# Talk:Ideal gas

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## comment

The entropy change for an ADIABATIC process between two well defined equilibrium states IS ZERO!! (the one written there is valid just because Cp-Cv=R for an ideal gas, but zero is what should appear in the table!). If the process is irreversible and adiabatic, all we can say is that entropy increases (whatever the system) - and the same two states connected through the reversible adiabat (isoentropic) cannot be connected through an irreversible, adiabatic process. —Preceding unsigned comment added by 18.82.6.138 (talk) 19:13, 25 September 2008 (UTC)

## old comment

The b term is an excluded volume term. It's there because gas molecules have a certain size, and two cannot coexist at the same place. Van Der Waals gas is very important because its theory is also the base for the description of liquid mixesUser:ThorinMuglindir (81.57.151.89) 11:53, 23 October 2005 (UTC)

"Generally, deviation from an ideal gas tends to decrease with lower temperature and higher density (i.e., higher pressure)[...] The ideal gas model tends to fail at lower temperatures or higher pressures[..]"
Maybe i am misunderstanding but if the deviation from the model decreases with temperature then it shouldn't mean that it will fail, actually the opposite.Ptsneves (talk) 18:24, 8 November 2010 (UTC)

## The Wikipedia needs to be written for the general reader

(First and Foremost)
With this in mind, it was rather foolish not to have even mentioned Charles's Law and Boyle's Law in this article, and so, I have added the following. One needs to realize that many people have heard of these laws in high school chemistry and general sciences courses - even if they never went to college, or perhaps majored in the humanities or the social sciences there.

"Among other things, an ideal gas would follow Charles's Law and Boyle's Law exactly at all conceivable temperatures and pressures, and an ideal gas would be impossible to liquify at any temperature or pressure."98.67.106.251 (talk) 19:22, 4 May 2009 (UTC)

Does anybody know about the deviation of real gas with ideal gas in PV/RT graph?

for ideal gas, pv/rt=1. for most of the real gas, (a)p<500atm, pv/rt<1;(b)p greater 500atm, pv/rt greater 1. for (a), it's intermolecular attraction factor; can some one explain the factor of (b) molecular volumn factor? I don't understand....

"Could please someone clarify whether a noble gas such as helium which I understand is normally monoatomic could be considered as an Ideal gas. As written in this article, an Ideal Gas is defined as molecules... L.L.

Although this is somewhat inconsistent with common usage, a molecule is technically just one, or more atoms. That is, even if an ideal gas is defined as consisting of molecules, that would include the noble gases, because one lone atom is still a molecule Brianjd
See molecule.
I find it very hard to believe that some people get wrapped around the axle concerning the concepts of monatomic (one-atom) molecules and polyatomic (multiple-atom) molecules. The word "molecule" includes all of these cases.98.67.106.251 (talk) 19:22, 4 May 2009 (UTC)
Some info has been added now which partially answers the question (see lead). It is summary level only however. David Hollman (Talk) 14:36, 9 September 2010 (UTC)

## Disputed

Perfect Gas vs. Ideal Gas

Umm, so why not build a Perfect Gas page (preferably with references - unlike this one:-) and correct and link the ideal gas page to it? (The current Ideal Gas entry is reference free and looks like much of it was lifted from a textbook.) ComputerGeezer (talk) 15:47, 31 January 2008 (UTC)
see, I would do that kind of thing but the amount of changes that need to be made are on the @ikiproject type scale. This whole article needs to be redone and split into various articles for the different topics. Basically, I can't do this on my own and honestly, I don't have enough time to re-write everything. I may have more time once I'm done with this semester but in the meantime I'll just leave stuff on the talk page and hope more people respond and want to help me re-write this article and write new ones.Katanada (talk) 09:47, 2 February 2008 (UTC)
So I joined the physics and chemistry Wikiprojects and I'm currently working on the gas page. I'll get back to this ideal gas page as soon as I finish that one! Katanada (talk) 07:40, 25 February 2008 (UTC)
Why not improve the article stepwise instead of disputing correctness? Bo Jacoby (talk) 15:50, 25 February 2008 (UTC).
Thats exactly what I'm doing this week! I'm finally on Spring Break. Please check out Gas to see the types of changes that I'm making. Katanada (talk) 16:23, 25 February 2008 (UTC)
I just finished gas. I'll try to get a start on this article soon.Katanada (talk) 04:22, 26 February 2008 (UTC)

## Perfect Gas vs. Ideal Gas

THEY ARE NOT THE SAME!!

-- yes they (usually) are (see below). —Preceding unsigned comment added by 146.6.143.48 (talk) 03:38, 20 February 2008 (UTC)

They are two completely different set of assumptions, they have nothing to do with each other. Whether or not they exist simultaneously is a different story, but thats not what I'm disputing here. Katanada (talk) 05:34, 20 February 2008 (UTC)

I suspect they are sometimes used interchangeably on some courses. However, a perfect gas is an ideal gas that has constant specific heat capacities. A semi-perfect gas is one which has specific heat capacites that are functions of temperature only. Specific heat capacities are in fact dependent on both pressure and temperature for real gases. The Perfect Gas page should be re-made. See http://www.roymech.co.uk/Related/Thermos/Thermos_fundamentals.html for example.

In many courses (especially for engineers) they are held to be very different things.

