Wikipedia:Peer review/Equipartition theorem/archive1

Equipartition theorem

This article concerns the equipartition theorem, a result of 19th century physics that has great generality and was instrumental in showing the need for quantum mechanics. The article is about to go to FAC, and preliminary comments and suggestions would be very welcome. Thank you! :) Willow 17:21, 22 April 2007 (UTC)[reply]

Review by Awadewit

Hello, Willow. Well, I don't know how much help I'm going to be since my math skills are limited. I have tried to focus my comments here on the lead, the history and on the prose (I'll do a source check in preparation for FAC later). I will add some more later; I have only gone through about half of the article.

I'm sure that someone spent a long time making that animation, so I hate to say that I found it distracting while I was reading the lead - but I did. Since I am unfamiliar with the equipartition theorem, I was really trying to concentrate on the text and the animation was really distracting. Just one reader's opinion, though. Maybe not next to the lead?

I improved the caption — is it any better? I'd kind of like to keep it, because it shows at a glance the kind of jittery thermal motion we're dealing with, and how amazing it is that we can compute an average energy, even when that energy is fluctuating wildly. Willow 19:18, 26 April 2007 (UTC)[reply]

The caption is better. I just thought I'd tell you about my wandering eyes. Awadewit 04:52, 27 April 2007 (UTC)[reply]

I had someone explain the equiptartian theorem to me before I read this article, which is good, because the lead was confusing for a non-scientist like myself. I was thrown by the first paragraph.

In its simplest form, equipartition states that every classical degree of freedom that appears only quadratically in the expression for the total energy contributes ½kBT to the average energy of the system in thermal equilibrium, and therefore ½kB to the system's heat capacity. Here, kB is the Boltzmann constant and T is the temperature. - I'm not sure what audience you are aiming for here, but this is hard to grasp. If your only audience is physicists, then I'm sure you are fine, but I always think that the lead, at least, should try to explain the concept in terms that an educated lay person, at least, could understand.

I totally agree, and I'm mortified after re-reading the article just how dense it and its editrix were. Will work on improving the whole article, although it could be a Long Road. :( Willow 18:57, 26 April 2007 (UTC)[reply]

I'm not sure that the whole article is a possibility, since it relies on a lot of previous knowledge of higher math - I just ask that the lead be comprehensible to an educated lay reader. Awadewit 04:52, 27 April 2007 (UTC)[reply]

The lead is jargon-heavy. I realize that some amount is necessary and unavoidable, such as "thermal equilibrium" and "specific heat," but what about "ergodic"? Although I am a curious reader, I am unlikely to click on all of these links to remind myself what all of these concepts are. Reduce!

Sacrificed "ergodic" as implicit in "thermal equilibrium", and too arcane for the lead. Willow 18:57, 26 April 2007 (UTC)[reply]

Ah yes, "the infamous ultraviolet catastrophe." We all remember that. It was when aliens hit the earth with their evil ultraviolet rays. :) Again, I just ask the editors to think about audience, particularly in the lead. Whenever we use words that imply a reader should already know about something (such as "infamous") we should be very careful.

My personal ultraviolet catastrophe happened when I forgot to use sunscreen once before a long bike-ride. ;) How embarrassing! :P OK, fixed (I hope). Willow 18:47, 26 April 2007 (UTC)[reply]

In Figure 1 you simply have the abbreviation for the elements. I suppose everyone looking at this page will know what elements you are referring to? No need to link those?

Added elements to caption. Willow 18:57, 26 April 2007 (UTC)[reply]

Just proofreading now.

There is an odd period separation after the Maxwell-Boltzmann equation. I tried to fix it but couldn't. On my screen, the period appears by itself on the next line.

I can't see this myself — do you still see it? Willow 18:57, 26 April 2007 (UTC)[reply]

It only appears on one of my computers. It must be one of those weird wiki-layout things. Awadewit 04:52, 27 April 2007 (UTC)[reply]

where NA is the Avogadro constant - "Avogadro's constant"?

Fixed up.

The symbol H is used for energy here because the energy function is often called a Hamiltonian. - this seemed a little wordy

Fixed up.

