# Talk:Heat capacity/Archive 2

## Awful caption needs changing

There is a nice animation with this caption...

'Heat energy stored in these motions does not contribute to the temperature of a substance.'

This is misleading and misguided. An improvement would be: 'as the temperature of a substance increases, the magnitude of motions like these increases'. Or ' When a body gets hotter, the heat energy supplied is going into motions like these. ' Or ' When a body's temperature is increased, the heat energy supplied is going into motions like these. '

Djcmackay 11:02, 25 January 2007 (UTC) David MacKay

## Merge with Heat_Capacity?

I don't see the reason for having a separate page called Heat_Capacity. The material here should be merged over.

Djcmackay 21:38, 25 January 2007 (UTC)

## Major Revision

The history prior to 7 July 2006 has been deleted because this article has been completely revised since then. Greg L 17:41, 21 July 2006 (UTC)

## S.I. Units

I'm a big fan of reporting units consistently. All disciplines tend to use specific conventions -- throw in holdovers from days gone by and it's easy to get confused. Should we change the tabulated specific heat capacity values to S.I. units, i.e. add the "x 10^3?" Todd Johnston 16:21, 8 June 2006 (UTC)

If "S.I. units" means the use of scientific notation, then no; that's what the SI prefixes are for. And in the specific case of the table that you were referring to, the floating point makes it easier for the average high-schooler to see the relative size of values; more mental energy is required to visualize that 8.91 × 10–3 is smaller than 1.2 × 10–2. This article can't realistically be regarded as a reference resource for scientists to use when they want to look up a value (they'll go to their books); it's a tutorial for people who want to learn about concepts. Greg L 17:44, 21 July 2006 (UTC)
The question is: is wikipedia purely for US-Americans with their archaic units of feet, inches, gallons, etc. or the English with their stones and pounds and pints, or is it more for a general public speaking a common language. Those who are unfamiliar with SI Units, may find the translation to their traditional units, like catty or werst, in the appropriate Wikipedia Page dealing with conversions of units.

## Check Specific Heat Capacity of Substances!

Hello,

I noticed two problems with specific heat capacity of the substances. Specific heat capacity varies based on temperature and phase. I reccomend setting the temperature to 298.15 kelvin because it seems the most popular in text books and manuals.

Please recalculate these values because what is currently shown is simply wrong!

The above comment wasn't signed (four "~" tildes) but a check of the history shows it was from Frozenport on 7 July 2006. I found this article quite wanting and have been revising it since 8 July 2006. One of the things I cleaned up was the table. I double checked each and every one of the specific heat values, deleted a couple that I couldn't confirm, added a few I thought were noteworthy, and added a column for molar heat capacity (Cp). It doesn't mean it's perfect and is completely free from errors; please advise if you find some. Note that a thermodynamic temperature of 298.15 K is precisely equal to 25 °C (which is the most common point at which to measure the physical properties of substances). Greg L 17:39, 21 July 2006 (UTC)

I think the heat capacity for gold is incorrect currently 0.2291 which is not 25.42J/K/mole / 197 g/mole the correct value I believe should be around 0.129 see http://www.efunda.com/materials/elements/HC_Table.cfm?Element_ID=Au I have edited it to be in line with this RichardMathie (talk) 18:12, 26 July 2009 (UTC)

## Talk blanked?

Hi,

I once posed a question here, that I now find missing. From the history is see that Greg L blanked all the previous discussions? Why? Shouldn't they at least be archived?

## SI units

The modern SI units for measuring specific heat capacity are either the Joule per gram per kelvin (J g–1 K–1) or the Joule per mole per kelvin (J mol–1 K–1). The various SI prefixes can create variations of these units (such as kJ kg–1 K–1 and kJ mol–1 K–1). Other units of measure are often employed in the measure of specific heat capacity. These include calories and BTUs for energy, pounds-mass for quantity, and degree Fahrenheit (°F) for the increment of temperature.

Can anybody tell me about the SI units above? I am doubtful because as far as I know, the SI unit for the mass is kilogram (kg).

Thanks for everybody help. Yves Revi 22:43, 28 October 2006 (UTC)

## water: specific heat capacity > 3R

-> more degrees of freedom or Dulong-Petit not the upper boundary or else ?

The molar mass of water is (2*1,008+15,999)g/mol = 18,015 g/mol. In 1g water are therefore 2*0,055509 mol H-atoms(!) und 0,055509 mol O-atoms.

The maximum value -according Dulong-Petit law- of the specific heat capacity of liquid water is therefore 2*0,055509g/mol*3R +0,055509g/mol*3R = 0,499958g/mol * 8,3145 J/molK =4,154 J/gK. But the real value is 4,18-4,19 J/gK. It's 0,7% bigger!(not much but well above the error boundaries)

What is the explanation of this? (31 October 2006)

Water is a bit over 3R per mole of atoms, but nevermind water. Liquid bromine has a heat capacity of 3.5 R per mole of bromine atoms (not molecules, where it is of course twice as much, but that doesn't count). I've failed to get anybody how knows how molar heat capacities happen. In theory, the max is 3R per mole of atoms, and any kind of bonding between atoms only can cut that figure down, because it results in quantum barriers to equal partitioning into kinetic and potential storage modes. The only thing I can think of is that we're getting partitioning into electronic modes of excitation (rather as in gas phase NO), and that gives additional degrees of freedom which we're only beginning to see the tail of. SBHarris 17:42, 9 December 2006 (UTC)
According to Herzberg, the lowest excited electronic state of Bromine is at 13814 cm-1, which is way too high to be thermally populated at room temperature. (In contrast, the first excited state of NO is 121 -1. A useful conversion factor to keep in mind for these sorts of comparisons is 300 K corresponds to 208 cm-1). So that can't be the explanation. I do wonder if you are trying to get too much out of the equipartition theorem by trying to use it to draw conclusions about liquid state heat capacities. Equipartition is really only useful if the potential energy is zero (free particles) or not too far from quadratic (crystals in the harmonic approximation.) If the potential energy is large but not anything close to harmonic, equipartion says basically nothing useful.--Rparson 22:57, 11 December 2006 (UTC)
I don't see why it shouldn't say something useful about MAXIMAL energy storage, which is what happens when you have an asymptotic approach to freedom from constraint in motion (as in free particles and particles near the bottom of quadratic potential wells where you can approximate the potential as square, and thus free). Again, if a atomic nucleus is free to move in 3 dimensions it should be able to store R per mole of nuclei per dimension. If things are screwed up by funny shapped potentials, all it can do is screw this up-- I can't think of any way it should be able to ADD to it.SBHarris 00:19, 12 December 2006 (UTC)
So what happens in the vicinity of the liquid-vapor critical point, where the heat capacity diverges to infinity? Yes, that's a mathematical singularity (it assumes an infinite number of particles) but it reflects a physical reality: the real, measureable heat capacity of a supercritical fluid in thhe immediate vicinity of the critical point is enormous. Ditto for the glass transition. It seems that when systems become large and "loose", so that small additions of kinetic energy can get dispersed into a wide variety of motions on all sorts of scales, heat capacities can get as large as one wishes.
Um, I was under the impression that the heat capacity of substances at glass transition or supercritical point was whatever they were for the substance on either side of the phase change, since the whole point of both of these states is that the enthalpy of transition goes to zero there. So why says the heat capacity of the stuff itself goes wild? I don't believe it. Some funny thing happen in liquid helium going from normal to superfluid, but that's due to the phase transition itself taking up energy and and heat capacity itself isn't high, just the CHANGE in heat capacity is high. SBHarris 11:25, 26 December 2006 (UTC)
No. Check out the articles on critical phenomena, phase transition, etc. In the neighborhood of a 2nd order phase transition, the heat capacity generically diverges to infinity according to the power law |T-Tc|, where the critical exponent ά depends upon a small number of "universal" parameters that characterize the type of phase transition. For the liquid-vapor critical point, ά is approximately 0.1 (www.nyu.edu/classes/tuckerman/stat.mech/lectures/postscript/lecture_25.ps), for normal-superfluid helium the measured value is 0.0127. As long as ά is less than 1 the singularity is integrable, so that the latent heat is zero, and with values like 0.1 or 0.01 you do have to get very close to the critical point to see the divergence, nevertheless it is there. Kenneth G. Wilson got the 1984 Nobel Prize for explaining how this comes about.Rparson 20:42, 26 December 2006 (UTC)
Nevertheless you do raise a puzzle, since I wouldn't expect liquid Bromine to be all that unusual. I do think that one should be careful because we don't have a whole lot of useful reference data here - the readily available data on heat capacities is mostly tabulated for elements and simple organics at standard temperature. I'd be interested to see what the heat capacity of, for example, liquid He or Ne is. It occurred to me that the value for Br2 might just be an error (it's been known to happen) but I traced it back to the NBS tables, which are about as authoritative as anything. —The preceding unsigned comment was added by Rparson (talkcontribs) 00:30, 14 December 2006 (UTC).
Perhaps the Dulong-Petit law does only apply to solids, where the structure doesn't change with temperature. (24 December 2006)

