Talk:Boltzmann constant/Archive 1

k is not one of the Planck units - it is one of the physical constants on which the Planck units are based. At least, that's what our current article says - I'm not arguing the physics of this situation. To maintain the information content, I'll put in links from energy, temperature, etc. to Planck units. -- Tim

Sorry. I wanted to put a link in to Planck units; I was hoping someone would corrent my phrasing rather than just remove ... :) -- Tarquin

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I have to say, CYD, I disagree with just about every change you made to my text in your latest edit. Apparently k is now "a fundmental quantity which relates temperature to energy". What were the other quantities you were thinking of? And is k really a quantity? What is it a quantity of? It seems to me that it's a proportionality constant -- you can't produce 3.6k of something, but you can use it to say 1K is equivalent (in some sense) to 1.38×10^-23J.

Why did you change the HTML specification of the value to <math>? The only visible difference is that it's not wikified anymore.

In my section on characteristic energy, I was attempting to hint at nomenclature used in solid state physics. I deliberately left out a specific example of what the characteristic energy is, because it shows up in both statistical mechanics and solid state/quantum. I wanted to give a sense that k is used in almost any field of physics involving temperature (which it is).

What's wrong with meV? 25.9 meV is so much nicer than 0.00259 eV.

Entropy is important, and I appreciate your new section on it.

"Historically, the units of energy and temperature were defined before it was discovered that they were related." True. "As a result, the Boltzmann constant is expressed using the unit of temperature, and not the other way around." You've lost me. Which other way around? "Conceptually, however, the Boltzmann constant is the more fundamental quantity." Nope, still lost. More than what?

I think I can see what you're trying to get at with those last few paragraphs. My interpretation of the physical situation is that the relationship between energy and temperature is similar to the relationship between distance and time. In both cases, there are two sets of units originally defined in terms of physical quantities (e.g. orange-red radiation and triple points). Theoretically though, it would be much more sensible to define c=1, or c=α (the fine structure constant), in just the same way as it would be more sensible to set k = 1 and use Planck temperature. We can't necessarily argue that physically, k should be 1, but it should definitely be dimensionless.

-- Tim Starling 05:34 May 3, 2003 (UTC)

I'm not particularly concerned about most of the changes, so I have tweaked them to suit your objections. --CYD

Thanks. -- Tim

As for the relationship between energy and temperature, the key idea is this: energy is a microscopic (mechanical) quantity, and temperature is a macroscopic (thermodynamic) one. The main reason Boltzmann's definition of the entropy is so important is that it shows us how this macroscopic property of a system emerges from the microscopic details of its constituents. If you know enough about the mechanical properties of atoms, Boltzmann's equation shows you how to define a quantity, the "temperature", of large assemblies of atoms. In this sense, Boltzmann's constant defines the temperature, and not the other way around. -- CYD

The distinction between Boltzmann's constant defining temperature and temperature defining Boltzmann's constant seems rather arbitrary to me. Temperature is defined either macroscopically, by the properties of gases, or microscopically, with 1/(dS/dE) and Boltzmann's formalism. But in either case, k is merely a proportionality constant, and tells you about the units used to keep the books, not the physics involved. By itself, it tells you very little about the concept of temperature. It is Boltzmann's formalism (or the properties of gases), not k itself, that defines temperature.

But I'm getting distracted by a discussion of physics, and forgetting our main goal. Would it be fair to say that if your final paragraph confused me, it's going to confuse the general public? If you can think of a more eloquent way to put your ideas, in such a way that seems intuitive and correct to me, I'll be happy. I know my current final paragraph says something completely different to what you were getting at, but I think some reference to Planck units is warranted. Tarquin tried to include something about them a while back, but I cut it out. -- Tim Starling 00:15 May 5, 2003 (UTC)

Relation between charge and thermal energy

k is a relation between temperature and energy for a single atom (or single mole). There are a lot of equations in electrochemistry where you want to relate temperature to energy for a unit of charge (because in electrics we are more interested in units of charge than in number of atoms). So I was wondering if there is any defined symbol for the quantity e / k or k / e (equivalently F / R or R / F)? --Chinasaur 01:51, 14 Sep 2004 (UTC)

The relationship between temperature and energy is special. At a certain (constant) temperature $T$ there is a corresponding thermal energy $k_{B}T$. Roughly speaking, the thermal energy sets the bar for the energy of microscopic energy fluctuations; if the thermal energy is higher, the fluctuations get correspondingly stronger. This is a fundamental part of statistical mechanics. One could, in fact, completely do away with the Boltzmann Constant and express temperature solely in terms of thermal energy. We're used to Kelvins, though (thermal energy is currently $3.92\times 10^{-23}J$ outside my place).

There is no such fundamental relationship between charge and temperature. The closest thing there is, is the unit charge, but some ions are 2+ or 2- or more.

