
You are making up rubbish now. I actually said the exact opposite of (1). I quote myself" I would argue that the fact that zero point motion cannot be passed to another object precludes it contributing to heat"

And I never said, at all, that temperatures can reach absolute zero in real experiments. I said the opposite, in fact.

I can only suggest you re-read what I wrote.

Messages:
6,923

9. ### rpennerFully WiredRegistered Senior Member

Messages:
4,833
The relation between motion and heat is much more nuanced than that 2 minute video clip would imply.

First, not all motion is heat. There is nothing wrong, in principle, with a rifle that shoots high-velocity shards of ice.
Second, not all heat is motion. Einstein helped unlock the heat message of spectral lines and along the way gave us the theory behind lasers.

Back in the bad-old-days (pre-relativity, pre-quantum physics) people didn't know if atoms existed. Chemistry seemed to work like atoms existed as elements combined in ratios which were easily explained if 16 volumes of hydrogen gas had about as many atoms as 1 volume of oxygen gas. So, envisioning molecules as idealized, point-like particles, the physicists (ignoring now the history of the chemistry-physics split) worked out how gases behave.

Steam engines were important then, and physicists worked out the laws of thermodynamics.

Uniting the two is the field of statistical mechanics which describes systems at equilibrium. This method of calculation proved so strong that it applies even in quantum mechanical descriptions.

So, for an ideal gas, the random motion of a gas at equilibrium is synonymous with its heat. But we know molecules aren't point-like so some of that motion may be internal, like rotation and vibration, so gases have higher heat capacity at high temperatures than then ideal gas model suggests. Likewise, we know that relativity applies and there is an upper limit on how much motion one may put into a system, but not an upper limit on how much heat.

But statistical mechanics can also tell us about a system without motion. If we have a collection of atoms each of which may be in only one of two stationary states, at finite temperature, naturally most of the atoms will be in the lower state. As the temperature goes higher and higher, the number of atoms in the lower state never falls below half. ( The proportion of atoms in the lower state is roughly $\frac{1}{2} + \frac{\Delta E}{4 k_B T}$.) Indeed, we can consistently describe the system in terms of either temperature or fraction of atoms in the lower state, so we can describe temperature in terms of that fraction: $T = - \frac{\Delta E}{k_B \, \ln (1 / f - 1 ) }$. No motion involved.

A similar treatment of atoms in a solid, gives each atom a state in a 3-D harmonic oscillator, $E_{n_x,n_y,n_z} = \hbar \omega \left( \frac{3}{2} + n_x + n_y + n_z \right)$
So we have the fraction in the lowest state as $\frac{e^{-\frac{3}{2} \hbar \omega / ( k_B T) } }{ \sum_{k=0}^{\infty} \frac{(k+1)(k+2)}{2} e^{-(\frac{3}{2} +k)\hbar \omega / ( k_B T) } } = \frac{1 }{ \sum_{k=0}^{\infty} \frac{(k+1)(k+2)}{2} e^{- k \hbar \omega / ( k_B T) } } = \left( 1 - e^{-\frac{\hbar \omega}{k_B T}} \right)^3$ .

So there is still zero point motion, but increasingly no more free energy as all the atoms pile up in the ground state. The same quantum mechanics which says there is zero point motion at the lowest possible state doesn't let you extract energy from it because there is no lower state.

exchemist likes this.
10. ### rpennerFully WiredRegistered Senior Member

Messages:
4,833
No. That's bogus. Thermodynamics and quantum physics are more fundamental than your naive notions of "freezing." There is no fundamental reason why Helium-4 needs to freeze solid. The potential well of the quantum oscillator in this case is simply too shallow to support a ground state.

11. ### SimonsCatRegistered Member

Messages:
213

Not a badly written post and does cover why heat isn't always motion; these special cases don't really apply to the argument because we are specifically talking about residual motion in context of zero point fields by linking thermodynamic properties to an equipartition-like approach.

12. ### SimonsCatRegistered Member

Messages:
213
Of course there is no fundamental reason why H-4 needs to freeze solid, because only such a statement is classical in nature. Clearly a system refuses to freeze over at the ground state because of the existence of residual motion. There are fundamental reasons why H-4 cannot completely freeze over, which is my point.

13. ### SimonsCatRegistered Member

Messages:
213
which is my point, naive as you think it is. You have to remember, we have to talk in less technical terms sometimes so an audience can grasp what the hell we are talking about.

14. ### rpennerFully WiredRegistered Senior Member

Messages:
4,833
Don't critique. Do better. I clearly am calculating canonical assemblies to get at my fractions.
1) H-4 is the unstable hydrogen isotope with 3 neutrons. You need to abbreviate Helium-4 as He-4 or $_2^4 \textrm{He}$ or $^4 \textrm{He}$. https://en.wikipedia.org/wiki/Isotopes_of_hydrogen#Hydrogen-4

2) You don't have "residual motion" unless the atoms are in a lattice already, i.e. a solid. So you can't explain why there isn't a solid by pointing at residual motion.

3) There is a fundamental reason the Helium-4 doesn't freeze under its own vapor pressure, which is that Helium-Helium attractions are short-range and weak while Helium atoms are light. Therefore the potential well would be narrow and shallow, but the physical excursions of helium in that ground state are large compared to the hypothetical lattice of a Helium crystal, so Helium-4 does not freeze, at atmospheric pressure.

Solid helium at 2.5 MPa (25 more than normal) and 1 K exists and we've know this for decades.
http://journals.aps.org/pr/abstract/10.1103/PhysRev.109.328
We've also modeled the freezing of Helium for decades and the system seems fundamentally well described by the quantum mechanics of bosons.
https://journals.aps.org/pr/abstract/10.1103/PhysRev.165.293
You have to remember the Terms and Rules and the Sciforums site rules mean we already have a culture.

15. ### SimonsCatRegistered Member

Messages:
213
I don't really get this sentence at all. Can you explain what you are saying another way?

16. ### exchemistValued Senior Member

Messages:
6,923
Thanks for this. I had forgotten about helium not solidifying even at absolute zero (in the absence of external pressure, that is). It seems to be a nice prediction of the effects of zero point energy.

But it brings to mind a question. Should one regard this as the existence of a bound ground state with such a weak confining potential that the atoms continually tunnel out (i.e. the wavefunction extends way beyond the barrier, with substantial amplitude), or is it rather that the lowest translational state (in a container of normal dimensions) lies above the top of the barrier, because it is so low?

17. ### rpennerFully WiredRegistered Senior Member

Messages:
4,833
I'm sure the right way to think about it is a rather specialized corner of condensed matter physics. It's probably not related to the dimensions of the container (since He-4 is a liquid, not a gas, prior to freezing) but the dimensions of the lattice formed by the minimum of the atom-atom potential.

As it turns out, the attraction between atoms is so weak that the lattice spacing is not a minimum of the atom-atom attraction. So the behavior of the ground state is not simply modeled as a harmonic oscillator.

A true explanation lies at the intersection of quantum and condensed matter physics, but I haven't found any references I would recommend on the subject.

http://www.physics.udel.edu/~glyde/Solid_H13.pdf

18. ### exchemistValued Senior Member

Messages:
6,923
Thanks, yes, it struck me last night that of course since it is a liquid then the quantisation of translational motion won't relate to the size of the container but will - if anything- be more to do with the free path of the atoms in the liquid. But then, if it can't even be modelled as a harmonic oscillator, that also can't really be the right approach. Hmm.

19. ### rpennerFully WiredRegistered Senior Member

Messages:
4,833
Semiclassical reasoning can only take you so far, and then it's time to break out the full quantum simulation ala quantum chemistry.