Tannoreth (talk) 12:14, 19 November 2008 (UTC)

Please sign your comments. I, as an aerospace engineer, recognize that the assumptions are VERY different. The differences make a HUGE difference in computational time for our models. I wish more people would understand this. Thanks for the comment Katanada (talk) 19:11, 7 November 2008 (UTC)
I am aggravated by your hair-splitting ("Haarspalterei" in German). The Wikipedia is written mostly for the general reader, and not for experts like you. Leave the Haarspalerei to works such as textbooks and monographs in aerospace engineering, physics, and chemical engineering.98.67.106.251 (talk) 19:22, 4 May 2009 (UTC)
Perhaps this is overkill but the following are the Cambridge Definitions of the terms ideal, perfect, semi-perfect, and imperfect
Ideal gases obey pV=RT and have cp - cv = R
Perfect gases are ideal with cp, cv and gamma = cp/cv constant
Semi-perfect gases are ideal with cp, cv and gamma functions of T
Imperfect gases do not obey pv = RT, cp and cv are functions of T and p and cp -cv does not equal R
--Tannoreth (talk) 12:19, 19 November 2008 (UTC)
Can you explain this to Itub? He/she doesn't believe me. I, unfortunately, don't have the time to pull all my books and go through Google and all this stuff to prove to him/her that there are actually differences in the models. If you go to gas I wrote all the different models I know of and have heard of. But yea... right now I'm bogged down with research work and flight control theory and all that wonderful stuff. I'll get back to Wikipedia writing when I have some free time =] Katanada (talk) 02:09, 4 December 2008 (UTC)
Guys, if I could field a suggestion- I too go by the "Cambridge" definitions of ideal/perf/semi pef etc. gases, but is it not just best to put a section discussing difference/ ambiguity, and let the reader decide for their application? I'm going to put my cards on the table and declare myself a noob, but one thing I can tell you is that this is *exactly* the sort of stuff that causes all manner of troubles to the reader, and also wiki is usually such a good help for cases when 1 text book says one thing, the other contradicts it. I just dont think claiming Perfect <=> Ideal is a particularily responsible thing to do.
--Ed84c (talk) 20:29, 05 May 2009 (UTC)

### Perfect Gas

A perfect gas is one with specific heats that are independent of the temperature T.

The “perfect gas approximation” has nothing directly to do with whether a gas is ideal or not (though because non-ideal gas behavior can appear at very low temperatures, cp may be considerably different at those temperatures than at, say, 300K).

As long as the number of DOF’s of the molecules does not change with temperature T, then the specific heats Cv and Cp will be constant and thus the gas will be “perfect”. A perfect gas is simply one that has constant specific heats.

Katanada (talk) 21:10, 11 January 2008 (UTC)

### Ideal Gas

An ideal gas is one in which the separation between molecules is sufficiently large (i.e., the density is sufficiently low) that intermolecular (van der Waals) forces are negligible, so that the gas satisfies the ideal gas law. A gas ceases to be “ideal” when the density becomes very large (e.g., at very high pressures and/or low temperatures), so that the intermolecular forces become large enough to produce substantial departures from the ideal gas law. The gas then instead follows non-ideal behavior of the form PV = ZRT where Z is a “Compressibility factor

Katanada (talk) 21:10, 11 January 2008 (UTC)

Looks like you need a reference here. Page 8 of Atkins' 8th Edition "Physical Chemistry, which is the canonical physical chemistry textbook around these parts, states in no unclear terms: perfect gas and ideal gas are synonyms. —Preceding unsigned comment added by 146.6.143.48 (talk) 03:36, 20 February 2008 (UTC)
Then the Atkins' 8th Edition "Physical Chemistry" is incorrect. There are 3 general models of gases: the "Real Gas" model is based on the generalized compressibility chart which introduces a 'fudge factor' (Z) into the IGL [PV=ZRT]. An "Ideal Gas" is just the specific case of the "Real Gas" model where Z=1. The "Perfect Gas" model is a specific case of an "Ideal Gas", they both obey [PV=RT]; however, the specific heats are assumed constants. Look it up on Google! :-) I have references from 3rd Edition Modern Compressible Flow, 2nd Edition Mechanics and Thermodynamics of Propulsion, and 4th Edition Fundamentals of Aerodynamics, and the NASA website.Katanada (talk) 05:51, 20 February 2008 (UTC)

## Real Gas

Why is there no article real gas? --Lode 16:44, 19 Jul 2004 (UTC)

There is no need for an article real gas. A real gas is just a gas.
Real gas redirects here - I have added a definition in this article. Brianjd 08:45, 2004 Dec 12 (UTC)
I dont think real gas should redirect here. It should redirect to gas. ~~
I agree - I changed it. PAR 00:23, 23 November 2006 (UTC)
A real gas is NOT just a gas! "Real gas effects" consists of taking into account fluctuations in heat capacity as a result of a temperature change (usually as a result of changes in DoF of the molecule) and compressibility. The modes of storing energy in a molecule changes as temperature increases. Katanada (talk) 21:34, 11 January 2008 (UTC)
Which is what a ... gas ... in real life does, innit? As opposed to an ideal or perfect or whatever gas. So, "real gas" redirects to "gas", as common sense would suggest. LjL (talk) 01:35, 7 June 2008 (UTC)
I'm a bit confused about your comment. Are you trying to make a joke? Katanada (talk) 14:58, 7 June 2008 (UTC)

## The entropy of an ideal gas

Well done, PAR. Just a few suggestions.

• We have once told that kN=nR, so don't repeat it
- done
• Use the dimensionless entropy S/kN
- I can't find a natural point for introducing this which doesn't clutter things except the final equation, when it is clear that everything is intensive, so thats the only one I changed.
• Don't restrict the analysis to monatomic gases, but use the symbol rather than the constant value 3/2 for the dimensionless heat capacity at constant volume.
- done
• An intermediate result would be helpful after the integral
- That integration was messed up - I fixed it, hopefully its clear now.
• The value of the Sackur-Tetrode equation is unclear: "The simple formula breaks down at low temp. So introduce the S-T equation. That breaks down too". So what is the point ? Bo Jacoby 12:47, 9 November 2005 (UTC)
- Tried to make that a little clearer. PAR 16:46, 9 November 2005 (UTC)

## Assumptions

Shouldn't there be a list of the assumptions made when dealing with ideal gases?

