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This whole "continuous process description" (within a conventional thermodynamical treatment) is a red herring you continue to raise. For quasistatic changes this is possible, but thermodynamics can in some cases also be used to compute the outcome of processes that are not quasistatic. Also for these cases, one can (in principle) define heat and work, and actually calculate them in some of such cases easily (e.g. the free expansion case is a rather trivial example). In general, this is a complicated matter, because in general you then do have to consider the real dynamics of the system, so you do have to give a "continuous process description", but this will be based on the real dynamics of the system, not on some efective thermodynamic description involving generalized forces.
In Reif's quantum mechanical picture, this is evident, he introduces the Hamiltonian of the system and says that the mean energy of the ensemble after the change is well defined given how the external parameters are changed. There is nothing to argue about that, if you have an initial condition for the ensemble, each ensemble member is in some well defined quantum state, and the time dependence of the external parameters is defiend, then the Schrödinger equation fixes the final state for each ensemble member and hence the mean energy change of the ensemble.
This means that you have to consider the dynamics of the system in terms of the molecules that make up the system. Obviously, that's not very practical to do exactly, but one can introduce stastistical methods that work well, see e.g. the last few chapters of the book by Reif.
So, it is still well defined in principle. Reif claims on page 71 that despite the complicated nature of this, it can be readily measured, giving some examples. Count Iblis ( talk) 16:00, 29 April 2012 (UTC)
I refer to Pippard, A.B. (1957/1966), Elements of Classical Thermodynamics, reprinted with corrections, Cambridge University Press, London. Pippard 1957 is listed in Reif's 1965 longer bibliography at the end of his book but is not suggested in the shorter reading lists at the ends of the chapters. Pippard 1957 is listed by Buchdahl 1966 in his bibliography of ten references. Pippard 1966 is listed in Callen 1985 in his list of six books on thermodynamics on page 485, with the comment: "A scholarly and rigorous treatment." Callen 1960 occurs in several of Reif's 1965 end-of-chapter suggested reading lists.
I will not try here to summarize Pippard. Enthusiastic editors may like to read what he says. Chjoaygame ( talk) 20:13, 1 May 2012 (UTC) Chjoaygame ( talk) 20:38, 1 May 2012 (UTC)
Let's discuss here this issue raised by SBHarris above in more detail. We know that we can avoid having to consider this by focussing on initial and final states that are in thermal equilibrium with well defined temperatures. If the work done by the system is known (and it is well defined in princile as pointed out in the book by Reif), then the heat absorbed follows from the First Law (which is thus taken the definition of heat). Then during the heat flow, a simple thermodynamic description isn't available, except in the quasistatic limit.
But we are not satisfied with this and we want to dig deeper. We should be able to bring two objects with different temperatures into contact with each other and see that the temperatures come closer to each other until they become equal and thermal equilibrium is reached. And this is precisely when heat flows between the systems. However, during this process the systems are not in thermal equilibrium, so you could question if ou could assign temperatures when the process of heat transfer is going on. Now, we know that in practice, there isn't much of a problem here, you can measure temperatures when heat transfer is going on. So, under not too extreme circmstances, we should be able to define temperatures.
Suppose then that during the process of heat transfer one object has temperature of T (in some sense). Without making that precise at this moment, we should note the following. If we were to interrupt the flow of heat (put an insulator between the two objects and let the object reach internal thermal equilibrium), then we could see a difference. In case of the heat flowing between the objects, there is obviously a flux of energy from the object, which is absent in the case of full internal thermal equilibrium.
If the object is a gas in a box, and we focus on a point inside the box, close to the boundary, then the moleculs there have a certain velocity disribution. In case of thermal equilibrium, there is no net transport of energy; the velocity distribution is Maxwellian. When the two objects are in thermal contact, there is a net flux of energy that moves thoough the box. This means that the velocity distribution is not of a purely Maxwellian form. We can understand this as follows.
When the two objects are in thermal contact, we have conduction of heat from one object to another and in a first approximation, you can describe this situation using time dependent temperatures, but if we want to take into account that the objects themselves have to conduct heat internally, then the objects not being in thermal equilibrium can to first approximation be described as there being local thermal equilibrium. So, to a good approximation we should have a Maxwellian velocity distribution where the temperature is position dependent.
Now, this is still not yet consistent with heat being conducted through the gas to the boundary of the box. Because we still have have a Maxwellian velocity distribution at every point, and then the flux of energy is exactly zero. However, once we take into account the finite mean free path of molecules in the gas, this changes things. If you imagien a plane parallel to the boundary of the box just inside the box, and look at the flux of kinetic energy of molecules that in both directions (left to right or vice versa). If we assume to first approximation that the velocity distribution is Maxwellian, then the fact that the molecules originate from one mean free path in one direction or the other, makes a difference. The flux from the two directions do not cancel, one flux is from a Maxwell distribution at a slightly higher temperature than the other. So, we then have net flux of energy toward the boundary of the box.