—The preceding unsigned comment was added by 84.152.105.34 (talk) 14:36, 24 December 2006 (UTC).

All: I originally used water as an example of the number of degrees of freedom because it was a substance familiar to all and is widely recognized for its high specific heat capacity. I also had visted several chemistry sites at universities that consistenly said water has six active degrees of freedom. Water apparently has more than six possible degrees of freedom but only about six or seven are active at 100 °C. It eventually developed that water was a poor choice to use in this article for illustrating the concept of degrees of freedom. By dividing the CvH of steam by that of the monatomic gases, one can see that water doesn't have a clean, interger number of degrees of freedom; it's more like 6.7 degrees of freedom. I don't know if there's some hydrogen bonding going on with steam at 100 °C or if a seventh, internal degree of freedom is active but is partially frozen out. Consequently, I substituted nitrogen in place of water. Nitrogen cleanly demonstrates the concept that the number of active degrees of freedom expresses themselves as a proportional increase in molar heat capacity under constant volume. I also added a CvH column to the table to help in illustrating this concept. Greg L 05:31, 25 December 2006 (UTC)
The Dulong-Petit law only gives a high temperature approximation for the mechanical atom movement. There are other ways (thermal) energy can be stored. In the water example, the structure of the liquide depends a little on temperature. So if water is heated, a part of the energy is used to make the structure a little more open. Near a critical point the structureal changes can get quite large an this way make the heat capacity very large.--91.3.124.78 (talk) 19:58, 9 September 2009 (UTC)

## Degrees of freedom in translational motion

Should:

six degrees of freedom comprising translational motion

three degrees of freedom comprising translational motion?

Pmilne 13:02, 4 November 2006 (UTC)

Also -

There is more than six DOF for water. I'll change it if no-one argues.--136.2.1.101 18:25, 10 November 2006 (UTC)

---

Specific heat capacity of steel?

## but my book says..

my book says that the specific heat of water is 4190, why is it differnt on wiki

Check the units in your book against the units on the table. The specific heat for water is around 4.19 Joules per gram per Celsius degree, but if you list it in Joules per kilogram per Celsius degree the value would be 1000 times greater - that is, 4190. (You'd also get 4190 if you listed the heat in kiloJoules per cubic meter per Celsius degree, although that equivalence only works for materials with a specific density of 1.) Jasonfahy 21:54, 5 December 2006 (UTC)

Yea, i checked um, AND asked my teacher the book had it as J/kg*C so now i feel kinda stupid Chuck61007

The specific heat of water depends on the temperature of the water (see Calorie). JIMp talk·cont 17:09, 29 November 2009 (UTC)
So does the specific heat of any substance! SBHarris 22:22, 29 November 2009 (UTC)
Good point. JIMp talk·cont 09:33, 13 December 2009 (UTC)

## Water vapor

I have corrected want to point out a serious misinterpretation of the heat capacity of water vapor. Water molecules do not have "a maxiumu of six degrees of freedom", they have nine, 3 each for translation, rotation, and vibration.The vibrational d.f. are mostly "frozen out" at T=100C, so the zero-order estimate for Cv is (3/2 R) for translation + (3/2 R) for rotation = 3R. For an ideal gas Cp =Cv + R, so you expect Cp approximately equal to 4R, ie. 33.26 J/mol K. This is slighly less than the value in the table, 37.47, just what one expects since the bending vibration is fairly low frequency and is therefore not completely frozen out. The fact that the final answer is close to twice that of a monatomic gas is a numerical coincidence - if the vibrational contribution were completely frozen, one would expect the ratio of the two Cp's to be (4R)/(2.5R) = 8/5 = 1.6 . I also have never heard of this "alternative convention", described in footnote 2, according to which a degree of freedom is counted in each direction. Unless someone comes up with a reference for this, I'm going to get rid of it.--Rparson 22:40, 11 December 2006 (UTC)

Yeah, I don't where the 6 vs. 12 degrees of freedom for water came from in this footnote. The atoms in a 3-atom molecule have a total of 3 x 3 = 9 ways to move in space with no bond constraints. Add bonds which are not frozen, and heat capacity goes up because you store 2 times as much per bond as in translation, due to the potential contribution. Without vibration you get (as you note) 3/2 + 3/2 = 3R/mole for translation and rotation of the molecule. Nevermind the Cp which is a red herring-- that's the Cv for no vibration: just R per atom for water. If you add the 9-6 = 3 vibrational modes, with R for each, you get 6R/mole = 2R per atom. Still not up to the max of 3R per atom of solids, but you expect to lose heat capacity simply because free water molecules in a gas have lost a bunch of ways to put energy into potential energy of vibration, due to all those missing bonds between molecules. The bigger the molecules you have in a gas with all vibrational modes excited, the closer Cv gets to 3R per atom. But of course Cv per mole goes up and up, the larger the molecules get. That's not a fair way to look at heat capacity, of course. SBHarris 03:06, 12 December 2006 (UTC)

## What does this mean?

'The standard pressure was once virtually always “one standard atmosphere”...' What in God's name is this supposed to mean?Edison 21:44, 22 January 2007 (UTC)

Well, air pressure is not the same everyplace, even at sea level. It goes up and down with weather and temperature and so on. So a "standard atmosphere" was picked as a standard condition for STP to measure things at. Do you need the exact number? There's a whole wiki on it at Atmosphere (unit). It might help if you'd refine your question. SBHarris 21:49, 22 January 2007 (UTC)

## ? What is with the deviation?

the article indicates that the specific heat of water is in the unit joules per kelvin per kilogram- yet the chart indicates that the specific heat of water is in joules per kelvin per gram. Which is correct? —The preceding unsigned comment was added by 75.8.123.248 (talk) 03:21, 1 March 2007 (UTC).

Both are correct. Water is 4184 J/K/kg (as stated in the opening para) or 4.184 J/K/g (as stated in the table). You have your choice of mass units and it affects the value of the number.SBHarris 04:09, 1 March 2007 (UTC)

Qskeptic —Preceding unsigned comment added by 203.101.236.10 (talk) 07:01, 27 May 2008 (UTC)

## SI Units redux

Sorry to respond 6 months after the fact. By suggesting we should report all values in SI units, I don't mean "scientific notation" -- I mean SI units, as in the International System of Units established, maintained, and kept current for over 40 years by the National Institute of Standards and Technology (NIST). SI units are the "basis of all international agreement on units of measurement," according not only to the NIST, but to Wikipedia's own page on the Metric_system.

Every discipline defines their own units best suited to communicating within that discipline. E.g. meteorologists rarely express pressure in the derived SI unit "pascals" because the "P" in "STP" is 101,325 Pa. Besides, the math is a lot easier if P = 1 atm.

