Climate Audit on thermodynamics

Posted by Tim Lambert on July 15, 2005
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John A, one of the bloggers at Climate Audit writes:

You should know that Lambert’s scientific knowledge is *ahem* “challenged”. Ask him if he’s discovered what entropy is and how it applies to closed thermodynamic systems.

What a guy.

Following the link, we find an anonymous person defending McKitrick’s false claim that average temperature has no physical meaning. I had explained that the physical meaning of the average temperature of two bodies was the equilibrium temperature you obtain when you let heat flow from the hotter body to the cooler one and that this was just the weighted average. Mr anonymous claims this is wrong because:

I’m sorry but I’m not going to quote you large parts of undergraduate texts on thermodynamics as it applies to closed systems where the energy is conserved. It has to do with the concept of Work and the quantity of disorder in a closed system called entropy. If you join two separate systems together then in order for the conductor to transmit energy it must do work. If it does work, the total amount of entropy must increase. In order for entropy to increase it must take thermal energy from the system. If it were not true then you could remove the conductor and the situation would be reversible. The result is that because entropy must increase, and total energy is conserved then the resultant temperature must be less than the “weighted average” of the two separate systems.

That’s why Lambert has run off like a little girl – because he’s realised he’s made a big mistake that could be spotted by any competent undergraduate of physics. The non-decreasing nature of entropy means that his simple argument falls to the ground.

It looks like John A thinks total energy = thermal energy + entropy, which is, umm, not exactly true. I think it is all explained here.

Update: Mr anonymous responds to my post asserting that he really does believe that total energy = thermal energy + entropy. The SI unit of entropy is Joules per Kelvin (as it says in the first paragraph of the Wikipedia entry on entropy that he cited). His equation makes as much sense as adding pounds to miles.

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Comments

  1. #1 Noumenon
    July 15, 2005

    Those threads you linked to in general have more reasonable and intelligent posts than the ones you’re quoting — they’re worth reading. Not impressed by this guy, though, he wants it too simple.

  2. #2 z
    July 15, 2005

    Mmmm…. nevertheless, if I have 1 kilo of H2 at 40 degrees and I add 1 kilo of H2 at 50 degrees, I am pretty sure that classical physics says I will end up with 2 kilos of H2 at 45 degrees, and the more ideal the circumstances, the closer I will come to this number. Whether one sums the kinetic energy of all the molecules and divides by the number of molecules, or one sums massheatcapacitytemperature stratified by temperature, their geographical distribution doesn’t enter into it.

  3. #3 Eli Rabett
    July 15, 2005

    John A misses the whole point about thermodynamics, because the root of the subject is that energy can be exchanged as heat as well as work. No work has to be done when two bodies are brought into contact, although energy in the form of heat can flow between them.

    Temperature can be defined in multiple ways. One way, which John A is sort of remembering is through the efficiency of a Carnot cyle using ideal gases. In that case, given two bodies at temperatures TH and Tc, the efficiency of the cycle (the work divided by the heat removed from the hotter (H) body)= 1-TH/Tc. This is often called thermodynamic temperature. The second thermodynamical definition is through an ideal gas thermomether T = PV/nR where P is the pressure, V the volume and n the number of moles of the gas. These are equivalent.

    Both of these definitions use ideal gases as working fluids, so in that sense, they are abstractions, although one can get arbitrarily close. The important points are that both definitions define a zero on an absolute temperature scale. In the Carno cycle example, when the colder body is at absolute zero the efficiency of the cycle is one. In the ideal gas thermometer, when the volume (or pressure) of the gas is zero, the temperature is absolute zero.

    As far as measuring temperatures, you can do that using the zeroth law which states that if the temperature of body A is the same as body B (the thermometer) and the temperature of body B is the same as C, then A and C are at the same temperature.

  4. #4 Joe
    July 15, 2005

    Why the reluctance to “quote you large parts of undergraduate texts on thermodynamics as it applies to closed systems where the energy is conserved”?