I.e. no intermolecular attractions etc...

The widipedia entry "gas" seems to list properties that I think are Ideal gas properties not real gas properties, I think that this needs clarification between the two.

An ideal gas is defined by its behavior, not by the statistical mechanics that explain its behavior. PV=NRT defines an ideal gas, no further assumptions are needed.
I think he/she/it meant "what assumptions are we taking when we treat a real gas as an ideal gas". These are now there.

## nR is amount of gas

Hi PAR. If n is the amount of gas measured in mol, and the gas constant R is measured in J·K−1·mol−1, then nR is the amount of gas measured in J·K−1. Bo Jacoby 17:35, 8 December 2006 (UTC)

Hi, I'll give a quick comment here, without reading the rest of the discussion (I'm giving myself a WP-pullout week due to irritations at WP:ELAC). With that said, R is just a constant, e.g. 1, 2, 3, etc., and n is a measure of the exact number atoms or molecular units in the ideal gas system, e.g. if n = 3.2, then there would be 1.93E24 atoms (or molecular units) in the gas phase system. As to nR, there is no special significance here; it is simply the value of the pressure times the volume divided by the temperature for any ideal gas at that value of n (as shown below). --Sadi Carnot 12:25, 13 December 2006 (UTC)
${\displaystyle nR={PV \over {\tilde {T}}}}$
But Bo, I don't understand the significance of R. If I multiply n by c, the speed of light, is nc the amount of gas in mol-m/sec ? PAR 20:24, 8 December 2006 (UTC)

If some fixed amount of gas has the pressure P, measured in pascal, and volume V, measured in cubic meter, and temperature T, measured in kelvin, then the product PV is measured in joule, and the expression PV/T, measured in joule per kelvin, happens to be asymptotically constant for sufficiently low pressure and correspondingly large volume. This constant value is an expression for the amount of gas, because it is proportional to the volume at constant pressure and temperature. Chemists, however, divide the mass (kg) of some substance by the molecular weight (kg/mol) to get the amount of substance measured in mol. The gas constant R is simply the conversion factor between these two units of measurement: mol and J·K−1. If the mol was never invented, then molecular weight would be measured in kg·J−1·K, and the gas constant would disappear from all the formulas. A third unit of measurement is the molecule. The conversion factor between molecule and J·K−1 is the boltzmann constant, and the conversion factor between mol and molecule is avogadro's number. Please don't introduce a fourth unit of measurement, mol·m·s−1. Bo Jacoby 06:09, 9 December 2006 (UTC)

I introduced the "nc" example to show why "nR" is not a good measure of the amount of gas. You say of "nR" - "This constant value is an expression for the amount of gas, because it is proportional to the volume at constant pressure and temperature." This is also true of "nc", so by your own reasoning, "nc" is a good measure of the amount of gas. The units are wrong. "Amount" has nothing to do with energy, so a measure of the amount of gas should not have "Joules" in it. "Amount" has nothing to do with time, so a measure of the amount of gas should not have "sec" in it. Both "nR" and "nc" are invalid because of this. The number of molecules (N) is a valid measure of amount, the mass (m) is a valid measure, the number of molecules divided by the number of molecules in a mole (mol) is a valid measure. PAR 13:59, 9 December 2006 (UTC)

Yes, nc could be used if no better measure existed, but n is a little better, and nR is much better. The mass of the gas is unnecessary and should be erased from the theory by Occam's razor. So the mol is unnecessary, (and so is the speed of light in this context). The simplest formula for an amount of gas measured from P,V and T is PV/T, and the SI unit for this quantity is J·K−1. You may multiply by constants to get other units, but that only complicates matters. (The standard cubic foot of gas refers to non-SI units of volume, pressure and temperature). The ideal gas law says that amount does relate to energy, because the amount of an ideal gas is PV/T, which is energy divided by absolute temperature. Bo Jacoby 23:34, 9 December 2006 (UTC)

Well, lets leave it out just because it is not commonly used. PAR 23:39, 9 December 2006 (UTC)

OK. It's a pity, though, because the WP article is not helpful for understanding. Even you did not understand the meaning of the gas constant. Why not leave it to people who do understand? Bo Jacoby 23:47, 9 December 2006 (UTC)

I fear this may be a issue of different terminologies used in different disciplines, but in my book the amount of substance has no vagueness and choice of dimension left to convention, but is a physical quantity with the SI unit mole and the common non-SI unit "number of molecules", related by NA. --Pjacobi 16:10, 11 December 2006 (UTC)
So, Bo, what about it? Do you have some reference for this usage? PAR 15:16, 12 December 2006 (UTC)

Your own writing says that Nk=PV/T where N is the number of molecules and k is measured in J·K−1·molecule−1, such that Nk is measured in J·K−1. What more do you want? I am merely clarifying what you wrote without quite understanding. Bo Jacoby 23:55, 12 December 2006 (UTC)

## molecules

I changed the word 'particles' into 'molecules' because these are the free particles of a gas. We are not talking about the number of quarks and electrons of the gas, but about the number of molecules. User Sadi Carnot reverted my edit. Please explain here on the talk page. Also you claim that "N is not the number of molecules, the Nk = nR edit is false and OR; + other grammatical and factual errors." I disagree. Please discuss first and edit later. Bo Jacoby 16:49, 14 December 2006 (UTC)

As user Sadi Carnot does not answer, I am going to revert his deletion. Bo Jacoby 13:11, 15 December 2006 (UTC)

Why don't you just leave it. Three people disagree with you. PAR 13:15, 15 December 2006 (UTC)