But everyone contributing to this page, and trying to learn from it, will have a different lexicon depending on their background, so we should adopt the universally agreed upon convention to minimize confusion. Those who've grown accustomed to discipline-specific units are typically still aware of and conversant in the SI equivalents. And anyone who is trying to learn this material, must see it first in SI untis, to understand how it connects to the broader framework of general physics. Todd Johnston 22:36, 3 March 2007 (UTC)

The introductory chapter of the book includes a discussion of units, but nowhere is mentioned the fact that the whole point of units is that you can choose whatever units are most convenient, such as using the (reduced) mass of the electron as a unit of mass in atomic physics.

Count Iblis (talk) 23:43, 24 April 2008 (UTC)
However, choosing convenient units is a relatively advanced concept that is best avoided when discussing elementary physics, and choice of units is dependent on the community. This article is (presumably) not addressed to any particular discipline, but to the public at large. If readers have learned physics at all, they have learned it in SI units. If they've seen the specific heat capacity of water before in a high school textbook, they've almost certainly seen it expressed as in coherent SI units as 4.2 × 103 J kg-1 K-1, or perhaps as 4.2 kJ kg-1 K-1. Why confuse them with the rather bizarre units of J g-1 K-1, which I guess are a confused hangover from the long-gone days of the CGS system? JCBradfield (talk) 20:32, 6 September 2008 (UTC)
Minor point: BIPM (internationally) not NIST. JIMp talk·cont 17:02, 29 November 2009 (UTC)

## Extensive measure vs. Intensive measure

Spiel496: Regarding this edit you made, I don’t understand why we are interpreting the meaning differently as I see you are a physicist. Maybe I'm wrong but it seems like simple reading. Note what Physlink’s Glossary says about the term. Search on the following text string to go to the relevant section: “Specific. In physics and chemistry”. PhysLink defines “specific” as follows:

Also, it seems that the opening definition in Intensive and extensive properties is clear as glass. It says

Clearly, measuring two grams of water produces a different value for the amount of heat energy required than does measuring just one gram.

The same Wikipedia article goes on to describe intensive measures. It says…

(my emphasis).

An example of an intensive property would be viscosity, the value of its measure is independent of sample size until you get down to microscopic amounts.

Why do you think specific heat capacity is an intensive measurement? Greg L (my talk) 00:05, 28 July 2007 (UTC)

I've carefully read the "intensive/extensive" business some more and believe you are right. I see that if you divide an extensive property by another extensive property, one gets an intensive property. Allow me to rewrite the article accordingly. My humble appologies. Greg L (my talk) 00:27, 28 July 2007 (UTC)
Done. Again, you were (very) right. And you even had the grace and patience to say "prove it" and slap the "citation needed" tag. I corrected it per your teachings but downplayed the intensive/extensive stuff. Any more than what's there now starts looking like a treatise that better belongs in the Intensive and extensive properties article. Greg L (my talk) 00:55, 28 July 2007 (UTC)
Wow, Greg L edits so fast, both sides of the conversation have been carried out in my absence. I guess I have nothing else to add, but to say that I like the way the article reads. Thanks for all the work you've put in the past few days. Spiel496 03:37, 28 July 2007 (UTC)
You’re welcome. I appreciate the attaboy. Greg L (my talk) 04:21, 28 July 2007 (UTC)

## Volume-specific measurement

The following text had incorrectly been in the Specific heat capacity article for 229 days:

The above text had been added, even though the following chart (and related text) had been in the article for months prior:

 Under constantpressure At constantvolume Unit quantity = mole Cp or CpH Cv or CvH Unit quantity = mass cp or Cph cv or Cvh

Please note that in the above chart, Cv and cv denote that a measurement was a constant-volume measurement of either a specific-mass or specific-molar quantity, not a “specific-volume” quantity. The alternative to a constant-volume measurement is a constant-pressure one (either Cp and cp). Accordingly, the following editors note (<!--text-->) was added to the “Unit quantity” section:

Greg L (my talk) 19:08, 3 August 2007 (UTC)

Well, there's a big difference between saying you disagree with some notation or that you haven't ever encountered it personally, and claiming it is incorrect. See Incropera and Dewitt, a standard engineering heat-transfer text, for multiple instances of volume-specific heat capacities for solids and liquids (C/V where V is volume) being given the subscript v (as in cv), as opposed to mass-specific quantities, which are given a subscript m. You could as easily have simply kept the data and added the notation that "Some idiot engineers do this, and Greg L. doesn't like it." Science isn't always nice and consistant, and notation is still not standard across all fields. FYI, there are instances where volume-specific heat capacities are actually an easier value to work with. An example is digitally-simulated weather calculations, where volume-parcels of air are the gridded variables, and all one cares about is the property of each parcel, even if its mass changes from moment to moment. IOW, whatever the column of air above any section of land contains, or what its temperature variations with altitude are, at least one can say by definition that it always has the same volume. SBHarris 18:49, 21 December 2007 (UTC)

## Merge?

As Greg L continues his editing rampage (in a good way) I'm curious to know his opinion, and anyone else's, on merging this article with heat capacity. It was brought up earlier on this page, but not discussed. All the interesting stuff in this article would be just as relevant in the heat capacity article or vice-versa. The only thing that distinguishes the two topics is the fact that "heat capacity is proportional to the amount of material". That statement is not interesting enough to warrant a second article. Spiel496 01:24, 4 August 2007 (UTC)

Ugh. I hate to think about it. I didn't know heat capacity was a separate article and was really surprised to learn that C is the symbol used for molar-based specific heat capacity as well as plain ol’ heat capacity (without the “specific”). Science seems to have several logical lapses—check out the naming convention for many chemicals. The heat capacity article is clearly more technically complex and is directed to a different type of reader. I think that would make merging damn difficult. I also don't quite understand why there would even be a separate article on heat capacity; If someone wanted to calculate the heat capacity of a swimming pool, they must first start with specific heat capacity to find out how much energy is required for a kilogram (liter), and work from there. And no one gives a damn about carefully performing a constant-pressure measurement on a swimming pool; they’re pretty much “by-gosh, by-golly” estimates subject to relatively great uncertainty. To this extent, the subject the article covers seems less scientific to me even though the article itself is geared to a more technical audience. That's my two-cents anyway. Greg L (my talk) 08:42, 4 August 2007 (UTC)
Update: Well, now I’ve done it. What is it that’s the sincerest form of flattery? As you will see, I folded pretty much all of the contents of Heat capacity into Specific heat capacity. At the same time, I fixed a number of errors and misleading advise in Heat capacity. Why incorporate one into the other? The two articles seemed extraordinarily redundant to me. If what I’ve done is a major Wikipedia faux pas, feel free to revert it. However, since nothing on Wikipedia is copyrighted, and since I didn’t delete the heat capacity article, I didn’t see the harm. I guess I’ll find out soon enough, won’t I? Greg L (my talk) 23:07, 6 August 2007 (UTC)
I have no experience with the formalities of a merge, but I put merge templates on both pages. The next logical step would be to remove the heat capacity article. Spiel496 05:59, 12 August 2007 (UTC)

Seeing no objections, I redirected Heat capacity to Specific heat capacity#Heat capacity and removed the merge templates. ←BenB4 11:42, 12 August 2007 (UTC)

Thanks BenB4. Greg L (my talk) 01:20, 13 August 2007 (UTC)

## Tables of Specific Heat Capacities

The two tables of specific heat capacities look very out of place, right in the middle of the article. You're talking physical theory and nomenclature one minute and then all of a sudden it switches to building materials? (Seriously. WTF? Didn't have the time to figure out who added the latter list from the history.) Even the first table could do with some explanation of why it's placed there.

