Talk:Heat capacity ratio

Intentional joke?
"Real gas relations [icon] 	This section requires expansion. (June 2008)"

... Yes. Yes it does. ;) -- Rei (talk) 15:36, 23 August 2016 (UTC)

IP question
What is the Cv value for Nickel, while the Cp is 460.6 J/Kg-K? — Preceding unsigned comment added by 132.205.16.185 (talk) 12:48, 30 May 2006

Merger proposal
Merger of Heat capacity ratio and Adiabatic index was proposed by Bryan Tong Minh on 11 January 2007.


 * Agree -Myth (Talk) 10:37, 5 February 2007 (UTC)
 * Agree with the provision that the new article will mention that both the term heat capacity ratio and the term adiabatic ratio are similar. Mausy5043 13:15, 5 February 2007 (UTC)
 * Agree Finn Mainstone 14.56 GMT, 27th Feburary 2007

Merger completed. -- Myth (Talk) 06:18, 2 March 2007 (UTC)

Table - what pressure were measurements taken at?
I am guessing that the tabulated values for the adiabatic index are at atmospheric pressure. If so, I think this should definitely be mentioned somewhere. Does anyone know? 84.12.252.210 15:16, 28 August 2007 (UTC)

Title of article: "Heat capacity ratio" or "Adiabatic index"?
I strongly believe that the title of this article should be "Adiabatic index", not "Heat capacity ratio". I'm a student in physics, and I have frequently heard the term adiabatic index thrown around, but never heard heat capacity ratio before. As an objective gauge of the popularity of the terms, a Google search for "adiabatic index" gets 76,000 hits, while "heat capacity ratio" only gets 17,500. One thing that heat capacity ratio has going for it however, is that it is more descriptive. -- Apetre (talk) 02:53, 5 December 2007 (UTC)


 * In my own experience, the word that is most frequently used to describe this quantity is "Specific heat ratio". The term "Adiabatic index" is sometimes used when it is in the context of the more general "Polytropic index".  I agree with Apetre that "Heat capacity ratio" is hardly used. Thunderbird2 (talk) 12:41, 5 December 2007 (UTC)


 * If I were looking for this topic, I would search for either of the terms "specific heat ratio" or "heat capacity ratio" (or "ratio of specific heats" or "ratio of heat capacities"), the former referring to the ratio of the intensive quantities, and the latter to the ratio of the extensive quantities. I regard both as equally correct usage. I've can't recall ever hearing the term "adiabatic index" for this ratio, and I'm a professor of physics, and have taught thermodynamics. Prfssr (talk) 22:37, 12 March 2010 (UTC)

Misleading explanation of why Cp differs from CV
The explanation in the 4th (?) paragraph of this article as to why Cp differs from CV is misleading. It gives the example of comparing the heats required to raise the temperature of a gas under constant pressure versus constant volume conditions, the former involving expansion of the gas, and therefore (positive) work being performed by the gas on the surroundings. This work performed is posited as the reason for the difference in Cp and CV. This is a common and misleading explanation. While this explanation is true for an ideal gas, it is not true in general that the reason for the difference in Cp and CV is solely due to the work performed. The work performed by a substance at constant pressure will be positive or negative, depending upon the sign of the thermal expansion coefficient of the substance, yet it is always true that Cp >= CV for all homogeneous, isotropic, one-component substances subject to only pdV work, so it cannot be that the work performed alone accounts for the difference in Cp and CV. For water between 0 C an 4 C, for example, the thermal expansion coefficient is negative, yet Cp > CV. That Cp >= CV for a homogeneous ... substance is a consequence of the Combined First and Second Laws of Thermodynamics, and is independent of the sign of the thermal expansion coefficient: Cp - CV = TVb2/k (Here b = thermal expansion coefficient & k = isothermal compressibility -- pardon me that I don't know LaTeX). For any homogeneous ... substance, from the First Law of Thermodynamics alone, we have CV = (dU/dT)V and Cp = (dU/dT)p + pVb. For ideal gases, (dU/dT)V = (dU/dT)p = constant = CV, and Cp > CV because b = 1/T > 0, but this is not true in general. In fact, for Cp to be greater than CV for a substance with a negative thermal expansion coefficient, (dU/dT)p must exceed (dU/dT)V. This demonstrates that Cp differs from CV not just on account of the work performed, but also on account of the difference in the temperature variation of internal energy under constant pressure versus constant volume conditions. The amount and especially the polarity of the difference (that Cp is never less than CV for a homogeneous ... substance, even when the work performed by the substance is negative) is a consequence of the Combined First and Second Laws of Thermodynamics. Prfssr (talk) 23:47, 12 March 2010 (UTC)