    Reif, Fundamentals of Statistical and Thermal Physics is a good standard text book, I would say. I have the 1965 edition. Turning to the example on page 141 we find:

    “Let us consider heat measurements by the method of mixtures in terms of specific heats of the substances involved. Consider that two substances A and B, of respective masses mA and mB are brought into thermal contact under conditions where pressure is kept constant. (For example, a copper block is immersed in water, the pressure being atmospheric.) Suppose that at this pressure the specific heats per gram of the respective substances are cA‘(T) and cB‘(T). Assume that before the substances are brought into thermal contact their respective equilibrium temperatures are TA and TB, respectively. Denote their final common temperature, after equilibrium is reached, by Tf. No work gets done in this process, so that the conservation of energy is expressed by (4.2.3) as

    QA+QB=0″

    Then we have some expressions that rewrite this in the case that specific heats depend on temperature. Turning the page to the top of page 142 we find (drum roll…)

    “This relation allows, for example, computation of the final temperature Tf if the other quantities are known. The situation is particularly simple if the specific heats cA‘(T) and cB‘(T) are temperature independent. In this case (4.4.12) becomes simply

    mAcA‘(Tf-TA)+mBcB‘(Tf-TB)=0

    If desired, this can be solved explicitly for the final temperature Tf to give

    Tf=(mAcA‘TA+mBcB‘TB)/(mAcA‘+mBcB‘)”

    John A’s belief that total energy = thermal energy + entropy is particularly ironic in view of Essex and McKitrick’s reliance on dimensional arguments.

  5. #5 Wrestlay El Diablo
    July 15, 2005

    You should challenge this gringo John A to a cagefight, hombre!

    Preserve your honour!

  6. #6 Tim Lambert
    July 16, 2005

    Mr anonymous (who may well be John A) has responded. It’s clear he has no clue what entropy is.

  7. #7 ben
    July 16, 2005

    Look up entropy and if you don’t think that Total Energy=Thermal Energy + Entropy in a closed thermodynamic system, then… [blah blah]

    hmmm… can you add entropy to energy and get energy? Last I heard, Entropy (of a system) is a measure of the *amount (or *number, or whatever, argh) of thermodynamic states available to the system. Is that right?

  8. #8 ben
    July 16, 2005

    oops, I still haven’t gotten the emphasis thing down.

  9. #9 Ian Gould
    July 16, 2005

    So according to Mister Anonymous. if I place an ice-cube in a glass of water the equalisation of temperatires must result in work? Where eaxctly in the system is this manifest?

    (I will admit here I am nearly as clueless abotu thermodynamics as Tim is accused of being. Never did that unit in High School I’m afraid.)

  10. #10 Chris O'Neill
    July 16, 2005

    Can you add entropy to energy?

    Without checking my engineering thermodynamics textbook I think the units of entropy used in engineering calculations are units of energy/units of temperature. So adding energy to entropy is dimensionally incorrect.

  11. #11 Tim Lambert
    July 16, 2005

    Yes, entropy is often measured in Joules/Kelvins. But really it’s dimensionless since temperature of something is just the average energy per degree of freedom of its particles. Which ties in with ben’s notion of entropy above.

  12. #12 Yelling
    July 16, 2005

    One of Mr. Anonymous’ problems is that, as noted he equates work with energy. While all work requires energy, not all energy produces work. Consider a 5 kilo weight on a table, it sits there, no work is done, no energy is consumed. Now take the same 5 kilo weight and hold it with your arm straight out. Now, unless you move the weight there is no work done but I think you can feel the energy being expended.

    However being an engineer I have been considering the ramifications of Mr. A’s physics. TO begin with we could make a pretty nifty solar cooler with no moving parts!! I don’t have the linkages yet, but I think there is a new type of engine in there as well.

  13. #13 Robert P.
    July 16, 2005

    Tim, “average energy per degree of freedom” is not a very good practical definition of temperature, because it relies on the classical equipartition theorem which (for the range of temperatures of interest here) is accurate for translations and rotations, but not for vibrations. You can get by with it by excluding vibrations, but a better solution is to define temperature in terms of the average translational energy per molecule – in thermal equilibrium, every molecule, has an average translational kinetic energy of 3/2 k T. This is also not an exact definition (it breaks down at very low temperatures, where equipartition fails even for translational degrees of freedom) but it’s entirely adequate for present purposes.

    This idea that “global temperature is not well defined” seems to have originated with McKitrick’s other co-author, Chris Essex. Essex does understand thermodynamics – I think that in a way he understands it a little too well, in that he focusses on the highly abstract and formal concepts of temperature that you need to work with in order to be exact about everything, and doesn’t appreciate that we’re not engaged in such esotericisms as comparing the brightness temperature of a laser beam to the spin temperature of a ferromagnet. We’re dealing with air.

  14. #14 Tim Lambert
    July 16, 2005

    You’re right, that’s a better definition.

  15. #15 Eli Rabett
    July 16, 2005

    Using statistical mechanics to define temperatures can be tricky and without advantage as the last series of posts show. Using a thermodynamic definition is best.

    In either case proper averages should use absolute temperature (this is not strictly required for an arithmetic average but is absolutely necessary for geometric averages because of the relationship between the internal energy and the temperature of a system). I thought this was the strongest point of Tim’s arguments about McKs averaging procedures.