There's another list under Orders of magnitude (specific heat capacity), which has different substances listed. Might it be an idea to move/merge these two there instead? (And provide a short paragraph linking to said article.) —Liyang 02:20, 1 September 2007 (UTC)

• You assume too much Liyang: your reaction is as if the table on building materials represents some sort of deliberate editorial decision by some sort of committee of professional technical writers. The table on building materials is simply a hold-over legacy artifact from the early days of this article. The larger table started out as a simple thing of humble origins and has grown with time to be something with a lot of valuable data. The juxtaposition of the two tables is now more striking. Wikipedia—being the collaborative writing environment it is—often has articles that suffer from “too many cooks in the kitchen” at one time or another. No one has had the heart to delete the building materials table. Instead of complaining about things, do something about it. But don’t wade in with a big eraser and just delete valuable information; improve the article by moving things around so the information is presented in a more logical fashion. Greg L (my talk) 20:52, 16 December 2007 (UTC)

## Joseph Black

Was Joseph Black a physician or a physicist? Bewp 13:53, 9 September 2007 (UTC)

I believe this is a pseudo-question, in the sense that in the XVIIIth century there was no such a thing as a "physicist", at least in the same sense we nowadays understand it. There was no formal, regular university education for Science in general (even the term "scientist" comes a lot later) - hence most scientists from the period had a background in Medicine or else. How to title these folks in nowadays articles has always been a tricky thing. Many authors prefer to state them simply as "thinkers". However, in many cases, as in Joseph Black's, the bulk of the work refers to one or two nowadays well established disciplines, such as chemistry and physics, so regardless of his previous background one could title him a physicist, if you want to, or a scientist, if one wants to encompass his also important contributions to chemistry, for instance. Nevertheless, many authors would rather, perhaps for the sake of historic correction, state his formal education background - and hence the title physician. Beto Pimentel (talk) 11:19, 2 April 2008 (UTC)

## Specific heat capacity vs. heat capacity

I think this article is rather confusing. In my coursebook on physics, specific heat capacity and (normal) heat capacity are treated as two different physical quantities (which I think is correct), while in this article I do not get a grasp on what the difference is. The "specific heat capacity" should I think always be written with a lowercase symbol ${\displaystyle c}$ while "heat capacity" is written with an uppercase symbol ${\displaystyle C}$. In this article, this is confused and not consequently done - I'll try to fix this. Also, the first formula that you see on the Specific heat capacity article, is the normal "heat capacity" definition.

To explain both quantities in one article seems to me like explaining heat and energie in the same article, or length and weight. In my opinion, they should again be splitted into two separate articles. There is some overlap, since the difference will be explained in both articles, but merging the two adds up to confusion. I'd like to hear other opinions before I do this. Anoko moonlight (talk) 14:50, 21 December 2007 (UTC)

First, some history: The "Specific Heat Capacity" and "Heat Capacity" articles were recently merged. They were evolving in parallel with a lot of duplicate information. The editor who merged them did a good job, but they were both pretty large to begin with, so the overall organization of the article may have suffered.
Once you've explained specific heat, there's not much to say about "heat capacity". The "Heat Capacity" article could simply say "The heat capacity of a sample of material is equal to its mass times the specific heat of the material." That isn't really interesting. Bigger objects have more heat capacity. What is interesting is that different materials have different specific heat capacities.
Spiel496 (talk) 20:20, 22 December 2007 (UTC)
Thanks for your feedback. Maybe it is not so clear with the present structure that heat capacity could have its own article, but the Dutch Wikipedia proofs that it is possible without much overlap (see [1] and [2] for resp. the Dutch heat capacity and specific heat capacity articles). Anoko moonlight (talk) 21:37, 22 December 2007 (UTC)

## Rotation of diatomic gas

Ok there is something I don't get about rotation of diatomic gas on the z axis (rotation around the axis of the molecule) if the wave function is cylindrical (which is true I suppose -but i am not sure- for diatomic gases such as H2), then there is no rotation possible.I mean that if the molecule has perfect indiscernibility through rotation on itself, you cannot talk about rotation. The rotation is not frozen out, it is not a rotation at all since you get the same object when you rotate it. When user says "Electrons in any atom can gain angular momentum, so options to rotate more are frozen out but never absent)", what is meant by "electron gain angular momentum" ?

By the way would not it be the same problem for monoatomic gaz? if the "electrons can always gain angular momentum", then we could say that the sphere (monoatomic gaz) can turn on itself and you should consider 3 degrees of freedom of rotation for monoatomic gaz which I have never heard of (of course they would be frozen as well I know that, I just want to know what happens theoretically if you could go at whatever temperature you wanted...).

Now I know that in most molecules, there will be P-orbitals that are not invariant through rotation. But what if there is only S-orbital that are available? Is that impossible?

Basically, molecules have much lower energy gaps between rotational energy levels based on nuclei changing angular momenta WRT each other (rotation on other than the interatomic axis). Electrons can rotate faster in a bond, but must be promoted into a higher energy (exited state) to do it. Generally these states involve a change in bond electron angular momentum (with respect to the bond axis). The free electron in one antibonding orbital of nitric oxide gives the gas come extra heat capacity at room temp by moving to an excited orbital with more angular momentum and energy. Of course it's the energy that's important-- angular momentum change isn't necessary unless you want to couple to photon absorption. Helium at high temps would have increased heat capacity from electrons jumping from 1s to 2s orbitals-- no change in angular momentum but yes in energy. Of course 1s to 2p involves a change in L.

Basically all this is why monatomic gases show no signs of "rotating". What would rotate? The individual electrons either have angular momentum or not, and changing it for each one comes with an energy price. You can't rotate the singe monatomic gas "atom" without making it equivalent to electrons increasing angular momentum, and that's already fixed. SBHarris 10:55, 7 September 2008 (UTC)

When you reason in terms of energy, You may consider the different energy levels accessible to the molecule (computed via the hamiltonian of the system), and you will see that there are levels of energy with non-zero angular momentum. And a rotation will correspond to a transition between a state of zero angular momentum and a non-zero one. —Preceding unsigned comment added by 217.128.252.209 (talk) 08:31, 2 April 2008 (UTC)
Angular momentum about what axis? If it's the axis that connects 2 nuclei, what is it that is rotating? For other axes, this is rotational degrees of freedom are discussed in the article. SBHarris 02:16, 4 June 2009 (UTC)

## Table of specific heat capacities

What makes certain "minima" and "maxima" "notable"? at first, i thought these might be the highest and lowest heat capacities in the table, but this is not the case. and are the bold numbers "notable" as well? in what way? The answers to these questions should be included with the table. in its current state, the colors and bold numbers are just confusing.--Jmjanzen (talk) 16:10, 23 May 2008 (UTC)

## Specific heat and the partition function

How come there's no mention of how the specific heat is related to the partition function? —Preceding unsigned comment added by 83.216.146.141 (talk) 13:34, 15 July 2008 (UTC)

We'll get there. That's a fairly complicated topic. SBHarris 02:13, 4 June 2009 (UTC)

## Polyatomic gases

I just moved this section down below monatomic and diatomic gases, and gave a linear polyatomic example for N2O. It many not be enough but it's a start. I think this fleshes out the gas part somewhat better. The sections treating actual heat capacity for molecules n >3 perhaps deserves more separaton from the discussion of quantum freezing out of modes. SBHarris 02:13, 4 June 2009 (UTC)

## Coherent derived unit representation (division vs. negative exponent)

I'm going to change the representation of the coherent derived units in this article to division (using solidus) versus negative exponents. SI allows either to be used, but Wikipedia (which doesn't require SI anyway) specifies to use the most understood form when writing to a general audience. Since a person generally learns the mathmatical concept of division prior to learning exponentals (and certainly prior to learning negative exponentals), more people in the general audience of this article will understand unit representation via division. 66.19.201.92 (talk) 18:39, 2 July 2009 (UTC)

## Bromine

The specific heat capacity of diatomic gases should be 7/2 R, but since the vibrational mode is frozen out most are less than 5/2 R. Presumably this is becasue the rotational modes are partly frozen out, but this is not explained. What puzzles me is why Br has a specific heat greater than 7/2 R. Could someone explain that? A B McDonald (talk) 13:47, 22 July 2009 (UTC)

Values for Bromine were wrong - now fixed A B McDonald (talk) 14:24, 22 July 2009 (UTC)

## Specific heat of water is incorrect, but correct me if I am wrong...

The article says the specific heat of water is 4186 Joules per kilogram, but cites a website which may not be reliable. A more reliable one, such as wolfram alpha which has all its data checked by real scientists, says it is 4.18 Joules per gram, and if it were 4186J/kg surely wolfram would have written it as 4.19J/g? —Preceding unsigned comment added by RLakshan (talkcontribs) 09:26, 17 August 2009 (UTC)

## error value in "Symbols and standards"

Under: Symbols and standards

Water (liquid): cp = 6.1855 J/(g·K) (25 °C), and… ...