Why can't these people explain their point of view? I hope we agree to create high quality WP articles. That Nk=nR follows from the original statement of the gas law. Agreed? That the gas particles are called molecules follow from the article on molecule: "The concept of a single-atom or monatomic molecule, as found in noble gases, is used almost exclusively in the kinetic theory of gases, where the fundamental gas particles are conventionally termed "molecules" regardless of their composition". Agreed? Bo Jacoby 13:27, 15 December 2006 (UTC)

It's not a "provable" point, its terminology. Do you have a reference for this usage? Some article or book which uses this concept? Otherwise, it looks like a made-up terminology. I think that is what people are objecting to. PAR 13:48, 15 December 2006 (UTC)

Hi PAR. Earlier, physicists were accustomed to use many units of measurements and to convert by means of conversion factors, but now the units are standardized and the conversion factors rarely occur in physical equations any more, and so a modern physicist doesn't recognize a conversion factor when he sees one. You yourself did not recognize R as a conversion factor in PV=nRT, even if it is the only constant amongst four variables. Traditionally there are many units of measurements for pressure, (pa, bar, at, atm, mmHg, psi) and for volume, (liters, cubic feet, barrels, gallons, pint, ounces ...) and absolute temperature (kelvin, rankine, ...), but there are only two units of amount of substance around, the mol and the molecule. So the gas law is written PV/T=nR=Nk, converting the number of moles or the number of molecules into the appropriate unit. The modern approach is to chose units such that the conversion factors disappear. Then the gas law is PV/T=n, where n is the amount of gas measured in the appropriate unit. This is easily understood by an old physicist, but not for a young one, and so the WP article must explain rather than take it for granted. As by now neither the reader nor the author understood the ideal gas law! Bo Jacoby 15:14, 15 December 2006 (UTC)

Again, do you have a reference? PAR 15:37, 15 December 2006 (UTC)

I probably have the same standard references as you do. I understand it. You don't. Bo Jacoby 16:21, 15 December 2006 (UTC)

It seems pretty self-evident to me that, while the term "molecule" might be misunderstandable (do you call a monoatomic molecule a molecule? yes? no? who cares?), the term "particle" is simply completely wrong. LjL (talk) 01:39, 7 June 2008 (UTC)
As a Chem 1A, Bio 1A level student, I experienced "molecule" and not "particle" in my textbook learning. Unfortunately, I don't have those textbooks now. My personal experience in reading this article is that "particle" clouded this issue enough that I resorted to this discussion page to find out why it is used. I find the fact that someone keeps changing molecule back to particle, without putting a citation themselves, sub-optimal. I appeal to Bo Jacoby to settle this on molecule, with a reference, for the sake of other amatuer scientists who may use wikipedia. How 'bout it? (user:manogor) 8 March 2010
I checked three books which I happen to have on hand. All of them use the term "molecule" when discussing the kinetic theory of ideal gas behavior. Only one used the word "particle" in any way, and it was in defining what was meant by gas: "a gas consists of particles called molecules". Otherwise the word molecule was used.
They were:
1. Physics: A Textbook for Advanced Level Students, Tom Duncan, Publisher: Coronet Books; (April 1983), ISBN: 0719538890, ISBN-13: 9780719538896, p.431
2. Essential Principles of Physics, Patrick Michael Whelan, M.J. Hodgson, Publisher: John Murray; 2nd Revised edition edition (18 May 1978), ISBN-10: 0719533821, ISBN-13: 978-0719533822, p.179
3. Chemistry: Facts, Patterns and Principles, 2nd Revised edition, W.R. Kneen, M. Rogers, P. Simpson, Publisher: Longman; (May 1984), ISBN-10: 020103218X, ISBN-13: 978-0201032185, p.72
(they are all high-school/bachelors-level as far as I can tell)
I see several issues with the article which this discussion raises.
1. The first is that we do not have a section clearly defining the assumptions (though kinetic theory may explain it) for what an ideal gas is.
2. The second relates to those assumptions themselves; one of the core ideas is that a gas which behaves like an ideal gas does so when intermolecular forces are insignificant - thus the gas might be approximated or modelled as a collection of point particles. However that particular use of the word "particle" isn't so clear; if that context isn't explicit, then a reader might assume that "particle" could mean: molecule, dust, spore, electron, etc. etc.
3. Almost the entire article is unreferenced; maybe some books use the word particle when describing, say, heat capacity, but that isn't clear at this moment in time.
My suggestions:
1. In general, use the word molecule.
Given that the sources which I have seen uniformly use the word "molecule" seems to clinch the issue with respect to verifiability at least for sections covered by the scope of those books; I also think using this term will cause less confusion with readers.
2. We should use the word "particle" where a specific model makes such a specific assumption (assuming someone provides a reference) -- but that usage needs to be stated explicitly in that context. i.e., "in this model for heat capacity the gas is assumed to be made up of non-interacting point particles" (I made up that particular sentance).
3. Add a section clarifying the kinetic theory assumptions
David Hollman (Talk) 15:20, 9 September 2010 (UTC)
Oh, I'm happy to make these changes as I have the source texts, but I wanted to get some feedback first. David Hollman (Talk) 15:21, 9 September 2010 (UTC)

## Difference between thermally perfect and calorically perfect gas

The article does not mention the difference between a thermally perfect and a calorically perfect gas.

A thermally perfect gas is defined as one which obeys the ideal gas equation: ${\displaystyle pV=nRT\,}$, whereas a calorically perfect gas is one which has constant specific heat (i.e. ${\displaystyle C_{p}}$ and ${\displaystyle C_{v}}$ are constant). When a gas is both thermally and calorically perfect, it is referred to as a perfect gas or an ideal gas. Also a gas can be thermally perfect and calorically imperfect, however, the vice versa is not true.