As another example, a harmonic oscillator such as a spring has a quadratic potential energy - something struck me as odd about "as another example"

Replaced with "Likewise,". Willow 19:18, 26 April 2007 (UTC)[reply]

In 1876, Ludwig Boltzmann expanded on this principle by showing that the average energy was divided equally among all the independent components of motion in the system. - "the system" or "a system"?

Great catch! :)

More generally, molecules were believed to be composed of parts (atoms) already in the 19th century, and should have much higher specific heats than observed, as noted first by Maxwell in 1875. - "molecules were believed to be composed of parts . . . which should have had much higher specific heats"?; also, it is not totally clear what Maxwell is noting - too many clauses

This one is thorny. Does it read any better now? Willow 19:18, 26 April 2007 (UTC)[reply]

Yes. Awadewit 04:52, 27 April 2007 (UTC)[reply]

The failure of the equipartition theorem to account for the specific heat capacities of solids and gases was addressed in several ways. - "addressed" is not quite right; what about something like "explained" or "rationalized"; also you have "defended" twice in that paragraph - it seems a little repetitive

Excellent! re-worded and simplified.

The simplest application of the equipartition theorem is to a simple harmonic oscillator. - Although this may be a technical term and I don't know it, it is odd to have "simple" repeat. Also, of course, this whole thing looks far from "simple" to me. That's one of those words that one should use sparingly like "clearly" or "obviously." I wonder if a synonym like "uncomplicated" might have better connotations. Maybe that's just me, again. I'm sure you meant to use "simple" in its "this is the most reductive" system way, but all of those connotations do one in.

Sigh, I cannot believe that I didn't notice that myself. :P OK, fixed up.

It seems to me that the article is overlinked in general. Deep into the article, "temperature" is linked, for example. I doubt that readers who have come that far really need that link. I am becoming a bit of a de-linker.

I'm a little too link-happy myself, which Opabinia is always rescuing me from. Will work on this as well.

Awadewit 19:51, 25 April 2007 (UTC)[reply]

I really, really appreciate all your work on this, especially when you have so much else going on, both here at Wikipedia and no doubt in the real world. There's definitely not an equipartition of reviewers, but I'm very happy that you came here to help out. Willow 18:57, 26 April 2007 (UTC)[reply]

Part 2

Take them or leave them.

I opted to "take" them; thanks! ;) Willow 11:49, 27 April 2007 (UTC)[reply]

The anharmonic oscillator — one in which the potential energy is not quadratic in the extension q — provides a complementary view of the equipartition theorem. - "An anhormonic oscillator"? - also, not clear to me why "anharmonic" is italicized
this latter equipartition result does not allow the average potential energy to be written in simple form - "in the simple form"?
In such cases, the kinetic energy of a single particle is given by a different formula - "is given by the formula"?
As a simple illustration, the gas particles may be assumed to be spherically symmetric (isotropic) and interacting only by a pair potential V(r), where r is the distance between the two particles. - something seems off to me here; is it wordy? are the verbs not parallel?
Therefore, the heat capacity of a gas of N diatomic molecules is predicted to be 7N · ½kB; p1 and p2 contribute three degrees of freedom each, whereas q contributes the seventh. Therefore, the heat capacity of a mole of diatomic molecules with no other degrees of freedom should be (7/2)NAkB=(7/2)R. Therefore, the predicted molar-specific heat should be roughly 7 cal/(mole·K) - three "therefores" in a row
This disagreement cannot be explained by using a more complex model of the molecule - "This disagreement" between what and what?
Taking the dot product of this equation with the position vector r and averaging yields the basic equation for Brownian motion - this structure seems a bit odd to me - maybe "and then averaging [insert appropriate noun]"
For small times, t << τ, the particle acts as a freely moving particle; the squared distance grows quadratically - "For short time spans"?
However, for long times, t >> τ, the squared distance grows only linearly with the time - "for long time spans"?
Do you need all of those "See also" links? Most of those are linked in the article, right?
One of your notes has a "this template is marked for deletion" box in it. Awadewit 04:46, 27 April 2007 (UTC)[reply]

Fixed all of these, I think. Thanks again for your help with the article, Awadewit! Wishing you serene contemplations of Locke, Willow 11:49, 27 April 2007 (UTC)[reply]