Talk:Heat capacity/Archive 2

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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)

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)

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-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)

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?

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

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)

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)

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:

“ Specific: In physics and chemistry the word specific in the name of a quantity usually means ‘divided by an extensive measure; that is, divided by a quantity representing an amount of material. ”

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

“ [A]n extensive property of a system does depend on the system size or the amount of material in the system. ”

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…

“ [A]n intensive property (also called a bulk property) of a system is a physical property of the system that does not depend on the system size or the amount of material in the system. ”

(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:

“ For liquids and especially solids in mechanical thermal applications, sometimes the specific unit-quantity is chosen as volume, and in this case the term volume-specific heat capacity or volumetric heat capacity is then used, and a subscript v is added. ”

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

	Under constant pressure	At constant volume
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, C_v and c_v 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 C_p and c_p). Accordingly, the following editors note (<!--text-->) was added to the “Unit quantity” section:

“ NOTE TO EDITORS: Please note that the subscript “v” in the symbol for specific heat capacity denotes that the value was a constant-volume measurement of a quantity expressed in terms of either mass or moles. It does not denote that the quantity was a “specific-volume” measurement. Please read the section of this article titled “Symbols and standards” and its paragraph regarding constant-pressure and constant-volume measurements. Although specific heat capacity may properly be converted and communicated in volume-specific terms for convenience in a particular application, it would be unscientific to measure and publish unit quantities for specific heat capacity in volumetric terms because a material’s density and thermal coefficient of expansion introduces two additional variables when converting to volume and when compensating to another thermodynamic condition. Too, precision would necessarily have to be reduced for materials with highly variable densities such as brick, stone, and wood. ”

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 c_v), 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. ←Ben^B4 11:42, 12 August 2007 (UTC)

Thanks Ben^B4. 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)

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 $c$ while "heat capacity" is written with an uppercase symbol $C$. 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)

• Additionally, in Heat is the same convention used as that I propose and believe to be correct; lowercase symbol $c$ = specific heat, uppercase symbol $C$ = "heat capacity" Anoko moonlight (talk) 16:31, 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'nt 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?

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.