The difference is important when dealing with large temperature ranges. In such cases one can assume the gas to be just thermally perfect but calorically imperfect. This allows the use of equation of state for ideal gas while also accounting for variation in the heat capacities ${\displaystyle C_{p}}$ and ${\displaystyle C_{v}}$ with temperature (which can be significant).

I am not sure where to include this in the article. So I am mentioning it here. -Myth (Talk) 08:12, 25 February 2007 (UTC)

I agree. But lets get the terminology right first. If a gas is thermally perfect but calorically imperfect is it still an ideal gas? I believe it is. Can we say a perfect gas is thermally and calorically perfect, while an ideal gas is thermally perfect and may or may not be calorically perfect? PAR 17:56, 25 February 2007 (UTC)
It is common to refer to a thermally perfect gas as ideal gas, because for many applications one is just interested in using the ideal gas equation. I just have one reference which makes the distinction in the definition. I think the context will make the definition clear in most cases.
Reference: Vincenti, Walter G.; Kruger Charles H. Jr. (2002) [1965]. Introduction to Physical Gas Dynamics. Krieger Publishing Company. pp. pp. 8. ISBN 0-88275-309-6. Cite uses deprecated parameter |coauthors= (help)
-Myth (Talk) 04:25, 26 February 2007 (UTC)
I cannot find any reference which says that the specific heats of an "ideal" or "perfect" gas are independent of temperature. All the references I have use "ideal" and "perfect" interchangeably, and only refer to a gas for which PV=NkT. I think we should overhaul the article to reflect this. PAR 06:17, 26 February 2007 (UTC)
The definitions are important when we are dealing with large temperature ranges over which the specific heat capacity can change appreciably. This is usually the case in combustion and gas dynamics. That's why many references will not be concerned in trying to distinguish between the different definitions.
btw here is another reference which clearly distinguishes between a calorically and thermally perfect gas (again it is in relation to gas dynamics)
Another reference: Anderson, John D. Jr. (2000) [1989]. Hypersonic and High Temperature Gas Dynamics. AIAA. pp. pp. 388. ISBN 1-56347-459-X. Google search result for this reference.
I don't think it is necessary to change the article to say that ideal or perfect gas only refers to ${\displaystyle PV=NkT}$, because that won't be the correct definition. It would be better to just add a statement clarifying that many authors refer to a thermally perfect gas as an ideal gas or a perfect gas and that the reader should be aware/careful of this. -Myth (Talk) 07:01, 26 February 2007 (UTC)
I am of the opinion that the difference is VERY important. It makes a huge difference. Every time I suggest it, I get shot down. So unless more people decide to be rocket scientists (which apparently are the only people in the world that care about large high-temperature variations) or some high-temperature chemists or something special like that -- I think we're going to end up arguing with people that want to keep Wiki at a quasi-high-school level instead of getting real definitions. (sorry for the rant.) .. Anyway, I've managed to keep it in Gas for a few years and less people attack me for it there. Katanada (talk) 01:52, 11 November 2010 (UTC)

## Totally wrong

Found this statement :Gases are most ideal at high temperatures and low densities.

This is WRONG since gases at higher temperatures will have MORE collisions hence the "ideal gas" property is lost (as you may be aware molecules have inelastic collisions hence kinetic energy is lost). Also at lower temperatures the distance between particles is greater, hence there is more interaction between molecules. Therefore, a gas which is at extremely high/low temperatures (in comparison to standard labratory conditions) will not obey the ideal gas laws fully.

The low density may also be checked.

I have removed this nonsense. Thanks —Preceding unsigned comment added by 121.222.226.157 (talk) 08:54, 23 October 2007 (UTC)

Actually, the statement that gases are most ideal at high temperatures and low densities is generally true. The point you make about more collisions at higher temperatures resulting in more lost kinetic energy is a second order effect since most molecular collisions are elastic. The first order effect of higher temperatures is that the internal energy of the gas is high enough to make negligible the long-range interactions between molecules. This is another point of confusion on your part -- the difference between collisions and interactions. "Interactions" refers to long-range forces that act between molecules, eg. van der Waals. In other words, the molecules move in a potential field due to the presence of other molecules. At high temperatures however, the kinetic energy term dominates and the potential term becomes negligible. At low densities, the average distance between molecules becomes greater, again reducing the interactions between molecules. Under both of these conditions, gases will tend to have internal energies that are strictly kinetic, ie. U = CvNkT. In other words, they become ideal... Peebeewee (talk) 22:20, 11 February 2008 (UTC)
It also depends on the gas itself and molecule dissociation which then deals with high temperatures (the dissociation point has a dependence on pressure as well). Somehow I feel there should be some talk about the compressibility factor in here to more clearly describe the "non-ideal-ness" of high-temperature, high-pressure gases. Katanada (talk) 01:51, 14 February 2008 (UTC)
I have added experimental values, at the Compressibility factor page - this should provide solid ground to solve this little dispute. Power.corrupts (talk) 13:05, 30 September 2008 (UTC)

## Absolute vs relative pressure

Isn't it wise to specify that p is the absolute pressure? Not only here, but virtually anywhere pressure is mentioned. Even if it were clarified somewhere else, which I don't know, this lack of information is unpractical to the average user. I'm asking because I'm new to WP and I don't want to mess around with articles! Podi74 (talk) 12:19, 19 December 2007 (UTC)

Yes, it would be useful to at least mention that the pressures in this article are absolute pressures, and not "gauge pressures". For atmospheric measurements near sea level on the planet Earth, in the English sustem of units, the conversition equation is approximately: Absolute Pressure = Gauge Pressure + 14.7 pounds per square inch. You may surely write a slightly-different equation when dealing with the unit pascal, which is one newton per square meter.98.67.106.251 (talk) 19:37, 4 May 2009 (UTC)

## moderate temperature

By introducing the undefined concept of 'moderate temperature' an editor has made the text nonsensical. Bo Jacoby (talk) 09:31, 20 February 2008 (UTC).