Table of specific heat capacities:

Water at 25 °C liquid Cp = 4.1813 J/(g·K)

The 2 figs in italics refer to the same constant, however they differ on the same page.

I think the error is in the former, the latter being the correct figure.

Tks

—Preceding unsigned comment added by 121.7.177.137 (talk) 13:26, 14 October 2009 (UTC)

). —Preceding unsigned comment added by 121.7.177.137 (talk) 13:23, 14 October 2009 (UTC)
It was just some vandalism that hadn't been caught -- fixed. Thanks for noticing. Spiel496 (talk) 15:22, 14 October 2009 (UTC)

Hi, if that the case then maybe anonymous free editing shouldn't be allowed. Anonymous users should however be allowed to 'discuss' wanted changes so that a registered moderator can make the necessary amendment. Case in point here about lax rules and the significant damage/ deception vandals can cause. Spiel496, thanks for the prompt correction. (Fr author of 1st msg w 'floating IP address') —Preceding unsigned comment added by 219.74.223.200 (talk) 20:17, 14 October 2009 (UTC)

## "Thermal Capacity" and "Specific Heat"

The terminology here is inconsistent both internally and with usage "in the wild", where there is also inconsistency. In particular, use of the term "specific heat" appears to predate the use of "specific heat capacity" as used in this article. I have two college physics textbooks by Robert Resnick and David Halliday, (Resnick, R. and Halliday, D.; _Physics, Part I_; 1966) & (Halliday, D. and Resnick, R.; _Fundamentals of Physics_, 1970) that define specific heat as "heat capacity per unit mass". Earlier college physics textbooks (I have Hausmann and Slack, _Physics_ (2nd ed.); 1939) and (Spinney, L. B; _A Text-Book of Physics_ (3rd ed.); 1925) that both define "specific heat" of a material as the ratio of the heat requried to raise the temperature of the material by one degree to the heat required to raise the temperature of water by one degree. A starting water temperature of 15°C is implied. Dictionary definitions, plus my 1975-76 CRC Handbook of Chemistry and Physics agree with this definition of "specific heat" as a unitless ratio.

To further complicate things, the CRC handbook agrees with Hausmann & Slack in defining "thermal capacity" to mean what this article calls "specific heat capacity", while the older Spinney book uses the same term "thermal capacity" to mean what Resnick, Halliday and this article refer to as "heat capacity"--a property of an object, not a material.

Reading this article, there are regular references to "specific heat" in the Resnick/Halliday sense of dQ/(m dT) or "heat capacity per unit mass". The Wikipedia article on Calorimetry uses "specific heat" to mean the same thing. Eric Weisstein's "World of Physics" (hosted by Wolfram Research at http://scienceworld.wolfram.com/physics/SpecificHeat.html) also lists specific heat as the primary term, noting that it is "also called specific heat capacity".

Maybe these modern writers are shortening the longer "specific heat capacity" term, but it seems unlikely that Resnick and Halliday were. It seems to me that some citation is needed here. When did the terms "specific heat capacity" and "heat capacity" become *the* terms in the senses used here, and by what authority. Husoski (talk) 06:06, 14 November 2009 (UTC)

Personally, I take specific heat to be synonymous with specific heat capacity, with dimensions of J/(kg*K) or J/(mol*K) or J/(cm^3*K) depending on the application. Some texts define it as a dimensionless quantity, which is a confusing convention that Wikipedia should avoid (in my opinion). Does there need to be an authority on the convention chosen? As long as the article is self-consistent, we're OK. Is it inconsistent somewhere? (I did remove the bit about "specific heat" being the incorrect term.) Spiel496 (talk) 06:07, 18 November 2009 (UTC)
The term "specific" means in general that you're dividing by some unit which EITHER makes the property "intensive" (not dependent on quantity of material); OR which makes it BOTH intensive AND dimensionless, because you're comparing it with a known reference substance. Example of the first is volume-specific, mole-specific, and mass-specific heat capacities, which all arise by dividing total heat capacity of a material by its volume, or molar content (assuming it's a pure substance), or its mass. This results in something with a new unit (obviously).

The older way of using the word specific is as a clue that something was being compared to some standard, like water, by further comparing the previous number to the corresponding one for water. And thus, you obtain a "water-specific heat capacity," which is dimensionless. The number 0.5 simply means it has 50% of the corresponding figure for water, but to get the units you have to see what they used for the water.

This is confusing because sometimes the WORD "water" is left off, so you have to know the reference to water is implied, if no units are given. The same thing happens with "specific gravity": it's really "water-specific gravity," and it's unitless. Something with a "specific gravity" of 9, that means it has 9 times the density of water, but no units are given unless you use the units you meansured density in, with water (mass per volume). Acceleration is sometimes measured in units of g's, and then it's "g-specific" acceleration and you have to know the units of a standard g. The older use of "specific" as comparing to some standard other than one involving an SI unit, is dying away. Nowadays, "specific" almost always means you divide by a new SI unit which relates, directly of indirectly, to amount of material. Water comparisons are out. Oh, yeah, sometimes even then they use the word specific, and don't tell you WHAT is the unit being used for the comparison. They say specific and mean "mass-specific." Since you might think volume or mole-specific, that's bad form. SBHarris 08:30, 18 November 2009 (UTC)

## Specific heat capacity of wood is incorrect

The given value is erroneous. I think it is the value in cal/g/K and I proposed a value of 1700 J/kg/K. It is not a precise value, being subject of variation with different types of wood and with humidity. I do the same correction in the french wiki page, with the same table translated from english page. A concluding remark for anybody who want to complete the talk : the german wiki page on the same talk is well documented.--Jean-Marc.Vignon (talk) 08:00, 24 November 2009 (UTC)

## [the problems of the global warming up, climate change.]

the compare for the climate change of sea water and air. —Preceding unsigned comment added by 67.115.155.131 (talk) 19:58, 7 December 2009 (UTC)

## Specific heat discussion in first paragraph doesn't match table

The heat energy required to raise water’s temperature one kelvin per kg is given as 4186 Joules per kilogram in the first couple of sentences but in the table is listed as 4.1813 J/(g*K). This is not consistant. 1 kg of water is not exactly equal to 1000 cm^3. Hcbonner (talk) 16:30, 14 December 2009 (UTC)

## Specific heat capacity of liquid water

The article states that the specific heat capacity of water is 4186 J/kg (3rd line from the top). This is wrong. The specific heat capacity of water is a function of temperature, fitting closely the following equation: Cp water(liq) = -1.0545E-04(T^3) + 1.1554E-01(T^2) - 41.296T + 9018, where T = degrees K. The Cp decreases from a value of 4210 at 273.16 K to about 4178 at 308 K, then it goes back up to about 4219 at the bouling point (373.15 K). Thus there are actually two temperatures where Cp = 4186. There are many references giving the actual numbers for Cp of liquid water as a function of T. Can somebody please edit the article to correct the error?Thermbal (talk) 20:53, 9 January 2010 (UTC)

The article is "Specific heat capacity", not "Empirical formulas for the specific heat of water". Adding that kind of detail to the lead would accomplish nothing towards the explanation of heat capacity. Spiel496 (talk) 18:42, 10 January 2010 (UTC)
Yes. Beyond nothing that ALL specific heat capacities are T-dependent, we should simply specifify the temp at which water has a heat capacity which is approximately 1 kcal/kg, so that the conversion from 4186 joules to 1 kcal becomes obvious. That happens at 15 C. SBHarris 23:29, 10 January 2010 (UTC)