The velocity distribution is then not precisely Maxwellian due to molecules traveling finite distances, and that then yields the non-zero flux of heat. This is then not a fully self-consistent way of looking at things, because we started with assuming that you do have a position dependent Maxwellian distribution and we end up with something slightly different. Of course, a purely Maxwellian distribution does not yield a nonzero energy flux, so however one arrives at this conclusion, the end result is that the flow heat is related to local termal equilibrium breaking down; the velocity distribution is not purely Maxwellian.
That's why saying that mere temperature differences explain heat flow is not sufficient. In terms of the two boxes this is analogous to saying that if you have just two objects at a different temperature, no heat will flow unless you bring them into thermal contact. But the act of doing that leads to non-equilibrium in the objects themselves. Before you brought the objects into thermal contact, the non-equilibrium of the two objects with each other could be described exactly with assigning two different temperatures to the objects. Bring them into thermal contact and this exact description will break down. And as I explained above, you can look at what happens inside the objects, exact local thermal equilibrium in an object is not sufficient to capture the heat flow.
Count Iblis ( talk) 23:10, 28 April 2012 (UTC)
When no work flows between systems (one system doesn't do work on the other) then conservatin of energy demands conservation of heat. So it's easy to fall into the trap of simplifying things, by picking systems in which no work done is done between systems. The problem (as noted below) is that in advection of heat, there is advection of mass, which amounts to bouncing some masses off another system, much like throwing rocks or shooting bullets at it. That's kind of like work. This is transfer of energy by the kinetic energy of the bulk flow (bulk current of advection), but there is not necessarily any entropy involved at the input, so it's a funny type of energy transfer. My example is a river of liquid helium at 0 K (helium is a liquid even at 0 K) which I can run into a test system (like it strike and splash off the face of your perfect cube, which is at some temp) at the speed of sound, or however fast you like, and thereby "heat up" (or add energy to) the second system (the cube), up to any temperature you like (until its atoms have the same kinetic energy as the helium atoms, energy will flow into the system I'm "heating"). But is it art? Is this process "heating"? Does it "count"? It's advective. It's kinetic. But where is my input temperature? S B H arris 00:19, 1 May 2012 (UTC)
Count Iblis writes above at 00:05, 16 April 2012: "Work is always well defined (being the change in internal energy due to the change in external parameters), heat transfer is thus also always well defined."
Count Iblis makes a fundamental mistake of simple physics in writing that comment.
In physics, change in internal energy is not well defined by change in external parameters alone. Also needed for a calculation of the change of internal energy is information about a non-deformation variable, such as pressure, or, dare I say it, temperature. The distinction between work and heat needs even more. For its calculation, it needs also the record of the course of the values of the conjugate generalized forces belonging to the external parameters.
Probably Count Iblis has made this fundamental mistake in simple physics because he has been muddled by reading the angel of muddle, Reif 1965. Count Iblis' mind is full of stories about quantum mechanical Hamiltonians, told by Reif 1965, that get him into muddles like this. Reif 1965 is full of hubris about how clever he is with his better way of teaching physics, but look at the result in this case!
Count Iblis writes also above at 15:32, 16 April 2012: "If you can't define heat in general (i.e. during non-equilibrium conditions), then you have a huge problem, because we all know that heat flows during non-equilibrium conditions."
One cannot be sure exactly what Count Iblis means by this loosely worded comment, but it looks hard to separate it from a statement that heat is convected during non-equilibrium conditions. Synthesizing this comment of his with his above fundamental mistake in simple physics, it seems likely that Count Iblis is making the fundamental mistake of thinking that because a body has a high density of internal energy, and some of its components are moving, that this constitutes heat transfer. With all respect to engineering terminology, physicists do not say that heat is convected. They say that internal energy is convected, but the above comment by Count Iblis looks hard to distinguish from a statement that heat is convected, though his comment is loosely worded and its precise meaning is indeterminate. More muddle probably arising from an overdose of Reif 1965. Chjoaygame ( talk) 08:28, 30 April 2012 (UTC)
In physics, heat is dealt with mostly by thermodynamics.
Thermodynamics is built on the distinction between heat and work. If work can be defined for a process, then heat is also defined for it. The modern approach to thermodynamics describes processes as passages between states, and for the states, it defines internal energy and entropy. Temperature is a necessary consequence. No temperature means that there must be something wrong with either energy or entropy; entropy is the weak point, because it needs the definability of work and heat. No temperature therefore logically requires no distinction between heat and work; that means no thermodynamic macroscopic description.