There are a number of things to unpack, including the assertion that ideal gases must have constant heat capacity. That’s predicted by the classical equipartition theorem of statistical mechanics, but quantum statistical mechanics shows that a gas can strictly obey Pv=nRT and have a temperature-dependent heat capacity. You might want to have a look at the perfect gas page. KeeYou Flib (talk) 04:57, 27 March 2022 (UTC)

Symbols used
The article says:


 * ...is denoted by γ (gamma) or κ (kappa). The latter symbol kappa is primarily used by chemical engineers. Mechanical engineers use the Roman letter k...

The last statement (use of k) seems contrary to the first (use of gamma or kappa). Which is correct (if either)? Anyone have the ability to consult the reference cited? I'll check the book I have but I can't compare to other engineering or physics fields.

(As far as it goes, in my mechanical engineering thermodynamics courses we used gamma, but doesn't necessarily imply it is the correct standard in that field.)

Dhollm (talk) 20:39, 21 August 2010 (UTC)

Thermodynamic Derivation
This section states: "The above definition is the approach used to develop rigorous expressions from equations of state (such as Peng-Robinson), which match experimental values so closely that there is little need to develop a database of ratios or Cv values. Values can also be determined through finite difference approximation." We need some proof that this is true. In Chemical process engineering, the 'rigorous' or 'theoretical' k value derived from an Equation of State (e.g. Peng-Robinson) can differ significantly from that used in many other parts of the industry (e.g. valve, compressor and turboexpander sizing). Thus some clarification of which k values are 'correct' and where the experimental data is would be welcome. TriMomma (talk) 18:47, 13 October 2011 (UTC)

It would be helpful to have a citation of what you are saying here; it could be used to improve the article. KeeYou Flib (talk) 05:00, 27 March 2022 (UTC)

Relation to Degrees of Freedom
It is not clear where the extra 2 degrees of freedom come from; what is the source of the equation γ = 1 + 2/f ? Why does expansion of the gas sample correspond to 2 degrees of freedom? — Preceding unsigned comment added by 89.197.3.130 (talk) 17:18, 27 February 2019 (UTC)

The significance of the ratio is not discussed.
There is no declaration of the significance of the heat capacity ratio in thermodynamics other than its rational quantity, per se. Examples are needed of the utility of cp/cv other than simply 'a method of deriving cv from cp'. — Preceding unsigned comment added by Hippocrocopig (talk • contribs) 16:26, 16 March 2016 (UTC) Hippocrocopig (talk) 19:55, 22 March 2016 (UTC)

Table value of dry air at 2000 °C highly questionable
The stated value of 1.088 does not agree with the general trend of the data and also disagrees with what is given in the German wikipedia. Has anybody got access to the souce books?--Polis Tyrol (talk) 10:46, 9 May 2017 (UTC)