## acronym

Perhaps RIPE would be a better acronym, rather than PRIE? PRIE is just a collection of letters, RIPE actually spells something, so it is easier to remember, especially for students. Just a thought. —Preceding unsigned comment added by 151.200.36.227 (talk) 04:15, 2 May 2008 (UTC)

## Units

Shouldn't the units be given for each of the quantities in the equation. The formula only works with that gas constant if SI units are used. Plenty of engineers (and some Americans?) still do not use SI. So if we are going to give a value for the gas constant instead of just a link, then the units have to be defined too.Yobmod (talk) 14:56, 10 February 2009 (UTC)

The equation itself doesn't depend on the units. So I think it's better to just note that the particular R and k are examples, given in SI units. I'll take a crack at that.COGDEN 21:58, 5 May 2009 (UTC)

## thermodynamics or statistical mechanics?

"...the classical thermodynamic ideal gas is based on classical thermodynamics..."? —Preceding unsigned comment added by Paranoidhuman (talkcontribs) 02:45, 12 August 2009 (UTC)

## Merge Ideal gas law into Ideal gas?

I'm not sure I see the benefit of having two separate articles. Its not that they are redundant (although there is overlap) but they seem to be intrinsically talking about the same thing, and it is just confusing to have two places to look for one topic. An ideal gas is by definition anything which behaves according to the ideal gas law. So I think there is a case to merge them. This would make it much easier to find what one wanted w/o searching through both of them.

If there is not support for this, then I think we will need to more clearly define the scope of the two articles. Personally, if I needed to know something about an ideal gas it wouldn't be 100% clear which one I should look in first. Thanks for your thoughts! David Hollman (Talk) 15:41, 9 September 2010 (UTC)

One kinda nice thing about having them separate is that the ideal gas law is so often applied to real gases. As it stands now, someone using PV=nRT on real gases can read up on the equation without also having to wade through all the intricate details of the theoretical substance it is based upon. (Keep in mind that ideal gases do not exist, although some gases do come pretty close!) As for the scope, that seems clear to me as well- the ideal gas law article is about the approximation PV=nRT, whereas the ideal gas article is about theoretical models of non-interacting point particles. The accuracy of PV=nRT does depend on how closely a gas comes to matching that theoretical ideal, so the gas law article should have some mention the ideal gas, and vice-versa; I think each article currently does a nice job of doing just that. In summary, my view is that the present situation is already pretty "ideal" (sorry; couldn't resist), so I'm not convinced that a merge would be an improvement. Riick (talk) 00:57, 11 September 2010 (UTC) fixed typo Riick (talk) 01:02, 11 September 2010 (UTC)
You make some valid points, which I've been thinking about. You're right about the scope being mostly pretty consistent. But the fact that there are two articles which, at least superficially, sounded like they would cover the same material, seems to be unnecessarily confusing -- when I first looked at them, the scope was *not* obvious, at least not at first, because I basically thought of "ideal gas" and "ideal gas law" being the same concept. I do appreciate that there are real gases which are treated as though they are ideal in some cases, but I think its equivalent to say "we're applying the ideal gas law to hydrogen" or "we're treating hydrogen as an ideal gas" -- ie, either article could be the right place to start reading if you needed information.
Hypothetically, can you see any downsides of a merge?
The only potential downside I could see of a merge is article length - it might be borderline on the long side. But I don't see any problems with some later re-factoring of the content if that was needed. Thanks! David Hollman (Talk) 19:00, 12 September 2010 (UTC)
The downside from my perspective is that a merge would make things more difficult for readers. For many people, the approximation PV=nRT is entirely about real gases. (In fact, just today I saw a book call it "the general gas law".) People trained this way would be confused and perhaps frustrated in finding themself reading some article about theoretical models, especially if all they really wanted was an answer to some basic question about the approximation PV=nRT. So yes I do see a downside to the merge; I think it would create confusion.
You've argued that PV=nRT defines an ideal gas. Another way of looking at it is that the whole purpose of the ideal gas concept is to explain the PV=nRT approximation. From that perspective, the merge should be going in the other direction! Of course, I don't think merging ideal gas into PV=nRT would be an improvement either. Instead, my point is that the parent-article / child-article relationship may not be as clear as it might at first seem. I really think this is one case where it's better to keep the article about the tool separate from the article about the theory. Riick (talk) 11:53, 19 September 2010 (UTC)
Riick, I think these are good points, I appreciate your perspective that "ideal gas" and "ideal gas law" are distinct concepts. Thanks for your input. Since no one else has chimed in, I've removed the tags. David Hollman (Talk) 13:24, 19 September 2010 (UTC)

## Perfect nonsense

This is nonsense:

${\displaystyle {\hat {c}}_{V}}$ is a constant dependent on temperature (e.g. equal to 3/2 for a monatomic gas for moderate temperatures)

Constants do not depend on temperature. 3/2 does not depend on temperature. The meaning is that ${\displaystyle {\hat {c}}_{V}}$ is constant for the simplified model of ideal gases but vary for real gases. So it should state that

${\displaystyle {\hat {c}}_{V}}$ is the dimensionless specific heat capacity at constant volume, equal to 3/2 for monatomic gas, 5/2 for diatomic molecules and 6/2 for more complex molecules.

Bo Jacoby (talk) 09:07, 12 September 2010 (UTC).