    Whether any averaging procedure is superior depends on a number of things. For example if the specific heat of the system (and its components) is approximately constant over the range of temperature variation, then an arithmetic average is best.

  16. #16 frankis
    July 17, 2005

    Suppose, for argument’s sake, solar irradiance were suddenly to increase such that satellites were recording an increase of lower troposphere temperature of (say) a few degrees C. “What nonsense!” might snort Professor Essex as steam flew from his ears “… and no scientific basis exists to show that its behavior has any implications for our lives!” [quote from 'Taken By Storm']. Does Essex have any understanding whatsoever of the natural world beyond the end of his own nose? Perhaps not, and I don’t think I’ll defend him as being somehow too bright to bother with the bearing on reality – the truth value even – of what he says and its implications, either. He’s not the first intellectual in history to prove himself a fool in his own words.

  17. #17 John Cross
    July 20, 2005

    I was interested in the thermodynamics argument raised by John on ClimateAudit so I posted a (polite) request for clarification from John about his position. I received no reply from John but Steve McIntyre did intervene on his behalf to effectively shut down the conversation. This seems to be strange behaviour from someone who feels that science should be open.

    In another unusual move, when replying to me Steve used my full name as opposed to the name I posted under (I used the name A(nother) John and in his reply Steve called me John (Cross). It seems quite unprofessional (and perhaps some might find it intimidating) to have your name posted like that if you disagree (in a civil manner of course) with the views of the site. Anyone who does not wish to be outed beware.

  18. #18 z
    July 20, 2005

    “It seems quite unprofessional (and perhaps some might find it intimidating) to have your name posted like that if you disagree (in a civil manner of course) with the views of the site. Anyone who does not wish to be outed beware.”

    Well, if it works for Karl Rove….

  19. #19 Dano
    July 20, 2005

    It seems quite unprofessional (and perhaps some might find it intimidating) to have your name posted like that if you disagree (in a civil manner of course) with the views of the site. Anyone who does not wish to be outed beware.

    Sorry to hear that, John.

    Of course, the site is a vanity site that exists to besmirch someone’s name, not about open science – you’re too polite to say it, so I’ll say it.

    D

  20. #20 Bob
    July 20, 2005

    …and now McIntyre is playing a lawyer on the internets. What a delusional opinion he has of himself…

  21. #21 John S
    July 21, 2005

    John C,

    I interpreted Steve’s intervention as saying that the thermodynamic whatever discussion was off topic and that there was a discussion over here where people could continue if they wanted. It really had little to do with him so it hardly struck me as shutting down open discussion of science (he’d probably nix a whaling argument as well).

    (My there are a lot of Johns around)

  22. #22 John Cross
    July 21, 2005

    John S (anyone know what the collective term is for a group of John’s – the mind reels with possibilities!)

    I think your point is valid – a moderator should be able to call discussions off limits if they wish. However my objection is when a moderator is not consistent in doing this.

    If Steve wished to shut down the conversation, then the time to do it would have been when John posted his initial comment about thermodynamics. Since Steve allowed this to go unchecked I feel that responses (as long as they are reasonable and polite) should also be allowed.

    I will also note that during the time that I was trying to obtain more information about John’s views there was a good (and interesting) exchange of views about Lomborg’s book which is surly no more off topic than a discussion of thermodynamics.

    Would you not agree or am I off base here.

    regards,
    John

  23. #23 Eli Rabett
    July 21, 2005

    The collective for a bunch of johns is a bowl if they are fixed and a row if they are portajohns. Now that was obvious.

    If this doesn’t get disemvowled all bets are off.

  24. #24 John S
    July 22, 2005

    John,

    If I were a moderator I could imagine letting a discussion go for a little while and then shutting it down if it started taking on a life of its own and taking over the ostensible purpose of the thread. I am not Steve so don’t know his thinking but I am prepared to offer him (and most people) the benefit of the doubt. I don’t think its possible to be 100% consistent, particularly if you generally take a hands off approach rather than jumping on everything as soon as you notice it.

    Jhn (the disemvowled)

  25. #25 cytochrome sea
    August 1, 2005

    John Cross, I noticed the reply with your full name as well and it didn’t sit well with me either. Perhaps since you had previously posted comments at climateaudit using your full name Steve didn’t think you considered your privacy there very important, although I am not defending this action. However, I do find it a bit ironic that you chose to post your complaint on this particular blog, considering the “per” -> “John Brignell” incident previously. Credit to Tim for publically making the correction though.