## Alloys

Is there a link to how to calculate the specific heat capacity of alloys, such as brass or mixed materials such as humid air? This might be interesting especially for the construction and HVAC industry active in continental, maritime and tropical climates. —Preceding unsigned comment added by 202.82.143.78 (talk) 03:34, 12 January 2010 (UTC)

## Unit quantity discussion

The note to editors claims that there is ambiguity about the unit quantity in specific heat? Where is that found? As far as I know, specific heat capacity (or anything specific to that matter) always refers to property/mass. For a unit quantity of mole, the name is molar. —Preceding unsigned comment added by Alexander.mitsos (talkcontribs) 23:30, 17 February 2010 (UTC)

No. The term "specific" simply means "divided by something". This, we have mass-specific, volume-specific, and mole-specific heat capacities. Often the "mass" is left out of "mass-specific" but we really should leave it in to avoid problems like yours. If you want a good example, consider specific gravity, which is density divided by the density of water. It's actually "water-specific density". But badly named. However, that's how it's derived, and that's where the word comes from. SBHarris 23:43, 24 February 2010 (UTC)
No, you are misinformed and Alexander.mitsos is quite right in his remark. When a physical quantity is referred to a 'specific quantity' it is by convention an intensive property, referenced to some measure of amount of matter, either mass (primarily in physics) or amount of substance (primarily in chemistry). There are quantities that are related to volume, indeed, but this must always be clarified by the mark 'volume-specific' property. Kbrose (talk) 01:18, 25 February 2010 (UTC)
I'm confused. I don't see how Sbharris's paragraph contradicts anything Kbrose just said. Sbharris doesn't deny that specific heat is an intensive property. He just says volume-specific heat has different units than mass-specific heat. Am I missing something? Spiel496 (talk) 04:13, 25 February 2010 (UTC)
No, actually you're not missing much. However, in physics, the qualification of a property as 'specific' implies mass independence, and not just "division by something", as suggested. sbharris' comment was to contradict the original poster's comment (as shown by the lead in "no..."), and resulted in his edit of the article to be reverted. Kbrose (talk) 04:41, 25 February 2010 (UTC)
Then this is just semantics. To determine the specific heat of a substance, Sbharris is pointing out that you divide the measured heat capacity of a sample by the mass of that sample. The result is a quantity that is independent of the amount of sample. I assume you don't dispute that. Now, regarding the units: The units of mass-specific heat are J/(kg*K). The units mole-specific heat are J/(mol*K). Is that right? Spiel496 (talk) 05:35, 25 February 2010 (UTC)

That is right. Although it turns out that many "specific" quantities are intensive, not all of them are, or else I would have said so. "X-specific" really does mean, in general, "per X", which means you divide by X. Specific impulse can be a real intensive quantity (impulse per mass), or it can be oddly expressed as an impulse (momentum change) per earth-weight, which isn't the same thing at all. Dividing by weight (making it weight-specifc) doesn't result in an intensive quantity, since you may be someplace in space where things have no weight, but you divided by mg instead of m, anyway. You've then just divided by earth g for no good reason. It's still called "specific-impulse" however, even if you express it in seconds, which means with the extra Earth-acceleration-division. A better example is the well known thrust specific fuel consumption of an engine. It has units of grams/sec of fuel the engine consumes per kilonewton of thrust. Hence the term "thrust-specific" not mass-specific. It's a specific but not in any possible way, an intensive quantity. The inverse of it is vaguely intensive (sort of, almost), but you see the point. We're not talking about its inverse. SBHarris 06:40, 25 February 2010 (UTC)

## Quantum theory and heat capacity

That some elementary quantum theory is necessary to calculate heat capacities, is an undergraduate textbook subject. For example, my own (dated-- 1966!) copy of W. Kauzmann's Kinetic Theory of Gases, has a full chapter on it. He not only treats the easy cases where the equipartition theory asigns the full R/2 heat capacity per degree of freedom in gases (with a guess as to which degrees will be fully excited and which fully frozen out) but also treats the harder cases in which either rotational or vibrational modes are only partly participating, so that heat capacities are intermediate. Example: chlorine has a Cv heat capacity of 2.5 R if no vibrational modes are exited, and 3.5 R if they all are. The observed value for 25 oC is 3.1 R in modern sources, (2.9 R in the heat capacity article, which needs changing; but 4.1 for Cp = 3.1 Cv in the clorine article)-- right in the middle of these two equipartitial values. The quantum theoretical value (from Kauzmann) assuming partial excited vibration is 3.1 R, which is better that his experimental data (which is 3.0 R). Evidentally, though, these things come out fairly well. I can give other examples in a table as Kauzmann does, and perhaps should.

Now, user:Kbrose has worked to remove all mention of quantum effects in the LEDE, saying (in the diff) "quantum theory is not used to predict thermodynamic systems, semiempirical methods are hardly successful." Rather than argue with somebody who does not know what he is talking about (this is not an expression of bad faith, it is a self-evident fact) I'm going to put the matter here and in some chem-group talk pages, and let you all tell him what I just did. Perhaps he'll listen to some of you. SBHarris 00:33, 25 February 2010 (UTC)

Your incivility of ground-less accusations is noted. Your user page states you are a physician, yet you do not use the scientific insight or language, that I found most physicians display, since they all have to take physical chemistry at some point. Most can discuss basic thermodynamics far more intelligently. Debye theory was developed well before quantum mechanics was established, the uncertainty principal was not formulated until some 15 years or so later. I removed the false statement from the lede and reformulated the remainder of the paragraph in acceptable language. Kbrose (talk) 01:06, 25 February 2010 (UTC)

Material written by sbharris and copied from kbrose talk page:

Incivility accusations-- the last refuge of the wrong. Physician I am, but I also have a degree in chemistry and enough understanding of the history of physics that I can obviously teach you something there, also. Now hear this: "Quantum mechanics" did not burst upon the world full-blown with the idea of the uncertainty principle in 1927. From Planck's discovery of his constant in 1900, right up to Heisenburg's first full treatment of QM in 1925, the idea of the quantum of action was used to solve or at least give results for many previously intractable problems in mechanics. Abraham Pais in Inward Bound (recommended) calls this era, the "old quantum mechanics." But it includes notable successes like mathematical solutions for the blackbody problem, the photoelectric effect, the hydrogen spectrum (and the K-alpha X-ray spectra of elements), the heat capacity problems we have noted, and an explanation of the Compton effect which proved the existence of photons to even the doubters. Don't dismiss it because it wasn't complete. When it worked, it worked better than what came before. As for my "scientific language," there's nothing wrong with it. If you don't understand that some thermal energy in solids is stored as potential energy of vibration, my understanding is superior to yours. I wrote large sections of the article we're discussing. Try reading it. SBHarris 01:54, 25 February 2010 (UTC)

## Excuse me?

In the article on specific heat capacity you have written:

Temperature is the result of the average kinetic energy of particles in matter, usually referred to as thermal energy in thermodynamics. Heat is transfer of thermal energy; it flows from regions of high temperature to regions of low temperature. Thermal energy is stored by matter as potential energy in the modes of vibration, representing degrees of freedom of movement. Each degree of freedom contributes to the heat capacity of a thermodynamic system.