Yup -- you're right :) ... Someone should change that if it hasn't been changed already. Cv is by no means a constant. Also, its not always equal to those numbers either... You can say that it is "generally" equal or something that is less restrictive... but then we'd have to have the quantum argument :( Katanada (talk) 01:45, 11 November 2010 (UTC)

## Multicomponent systems

The last sentence in this section seems spurious or at least sits at the wrong place: "Ideal gasses are not found in the real world. So they are different from real gasses. There are basic assumptions made in the kinetic theory of gasses".

Second: in this sentence gasses is written with double S. http://www.collinsdictionary.com/dictionary/english/gas says both forms are allowed, but the other occurrences on this page have a single S. --46.115.56.114 (talk) 00:07, 23 August 2012 (UTC) Marco Pagliero Berlin

Agreed and deleted. Next time, you can delete such a sentence yourself, as long as you explain your reason in the edit summary or on the talk page. Han-Kwang (t) 11:28, 25 August 2012 (UTC)

## Ideal Gas Assumptions

Spherical particles are not necessary, only that the interparticle distance be large. What is needed that rotational energy is negligible. Spherical particles will have a rotational energy. If they are small enough, it will be negligible. I will change this soon. PAR (talk) 16:24, 14 September 2012 (UTC)

Classical thermodynamic ideal gas description contradicts the definition of an ideal gas. The definition states "composed of a set of non-interacting point particles". Classical thermodynamic ideal gas description talks about spherical particles that collide. This sounds wrong and should be removed or explained properly. — Preceding unsigned comment added by 2401:FA00:0:3:BE30:5BFF:FEE1:EBF4 (talk) 04:53, 30 October 2013 (UTC)

There is no need to include the requirement of "non-interacting" particles to obtain an ideal gas. That is overly restrictive. A better definition of an ideal gas would be that it is any gas which obeys the ideal gas law. Going beyond that, to pick a specific model which obeys the ideal gas law and saying that is the only ideal gas, is too much. The "definition" of an ideal gas in the first paragraph needs more careful thought. 3piecesuits (talk) 07:30, 29 December 2013 (UTC)
If that's the case, it would be nice to include an example of a gas with interacting particles that is nevertheless ideal. Do you know of one? PAR (talk) 15:03, 30 December 2013 (UTC)

## Barred variables - what does this mean?

I'm still trying to understand the heat capacity section. If you compare to the article on Heat capacity, there's no point where the variables with bars over them are introduced. I can't see such an introduction in this article.

Now, there is a meaningful difference between the heat capacity and the specific heat capacity. But this is generally designated with upper case versus lower case. It's not clear at all what the bars above the variables mean. I think some description should be added. But I don't know what it means, so could anyone help me? -Theanphibian (talkcontribs) 19:39, 21 March 2014 (UTC)

## Place for an interactive ideal gas simulation?

I have a very nice ideal gas simulation (in Java) available here: http://www.ics.uci.edu/~wayne/Gas . Does anybody I'm totally new to editing Wikipedia articles and don't know if it would have a place or if so where to put it. If anybody thinks there is a place for such a simulation please contact me at whayes@uci.edu (Wayne Hayes, UC Irvine) Waynehayes (talk) 14:40, 15 April 2014 (UTC)

Here is a simulation.Chjoaygame (talk) 22:00, 15 April 2014 (UTC)

## Definition of ideal gas

It should include that particles can collide, but only elastically; otherwise since they do not "interact" (and their volume is zero) it seems that they do not collide. — Preceding unsigned comment added by 84.120.147.21 (talk) 07:45, 29 August 2014 (UTC)

ok.Chjoaygame (talk) 11:02, 29 August 2014 (UTC)

## two equations of state?

Is it really necessary to have two equations of state in the "Classical thermodynamic ideal gas" section? Isn't the whole point of an equation of state that it completely describes the system? Any other equation of state would be redundant (although perhaps more convenient). In this specific case, the fact that the internal energy of an ideal gas is a function of temperature only comes straight out of the total differential of U(T,V) with the use of a few Maxwell relations and the first equation of state (PV = nRT). Consequently, the second equation of state isn't necessary to satisfy the property of being a function of temperature only. Also, is it really necessary to include all of the dimensionless quantities in this article? The article should, first and foremost, be intended for the lay audience, not specialists. Does anyone else think that dimensionless quantities are a bit to over-the-top for such a basic sections of the article? JCMPC (talk) 00:10, 19 October 2014 (UTC)

