Talk:Specific heat capacity

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Contents 1 Awful caption needs changing 2 Merge with Heat_Capacity? 3 Major Revision 4 S.I. Units 5 Check Specific Heat Capacity of Substances! 6 Talk blanked? 7 SI units 8 water: specific heat capacity > 3R 9 Degrees of freedom in translational motion 10 but my book says.. 11 Water vapor 12 What does this mean? 13 ? What is with the deviation? 14 SI Units redux

[edit] 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

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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 noteworth, and added a column for molar heat capacity (C_p). 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)

[edit] 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?

[edit] 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)

[edit] 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-T_c|^-ά, 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 (talk • contribs) 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 C_vH 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 C_vH column to the table to help in illustrating this concept. Greg L 05:31, 25 December 2006 (UTC)

[edit] Degrees of freedom in translational motion

Should:

six degrees of freedom comprising translational motion

read

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?

[edit] 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

[edit] 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)

[edit] 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)

[edit]  ? 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)

[edit] 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)