The first part of the first sentence is true, the second part is not. Thermal energy is not temperature; it is energy content. Thermal energy is also not kinetic energy, either-- in a solid only 50% of the thermal energy is kinetic energy, and other 50% is potential (excluding any odd storage in subatomic degrees of freedom like electronic excitation, nuclear magnetic effects and so on). The only place thermal energy is kinetic energy, is in monatomic gases! Thus, the third sentence is also wrong (unless you qualify it in that sense). Finally, the last sentence is also wrong without qualification: it is quantum mechanics which tells us whether any given degree of freedom contributes to heat capacity, and how much. Some contribute nothing at all (as for example in many gases at room temp). Your edit diff says: "This whole paragraph is such poor science, movable energy? quantum theory is not used to predict thermodynamic systems, semiempirical methods are hardly successful." First of all, the definition of heat is "the process of energy transfer from one body or system due to thermal contact," so what's poor science about saying it's "movable energy"? If you don't like the term, replace it with "transferrable energy due to thermal contact." Second, quantum theory is indeed used to calculate many heat capacities, and to very good result. I'm not talking about general thermodynamic systems, I'm taking the thermodymic property which is the topic of THIS article. In fact, the quantum calculations are excellent for predicting heat capacities for gasses, even in temp ranges where some degrees of freedom are only partially excited (including prediction of what those will be for any given molecule), and even in solids, the Debye theory provides reasonably good numbers for crystalline insulating solids at low temperatures. Out of curiousity you have a Ph.D. in WHAT? SBHarris 23:12, 24 February 2010 (UTC)

I see that you are confusing thermal energy with internal energy. Internal energy is the sum of potential energies (of all kinds) and the kinetic energy. Thermal energy is kinetic energy only, namely the energy exchange when systems are in thermal contact, in which case it is called heat, the transfer of thermal energy.
Where did you get the 50% from?
From ab initio methods, we can only predict the simplest of all systems today. Gases are the simplest of systems, since we can neglect a lot of the interactions that are most difficult to deal with by quantum mechanical methods because of the complexity involved. Debye theory is not a quantum theory, it's a phonon model of classical oscillators used in thermodynamics, like Einstein theory. Debye theory is further only good at very low temperatures.
the article claimed that this works for 'many substances under many conditions' which is clearly wrong, far from the truth.

Kbrose (talk) 23:49, 24 February 2010 (UTC)

Of course Debye theory is a quantum theory. A "phonon" is by definition a quantum "object"-- specifically a quantum of vibrational energy. Any theory of mechanics that uses Planck's constant is necessarily a quantum theory. Maybe not one that uses the Schroedinger equation, but that doesn't mean it's not QM.

If you had trouble with the fact that quantum theory works well only with gases (which of course there are a great many, and many, many cases) and in some kinds of solids at low temperature, you could have put that. Not delete the thing entirely. It's also a little unfair to imagine that quantum theory doesn't work with solids at higher temperatures, since it gives the same predictions as classical theory for most solids, and for those that don't fit classical theory, like diamond or beryllium, quantum theory tells us why.

I got the 50% from the obvious fact that thermal energy in solids is stored in 6 degrees of freedom to give the Dulong-Petit heat capacity of 3R per mole/atoms. If it was all kinetic energy, as with a monatomic gas, it would obviously be just half as much. You are completely wrong about thermal energy. The whole point of heat capacity is that when systems are in contact, they transfer their entire thermal energy, including that stored as the 50% of vibrational energy which is vibrational potential energy (the other 3/2 R in a solid which is NOT vibrational kinetic energy). Objects on a spring have half their energy as kinetic and half potential (on average). Adding up many small objects, and this averages out to 50:50. You are the one confused about "internal energy," a concept that includes many other kinds of potential energies (bond energies and such) that aren't transferrable as heat, and so do not contribute to either thermal energy or heat capacity (not relevant).

It's rather incredible to me that although you understand that temperature has to do with kinetic energy only, you do not understand that this kinetic energy is in contact with other reservoirs, so that thermal energy can be stored in many other ways in most substances (certainly all but monatomic gases), and so these other ways of storing energy much be taken account of, in order to get numbers for heat capacity. Had you read and understood the paragraph you removed discussing this, you actually might have learned something there. Too bad.

You simply don't understand this and you confuse basic terms. Specifically, you are confusing thermal energy with internal energy; internal energy is also called the thermodynamic energy and this may be too much for you to get straight.
When two system are in contact, they do not transfer their entire thermal energy, as you state, they exchange heat only until their temperatures are equal, when equilibrium is reached and the free energy is zero.
It really would be best for you to step back from attempts to WP:OWN this article and let others improve the material.
Kbrose (talk) 03:24, 25 February 2010 (UTC)

I'm not confusing internal energy with anything. You brought that term into the discussion, and it has nothing to do with heat capacity. Thermal energy does have everything to do with heat capacity, but THAT term includes potential as well as kinetic energy for solids, in contradition to what you wrote. I simply tried to point that out, and ran into obfuscation. Get over it. And yes, I think it goes without saying that heat transfer stops when temperature difference drops to zero. Do you really think that I, or anybody else here, thinks differently? However, so long as heat is transferred, it includes the part of heat-energy that is vibrational potential energy, in all substances except monatomic gases. Simple enough. SBHarris 06:55, 25 February 2010 (UTC)

So, what do you think this means:
${\displaystyle \left({\frac {\delta Q}{\ dT}}\right)_{V}=\left({\frac {\partial U}{\partial T}}\right)_{V}=C_{V}}$

This defines the heat capacity at constant volume. I'd be curious to know what you think U stands for, if not the internal energy. And if you can't accept simple references, you might want to compare this with Richard Feinman's Lecture on Physics. I am sure he has better skills to convert you than I do. Kbrose (talk) 17:09, 25 February 2010 (UTC)

The question is, can he convert YOU? Of course U stands for internal energy in Feynman—he says it does. He also says (if you have volume I, it’s in chapter 40, p. 7), that for a monatomic gas, internal energy is the kinetic energy. Just what I myself said, just above (“simple enough”). But for more complicated assemblies of polyatomic molecules in which atoms may vibrate about bonds, Feynman notes internal energy includes potential energies of vibration also (page 8). Stick that into your formula for heat capacity and you find that heat capacity may then be dependant on such vibrational potential energies, as they are legitimate degrees of freedom in some cases, where energy may be stored. Honestly, when kiddie websites say something else, and then you quote Feynman at me, you ought to now take Feynman’s word for it, and leave it.

Actually, however, let me add that although Feynman is not wrong, there are other definitions for absolute “internal energy,” which is a poorly defined quantity if you make the mistake to attempt to define it as other than a “perfect differential” dU or dE (which is the only way it’s actually defined, without any question, in thermodynamics). Feynman’s definition of U is one of many, but it doesn’t matter, since he never uses U again, but rather the differential form. Feynman’s equations above (from chapter 45) involve differentials, not absolute U or E or Q. The fact that dU = dQ certainly does not imply that U = Q, because there’s a constant of integration there to ruin things, since you can set it to any value you like. Thus, if we remove (essentially) all the heat content from an object by cooling it to (essentially) absolute zero, that does NOT imply that its “internal energy” is necessarily now zero! You can decide what it is, because that's the integration constant. This internal energy at absolute zero actually has a name: it is called “zero point internal energy.” It includes some atomic kinetic and potential energies, because atoms are never still. And other energies as well, if you want to count rest energies of atoms, subtract negative contributions of bond energies, and so on. Which is why internal energy doesn't work to calculate heat capacities, but changes in internal energy does (a change in any kind of energy, due to heat, can works to define heat capacity: but you use dQ/dT = Cv = [1/c2]*(dm/dT), which is true, that doesn't prove mass really has anything to do with heat capacity; rather, it's the CHANGE in mass).

If you wanted to define E_zeropoint or U_zeropoint as being 0, nobody would care, because in thermodynamics, it’s mainly the Gibbs differential equations that count. With the exception of entropy, nobody cares about the “absolute value” of state functions very much, since for internal energy the absolute value is hard to define, because it depends on what things (what bonds and rest masses and so on) you want to include. [3].