  26. #26 John Cross
    August 1, 2005

    cytochrome sea:

    I do remember the Per/ M. Mouse/ etc incident. My argument would be that I always try to be polite (although sometimes insistent) in my posting. I believe that Per went as far as to call Tim a liar and I seem to recall that the word moron was used.

    Anyway, while I don’t mind being outed, there are those who do like to remain anonymous. I really posted it here as a warning to others to stay clear of Climate Audit if you wish to keep your anonymity.

    Regards,
    John

  27. #27 TCO
    August 7, 2005

    Agreed that the thermo thing is silly. But how can you blame Mc for that. He’s not the one advancing it. His point (which besides is an aside) has more to do with how do you weight. Is it purely an area average? should seas be weighted more heavily?

  28. #28 Tim Lambert
    August 8, 2005

    TCO, John A made the silly claim about entropy, but McKitrick also made false claims about thermodynamics, see here.

    And he’s not just saying that you should use different weights, but that it is just as valid to use a geometric or harmonic mean.

  29. #29 TCO
    August 8, 2005

    I think you have a fair point about arithmetic averaging making more sense than geometric if you want to understand how a system overall is changing. I can’t recall…what is geometric averaging ever used for. Arithmetic is all I know about.

    Anyhow: the base question is interesting. How does one get an average temperature? (What is the most meaningful?) Is it an area average? ARe the seas underweighted (since people don’t live there) or overweighted (since there is higher heat capacity) or just same weighted (since we figure heat capacity will show it’s face by limiting changes)?

    Is it the surface temperature that matters or the atmospheric? What about as you move down in depth in the ocean? Or even the ground?

    Thought experiment: If you had one world in which the oceans heated up by a degree and the land not at all and then one where the opposite occurred, which would be worse in terms of impact on humans (by direct effect of temperature, by icecap melting, by hurricane spawning, etc.)?

    Just trying to think about this…

  30. #30 TCO
    August 8, 2005

    Please don’t ban me for multiple posting:

    ‘nother related thought. The “ill effects” of GW depend on how it is distributed, spatially, no? One could imagine certain changes which would cause more or less icecap melting for instance. Of course, the system itself (the world) will adopt only one of these arrangements. But doing the thought experiment of how the different worlds would look, just shows the importance of starting to understand in greater detail what a post-GW world will look like.

    Oh…and I know this sounds silly, but it is interesting to me from a popular science standpoint. Let’s say the GW continues as expected and that no major efforts are made to stop it. Any chance of palm trees in Virginia in my lifetime? How will climate at different places in the US change? Would expect some the get “better”, some “worse” and some to show less changes than others. No? Fascinating.

  31. #31 Robert P.
    August 8, 2005

    John A. seems to have abandoned the argument, at least on SourceWatch (assuming that he is the anonymous poster there). My guess is that he finally figured out that he was wrong, but does not care to admit it.

    Regarding the question of averaging, Eli Rabett has made the very good point that the arithmetic mean is the only choice that is independent of (or more precisely, “covariant with respect to”) the choice of temperature scale. Moreover, the First law of thermodynamics does indeed provide “guidance” in this respect, as does basic kinetic gas theory – they both guide one towards the arithmetic mean rather than any other. None of these arguments pins down the choice of weights in the arithmetic average, however. In this limited respect, Essex and McKitrick are correct, I think – global temperature is an “index” rather than a physical property, and different choices of index will be useful for different purposes.

    I’ve been thinking that it’s useful to make an analogy to the Stock Market. Various indices are commonly used to measure the performance of the market – Dow-Jones, S&P 500, Russell 3000 – and these correspond to different weighted averages of stock prices. They do behave somewhat differently from each other, and these differences are useful in that they emphasize different segments of the market. However, one could also devise some really perverse indices – for example, setting $100 per share as the reference point and measuring each share price with respect to that, then taking the root mean square average so that positive and negative deviations from $100 are mapped onto the same number. It would be easy enough to devise an index that turns the tech crash into a rise by proceeding this way. The fact that an index is not unique does not mean that all conceivable indices are equally valid.

  32. #32 TCO
    August 8, 2005

    Agreed on the index concept. Let’s say we even agree on the weighting scheme (not sure what was done in the ‘real’ work), for sake of argument simple average by area on a land mass only basis. Obviously one can imagine situations which are the same in terms of index but different in effect. For instance one case that has no change from present. and one case where the hot parts get hotter and the cold parts colder. These would both be = zero delta. But the effects on human occupation, on storm generation, on sea level) etc, would differ.

    Note, that I’m not devaluing the simple average. I think we can learn a lot from that. Nor should we let a desire for more knowledge stop us from using what we have. I would think both Mann and MicItrick would agree with this.

    For me…I just find it fascinating to think about.