And from a theoretical point of view the value should not be lower than 1,28. 134.169.50.143 (talk) 13:04, 25 January 2018 (UTC)
 * I do not have access to a book source, but I can use Python / Cantera:
 * This yields a value of 1.2917. The source is a Janaf polynomial table, which I assume to be taken from a reputable source (NIST?), and should be about right at these temperature/pressures (that is supposed to be able to model combustion, and 2000°C is in the ballpark of adiabatic flame temperatures).
 * The value given in the article might be a typo for 1.288, but without the source to check, I will remove it altogether. Tigraan Click here to contact me 16:46, 25 January 2018 (UTC)
 * Also, for whoever wonders where the "1.28" from 134.169.50.143 comes from: for an ideal gas, the ratio is given by the number of degrees of freedom. Air is made of N2 and O2 mostly, which have each at most 7 DoF (3*2 for the spatial location of each molecule plus 1 for torsion of the double covalent bond). Hence γ is at least 9/7 (about 1.286). This being said, I am not entirely sure what happens when the "ideal gas" hypothesis breaks down at large temperatures. Tigraan Click here to contact me 16:57, 25 January 2018 (UTC)
 * This is a rather nonsensical "explanation". As written in the article itself, at moderate temperatures N2 and O2 have 5 degrees of freedom: 3 translational + 2 rotational (diatomics cannot rotate around the internuclear axis). At high temperatures, the vibrational excitation becomes important (hω ≈ 2360 cm−1 ~ 3400 K for N2, hω ≈ 1580 cm−1 ~ 2300 K for O2) and adds 2 more effective degrees of freedom (1 from kinetic energy + 1 from potential). This gives the limit of 7 effective DoF, and thus γ = 9/7 ≈ 1.286. However, at 2000 °C, O2 and N2 partially dissociate and react to form NOx, so that "air" actually becomes a complicated mixture, which has some heat capacities, but calculating them is not so trivial. — Mikhail Ryazanov (talk) 07:21, 1 May 2018 (UTC)
 * Yes, Mikhail, absolutely. I've made a number of edits which I hope improve the page's explanation. Also Tigraan, I have to confess that I have no idea what you mean by "torsion of the double covalent bond." Can you supply a reference? KeeYou Flib (talk) 21:04, 26 March 2022 (UTC)

While trying unsuccessfully to find the ISBN for the 10th edition of Lange's handbook (ref 2), I found that the text of the 15th edition has been posted online and it does not contain a listing of specific heat ratio, only of molar $$C_P$$. I suspect that the table entries taken from Lange have been calculated using $$C_P - C_V = R$$, which, per the article, is not particularly accurate for real gases. It would be great if someone could find the time to replace the table with more accurate and reliably sourced data. PaddyLeahy (talk) 11:46, 31 March 2020 (UTC)

Values - using NIST tables?
Somewhat an answer to above, but more generally I consider replacing the table with values from https://janaf.nist.gov/. I want to check if there is strong opposition before doing the copy-pasting, though.

The NIST tables give Cp values. If I read correctly, in particular section 6.1, they used experimental data to fit the constants in ab initio calculations, then ran a fit through the results, and that is what the tables show. Importantly, the calculation make the assumption that gases are ideal.

My feeling is that if we trust NIST data for Cp, we implicitely trust the ideal gas hypothesis baked into them (for the gases, temperature ranges, etc. they give). In that case, we (Wikipedia editors) are not doing WP:OR by using it to compute γ from the source's Cp.

Thoughts? Tigraan Click here to contact me 10:38, 3 April 2020 (UTC)

Molar heat capacity notation
Under ideal gas relation should a bar be added on top of Cv and Cp since they are molar? (to match notation above it) Rmb87 (talk) 15:17, 26 March 2022 (UTC)


 * Actually, they are not molar. However there are some other problems with this section and I'm going to make some edits to try to fix them. Thanks for your suggestion. KeeYou Flib (talk) 20:21, 26 March 2022 (UTC)
 * I've made a number of changes to the page. There were a number of errors, which I've now fixed. I hope the article is clearer and would be happy to have feedback. KeeYou Flib (talk) 20:54, 26 March 2022 (UTC)

Table value of dry air at 15 °C highly questionable
A. It doesn't follow the trend as a data point (perhaps it's a typo of negative fifteen?)

B. It's listed in the table after 1000 °C, making the table unsorted.

Very suspicious in my opinion.

--RProgrammer (talk) 16:12, 9 April 2022 (UTC)

Isentropic exponent is not the heat capacity ratio of a real gas
Article mentions in the first paragraph that the heat capacity ratio (gamma) is also known as the isentropic exponent (kappa) for a real gas. This is IMHO misleading. Whereas for an ideal gas, kappa is the same as gamma, for real gases, the two are different. For instance:

I think kappa deserves a separate treatment, as in a dedicated section in the article. The two properties are often erroneously used interchangeably. --Hummeling (talk) 16:54, 15 June 2022 (UTC)
 * That's a good point. The article is really about heat capacity ratios, so I don't know about adding a whole section about kappa and its uses - that would be more appropriate on the adiabatic expansion page. But I agree with you that the comment about kappa on this page definitely needs correcting/addressing/clarification. Feel free to make fixes yourself if you feel that you're up to it, or make suggestions here; otherwise I'll take a shot at it when I can find time. Qflib, aka KeeYou Flib (talk) 17:42, 16 June 2022 (UTC)