Boltzmann's constant and Entropy

Quote:

With 20:20 hindsight however, it is perhaps a pity that Boltzmann did not choose to introduce a rescaled entropy such that

${S^{\,'}=\ln \Omega }\;;\;\;\;\Delta S^{\,'}=\int {\frac {dQ}{kT}}$

These are rather more natural forms; and this (dimensionless) rescaled entropy exactly corresponds to Shannon's subsequent information entropy, and could thereby have avoided much unnecessary subsequent confusion between the two.

I know some physics researchers have jumped the gap regarding this, and as a natural consequence, they will express temperature in the same unit as energy. I'll try to find a reference for that.

What is $\Omega$ and what is Q? The article makes no mention of what these represent. GoldenBoar 00:21, 8 January 2006 (UTC)

-- For example, the Planck system, mentioned at the end of the article. But I think you're right, it's not just in those units that people "drop the k". Jheald 10:25, 5 November 2005 (UTC)

-- the great Landau and Lifshitz adopt this convention, using an energy scale for T so k disappears (Statistical Physics, Part 1 (3e, 1980), Oxford: Pergamon Press). Jheald 21:52, 8 November 2005 (UTC)

although that is probably not a good idea to adopt these conventions in an article, with a reference to quote that might be worth mentioning, either in here or in the temperature article. ThorinMuglindir 22:31, 8 November 2005 (UTC)

I am of the opinion that k is arbitrary, precisely that cutting kT into k and T is arbitrary, so that T is just as arbitrary. Because temperature is an energy scale. Think of it this way: I don't understand why temperature is given in here as a base unit of SI system. Because, if you get rid of charge, or mass, then you can't have the same physics anymore, you completely lose the corresponding parts. But, if you count temperature as energy, and remove all occurrences of Boltzman's constant in expressions where you meet it, then this doesn't change anything to the objective meaning of your equations. You retain exactly the same physics. ThorinMuglindir 01:28, 5 November 2005 (UTC)

Boltzmann's constant k is the bridge between the macroscopic and microscopic physics. Macroscopically, the amount of matter is measured in joule per kelvin, according to the ideal gas law: volume×pressure/temperature. Microscopically, matter consists of molecules. k tells how many J/K make a molecule. You may say that k is the size of one molecule. The kelvin temperature scale is somewhat arbitrary, being based on the triple point temperature of water, which is not of fundamental physical significance. Measuring gas in molecules give the temperature unit joule per molecule. k joule per molecule = 1 kelvin. Bo Jacoby 22:24, 29 January 2006 (UTC)

eV/K value

Is there any reason to mention the value of 1/k in K/eV instead of simply listing k in eV/K. I would change it, but I suppose there is a good reason to give the value of 1/k instead of k Glaurung 15:09, 18 January 2006 (UTC)

I agree. I think it should be changed. It is just as easy to divide by k as it is to multiply by 1/k. In addition, it is clearly more consitent to use dimensions of energy per absolute temperature regardless of the units of measure (joules/kelvin versus electron-volts/kelvin). -- Metacomet 00:34, 20 January 2006 (UTC)

I went ahead and made the change, along with a few other things. -- Metacomet 00:49, 20 January 2006 (UTC)

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Why is eV/K even given? It's a simple enough conversion, and the aside about the conversion factor is especially asinine; it follows naturally from the definitions of the units! --Belg4mit 16:13, 21 August 2006 (UTC)

Measurement

Has the measurement changed over time? My calculator (a Casio from about 10 years ago) lists k as 1.380662E-23, while the google calculator and this page both say 1.3806505E-23

Ojw 14:52, 23 January 2006 (UTC)

My calculator(HP 49G+) also shows the order as being 10^-23. It's fairly important that this gets fixed, so if nobody objects I'll change it.

66.189.211.162 07:19, 1 February 2007 (UTC)

Ahem ... I love calculators, but when it comes to looking up constants, why not use the CODATA reference that is clearly given in the article? --DrTorstenHenning 08:56, 1 February 2007 (UTC)

66.189: Looks like the article had been sneakily vandalised about 2 hours before you read it. Thanks for spotting it & flagging it up.

In future, if you see something like this that looks odd, look back a few revisions in the history tab and do see if it's a recent change. If no explanation's been given, and it looks like vandalism, then it probably was - feel free to correct it back again, and stop people being misled. Jheald 14:13, 1 February 2007 (UTC)

Physical meaning

A long section of this article is called 'Physical significance'. However it has always seemed to me that this constant has none - it is simply (like Avogadro's number) a dimensionless conversion factor. The paragraph that starts 'In hindsight however, it is perhaps a pity ...' doesn't really make sense, because there is exactly the same justification for measuring entropy in macroscopic units as there is for measuring temperature in such (i.e. K, rather than J or ev). Should this be rewritten? The way, the truth, and the light 23:14, 1 May 2007 (UTC)