It is proper to supply several equations of state for a collection of matter. An equation of state usually does not express all the thermodynamic information for the collection. Often there are stated a thermal and a caloric equation of state, alternatively about temperature or internal energy. It is the thermodynamic fundamental or characteristic equation, not an equation of state, that in general gives all thermodynamic information. The reason for this is that thermodynamics needs two cardinal functions of state, entropy and internal energy.Chjoaygame (talk) 02:06, 19 October 2014 (UTC)
Chjoaygame, do you have a reference to what you are saying? I am not entirely sure what you mean. Maybe I'm using my terminology incorrectly, but aren't the fundamental equations relationships between state variables for all systems, regardless of composition. The equation of state would then used so that the fundamental equations can be applied to specific systems? Thanks. JCMPC (talk) 16:30, 19 October 2014 (UTC)
Callen, H.B. (1985) second edition, Wiley, Section 2-2, p. 37. A single equation of state, separately, in general does not express all the thermodynamic facts about the body. Several are needed. Equations of state are not thermodynamic characteristic or fundamental equations. These equations tell about the particular peculiar constitutive characteristics of particular bodies. Thermodynamics places restrictions on what are physically possible constitutive characteristics. Those restrictions are in a sense universal, but the constitutive characteristics are peculiar to each particular kind of body.Chjoaygame (talk) 18:00, 19 October 2014 (UTC)
OK, thanks for the clarification. I now see what you mean. It seems like most of the references that I use use less rigorous (and slightly ambiguous) definitions for equations of state and fundamental equations than what Callen uses. That being said, can't the second equation just be obtained from the total differential of U(T,V), where the partial of U with respect to V at constant T will be zero if one uses PV=nRT, which would yield the result that the internal energy of an ideal gas is dependent only upon the temperature?
Even with that issue addressed, something still doesn't sit right with me about this section. What do you think about my idea to remove the dimensionless heat capacity and just write the second equation of state as U=CvT? Also, what do you think about moving the "derivation" of the ideal gas law into the ideal gas law page (which doesn't go into the detail presented here). Finally, what do you think about breaking this section up into two parts: an empirical/macroscopic description that includes the two equations of state and a theoretical/microscopic description that includes all of the bullet points currently at the end of the section? JCMPC (talk) 20:26, 19 October 2014 (UTC)
"That being said, can't the second equation just be obtained from the total differential of U(T,V), where the partial of U with respect to V at constant T will be zero if one uses PV=nRT, which would yield the result that the internal energy of an ideal gas is dependent only upon the temperature?" The fundamental thermodynamic equation contains all thermodynamic information. That is why it is called the fundamental equation. From it can be deduced all the equations of state. But in general they cannot be deduced from one another. And all of them are needed to reconstruct the fundamental equation. That is why they are only rated as equations of state, not as fundamental equations. The result that the internal energy of an ideal gas depends only on temperature is not deducible from the PV=nRT formula. Textbooks are appropriate at this stage. Tschoegl is excellent, and contains more information.
I think it would not be good to replace the dimensionless specific heat capacity by the heat capacity and remove the mole number and gas constant. I don't see why the derivation of the ideal gas law should be removed from here. I have split the section as you suggest.Chjoaygame (talk) 05:41, 20 October 2014 (UTC)
I think that my points/questions are being lost due to semantics. No matter, it's not really a discussion for this venue anyway since my initial concerns have already been addressed. Would you mind explaining why you don't think it would be a good idea to replace dimensionless quantities? In general, dimensionless quantities tend to be more abstract and I think that this page (which is likely to be visited by a large number of people since ideal gases are taught in many introductory courses) would benefit the general reader more by using less abstract language. Also, I don't suggest removing the derivation of the ideal gas law since that would clearly omit very important information on the topic; however, I do suggest to move it to the page ideal gas law since that page specifically deals with the ideal gas law. In my opinion, the main point of the current article is not to emphasize the ideal gas law (i.e. the equation), but to focus on the ideal gas as a theoretical concept by discussing, for example, the macroscopic and microscopic properties of ideal gases (e.g. temperature-only dependence and non-interacting particles). JCMPC (talk) 15:02, 26 October 2014 (UTC)
I don't think the general reader needs that supposed benefit, and the serious reader would lose, because the logic is good as it stands. There are three equations of state of which the ideal gas law is one. Rather than remove the one present equation of state as detailed, and mention of the second, I would prefer to see the second one detailed here, and also the third. Moving the derivation from here to the ideal gas law article would suggest expunging the second and third. Why not just upgrade the derivation of the ideal gas law in its own article? Or delete the ideal gas law article?Chjoaygame (talk) 16:31, 26 October 2014 (UTC)

## undid faulty good-faith edit

I have undone a faulty good-faith edit that has an edit summary "corrected standard molar volume. It is 22.4 at 101.325 kPa".

The relevant sentence, as I have restored it, reads

One mole of an ideal gas has a volume of 22.7 L at STP as defined by IUPAC.

In chemistry, IUPAC has established two standards:[1]
1. ^ A. D. McNaught and A. Wilkinson (1997). IUPAC. Compendium of Chemical Terminology (2nd ed.). Oxford: Blackwell Scientific Publications. ISBN 0-9678550-9-8. Standard conditions for gases: ... and pressure of 105 pascals. The previous standard absolute pressure of 1 atm (equivalent to 1.01325 × 105 Pa) was changed to 100 kPa in 1982. IUPAC recommends that the former pressure should be discontinued.

By my arithmetic, 22.4 × 101.325 ÷ 100 = 22.6968.

It is more or less routine that this correction appears here.Chjoaygame (talk) 05:42, 14 December 2015 (UTC)

## Entropy of ideal gas (again)

The expression for computing the entropy of ideal gases given in the text as

${\displaystyle \Delta S=\int _{S_{0}}^{S}dS=\int _{T_{0}}^{T}\left({\frac {\partial S}{\partial T}}\right)_{V}\!dT+\int _{V_{0}}^{V}\left({\frac {\partial S}{\partial V}}\right)_{T}\!dV}$

is a little problematic. The entropy is a function of temperature and two extensive variables ${\displaystyle V,N}$:

${\displaystyle S=S(T,V,N)}$

therefore, tho compute the change in the entropy during a transformation, we must write

${\displaystyle \Delta S=\int _{T_{0}}^{T}\left({\frac {\partial S}{\partial T}}\right)_{V,N}\!dT+\int _{V_{0}}^{V}\left({\frac {\partial S}{\partial V}}\right)_{T,N}\!dV+\int _{N_{0}}^{N}\left({\frac {\partial S}{\partial N}}\right)_{V,T}\!dN}$

Somehow, the third term (the variation in ${\displaystyle S}$ due to variation in ${\displaystyle N}$) has been omitted, but the correct expression for ${\displaystyle S}$ is obtained when ${\displaystyle N}$ is varied in the section on chemical potential. This need some clarification/cleaning. — Preceding unsigned comment added by BahramH (talkcontribs) 05:43, 22 August 2016 (UTC)