Anyway, the poor state of the wiki on internal energy (which again is not heat content just because if you add heat, it changes by the same amount) doesn’t suggest these problems, but reflects the depredations of user: Sadi Carnot, who has been scarce since being identified as a socker in Oct. 2007. Sadi also had the idea that every single thermodynamic term had a single and correct definition, and that one was the one he liked. Perhaps it’s time, with the stimulus of assertions by Kbrose, to undo some of the damage that was done to the thermodynamics articles 3 years ago. SBHarris 02:16, 26 February 2010 (UTC)

• Kbrose please stop making the article worse and at least discuss your edits on this talk page first then gain consensus for them before adding them into the article. Glider87 (talk) 12:30, 25 February 2010 (UTC)
And where are you coming from all of a sudden? Kbrose (talk) 17:11, 25 February 2010 (UTC)
SBHarris is right about ... well pretty much everything. If you need another book to glance over stuff, pick F. Reif's excellent Fundamentals of Statistical and Thermal Physics. I don't know how there can be dispute over this materials, it's basically all covered 3rd year thermodynamics class. Headbomb {ταλκκοντριβς – WP Physics} 04:51, 26 February 2010 (UTC)

## Now we're citing educational websites for children, as sources for physics

In his zeal to make us all believe the fiction that "thermal energy" in solids is a total of kinetic energy, we have an editor who has added cites 4 and 5. Although WP:RS deprecates web and self-published sources, and encourages scholarship which is to say, "published in reputable peer-reviewed sources or by well-regarded academic presses," instead we get a commercial dot.com website run by http://www.ronkurtus.com "School for Champions". Last publication: Tricks for Good Grades: Strategies to Succeed in School. And let's hope Ms. Teacher doesn't know much quantum theory of heat capacity.

For grins, I cannot resist giving some of what this website says about thermodynamics:

Thermal Energy is Total Kinetic Energy by Ron Kurtus (revised 22 March 2007): The thermal energy of an object consists of the total kinetic energy of all its atoms and molecules...The Kinetic Theory of Matter states that matter consists of atoms or molecules in random motion. Those moving particles can transfer their kinetic energy to other nearby particles. The total kinetic energy of all the particles in an object make up the thermal energy of that object.

"The kinetic theory of matter"? Bet you never heard of it. That's because Kurtus just made it up. And if you can't figure out why he doesn't don't know better, there is a quote about this here series, asserting that he knows better than the texts:

Heat is the movement of molecules. It is the sum of their kinetic energy. In many physics textbooks, they look at heat as some sort of substance and heat energy as something independent of kinetic energy. In our lessons, it is just another form of kinetic energy.

So, it doesn't matter if our lessons are wrong. They're our lessons, and we're sticking to them. :0

And finally a definition of thermal energy that includes the kinetic energy of electrons, protons and neutrons:

This motion is the culmination of the constant little movements, wiggles, jiggles, and vibrations of those atoms and molecules that make up this human. In describing the capacity of all this atomic and molecular movement to do work, physicists refer to it as thermal energy. Remember, energy is defined as the capacity to do work. These constant wiggles, jiggles, and vibrations are called translational, rotational, and vibrational movements. If we move further down the scale, thermal energy is the culmination of the kinetic energy of the movement of the constituent parts of an atom (electrons,protons, and neutrons).

. Bet you didn't know thermal energy included the movement of consituent neutrons in atoms.

I've put a Template:RS template on this source. Rarely have I encountered a science "source" on the web that needed it so badly. SBHarris 08:44, 25 February 2010 (UTC)

No, I didn't know most of the nonsense you claim, indeed. Thank goodness. Kbrose (talk) 16:55, 25 February 2010 (UTC)
• I have removed the unreliable source and offending material because it is no good leaving rubbish in an article for too long. Kbrose please talk, gain consensus then if you get that then change the article. Glider87 (talk) 12:35, 25 February 2010 (UTC)
He put them back and I took them out again. This is not a common term. It actually redirects to internal energy on WP, which of course does not only mean heat kinetic energy. For a web definition which says that "thermal energy" includes both kinetic and potential energies, see [4]. I think we're going to have problems with User:kbrose SBHarris 00:40, 26 February 2010 (UTC)
Kbrose, talk first then gain consensus then change. Your recent contentious edits to a couple of articles when there are editors saying "stop!" does not look good. Glider87 (talk) 03:22, 26 February 2010 (UTC)
• Ditto; what Glider87 said. To Kbrose: It is clear that you are editing against consensus. Please use this discussion venue to discuss your views and then make changes if there is a consensus to do so. Do not use this venue to explain your thermodynamic theories after you’ve ignored what others are trying to explain to you and you simply to wade into the article and do what you please. The same goes for other thermodynamic-related articles here on Wikipedia. There appears to be a common thread to your edits that is fouling things up wherever you go. You might consider the possibility that if you go to Wikipedia’s many thermodynamic-related articles and wonder “how can everything be so screwed up across the board,” that there is another explanation for your observation. To that point, Headbomb, in his 04:51, 26 February post, above, made an insightful observation that would remedy this needless conflict if you took it to heart. Greg L (talk) 03:26, 27 February 2010 (UTC)

## References

Feynman's name has been misspelt in ref.6 (spelt as Feinman) —Preceding unsigned comment added by 202.56.7.137 (talk) 14:29, 15 April 2010 (UTC)

## Heat capacity / Proposed article title change

Why on earth don't we have a proper article on Heat Capacity ?

At the moment anyone looking up Heat Capacity gets redirected to Thermal mass -- which I suppose is indeed a synonym for heat capacity used in the building trade; but certainly shouldn't be our main article on the subject.

I understand that there was a merger a while back; but surely the primary quantity here is the heat capcity. That's the one that turns up again and again as in fundamental thermodynamical equations as CV and CP. Specific heat capacity is a derived quantity, obtained by deriving the fundamental extensive quantity by the mass.

I came here looking for how WP treats negative heat capacities, for instance as found for gravitational objects like stars, and also black holes. Instead, I was surprised to find we evidently now don't have a self-standing article for heat capacity at all.

I also note that molar heat capacity currently redirects here.

If we're going to have a single article to cover heat capacity, molar heat capacity and specific heat capacity, then it's name should be heat capacity, and it should be written as such.

I therefore propose a move to heat capacity as the main title for this article, over the current redirect. Jheald (talk) 14:21, 23 April 2010 (UTC)

The best approach seems to me to unmerge heat capacity -- the old version of that article seemed a better jumping-off point for an article on heat capacity, rather than the current version of this one. So that's what I have done.
I propose now to strip out material from here which is handled in parallel in the other article. Given restoration of the other article, this article should be slimmed back to just what is specific to specific heat capacity. But it seems to me there is enough additional specific material here that it is worth not eliminating this article entirely, so as not to weigh down the main specific heat article with so much stuff. Jheald (talk) 10:00, 25 April 2010 (UTC)
I disagree. Well, I'm not sure exactly what you're planning, but I probably disagree.
When the merge was proposed 30 months ago, the two articles contained a lot of duplicate information. (See "merge" section above.) Editors were contributing to one article without knowledge of the other, which is a waste. Believing the topics to be pretty much identical, editors chose to merge the articles into the Specific Heat article. Since that time, extensive editing has gone into this article. Much of the material in "Heat Capacity" is effectively an older revision of the same topic.
Before you start undoing two years of conscientious work, please list here which topics you think don't belong in the Specific Heat article, 'cause I don't see the difference between the two, other than the trivial "divided by the mass". Spiel496 (talk) 05:12, 27 April 2010 (UTC)
Okay, taking that on board, I have now moved the whole of this article (rather than just most of it) to Heat Capacity, and then made minor tweaks to present heat capacity, rather than specific heat capacity, as the primary quantity.
If we go down that route, this article would then become a redirect to Heat capacity, as I first suggested above, so that the two would remain merged. Jheald (talk) 10:35, 29 April 2010 (UTC)
See Talk:Heat capacity#to do for some things that I am aware still need some attention. Jheald (talk) 11:25, 29 April 2010 (UTC)
Okay, I have no objections to that. We should redirect Specific heat capacity to Heat capacity. Spiel496 (talk) 04:32, 30 April 2010 (UTC)
Done. Jheald (talk) 08:25, 30 April 2010 (UTC)