What about the statistical definition of entropy? It is the amount of information needed to take you from the macroscopic thermodynamic description to the microscopic description. You need the macroscopic description in order to define the entropy by the statistical definition. No macroscopic thermodynamic description implies no entropy by the statistical definition.
There are various axiomatic schemes for the macroscopic thermodynamic description. The Carathéodory one is considered by many to be the most mathematically elegant. But it contains the same physics as the other schemes; it differs only in the mathematical structure. The insistence on excluding temperature from the definition of heat is for mathematical elegance, not for any sound physical reason. Actually Carathéodory himself in his own scheme defines temperature but does not define heat at all. One wonders then why it is so burningly important for some that heat should be defined without reference to temperature.
On the other hand, admitting empirical temperature and constructing the other concepts from it has a good intuitive as well as physical basis. There are those who hate that thought. That's a good part of why they like to insist on the exclusive dominance of the Carathédory–Born approach that, in some form or other, dominates many, but not all, modern texts. Chjoaygame ( talk) 06:06, 4 May 2012 (UTC)
I refer to Landsberg, P.T. (1961), Thermodynamics with Quantum Statistical Illustrations, Interscience, New York, volume 2 of the series edited by I. Prigogine, Monographs in Statistical Physics and Thermodynamics. This is one of the ten general references named by Buchdahl 1966. Landsberg also wrote another book (1978) listed by Callen 1985 in his bibliography for statistical mechanics, entitled Thermodynamics and Statistical Mechanics, Oxford University Press, Oxford UK, ISBN 0–19–851142–6, which has Chapter 1, pages 1–4, copied with hardly any changes from §1 of Chapter 1 of the 1961 book.
Landsberg is a Carathéodory man to his finger tips, with much attention to finer mathematical matters.
In Chapter 2, on page 6 of the 1978 book he allows two systems, specified by sets of independent variables {x1} and {x2}, to interact thermally till they reach thermal equilibrium. Then he writes: "Thus thermal equilibrium is specified by a relation f12({x1},{x2}) = 0 . This relation is assumed to be unique in the sense that, if all but one variable is known, f = 0 determines the remaining variable uniquely. This remaining variable is in fact a measure of the temperature."
Landsberg is recognizing that Carathéodory's non-deformation variable "is in fact a measure of [empirical] temperature". Carathédory does not mention this in so many words, but just goes on to develop absolute thermodynamic temperature before introducing the word temperature. But his systems already have empirical temperatures existing in their presupposed physical constitution.
From this I infer that Landsberg explicitly recognizes the existence of empirical temperature as presupposed for the definition of thermal interaction leading to thermal equilibrium. This is in agreement with the view of Kittel & Kroemer 1980.
I claim that it is also in agreement with a natural reading of Reif 1965. For example, Reif 1965 on page 94 writes: "Let us now discuss in greater detail the thermal interaction between two macroscopic systems A and A′. We shall denote the respective energies of these systems by E and E′." I observe that E and E′ are non-deformation variables of Carathéodory and thus qualify as empirical temperatures. It is evident that, in their very essence, Reif's macroscopic systems are such that temperature is definable for them. The issue is not whether Reif has mentioned this at any particular stage of his presentation. The issue is as to the physical character of his systems, whether or not temperature is definable for them. It is. Chjoaygame ( talk) 07:15, 6 May 2012 (UTC)
I think that this section can and must be improved:
Please agree or disagree with this point of view.
( Adwaele ( talk) 09:40, 18 May 2012 (UTC)).
I agree with your criticism. There is no notice given there in the article that it is intended there that the process shall be at constant pressure. Chjoaygame ( talk) 10:26, 20 May 2012 (UTC)
I agree that the notation δWboundary and δWother needs clarification, as well as a reliable source. Chjoaygame ( talk) 10:29, 20 May 2012 (UTC)
I don't find the present statements about this to be objectionable. Chjoaygame ( talk) 10:31, 20 May 2012 (UTC)
It be possible for a statement like this to appear in the article:-
"The SI unit of heat is the Joule. Heat can be measured with a calorimeter, or determined indirectly by calculations based on other quantities, relying for instance on the first law of thermodynamics"?
It is a statement of what heat is, devoid of any reference to temperature!
Is there a reliable source for it? Otherwise it should go. -- Damorbel ( talk) 16:01, 23 May 2012 (UTC)
The opening section has:-
Because it is by definition a transfer of energy, heat is always associated with a process of some kind, and "heat" is used interchangeably with "heat flow" and "heat transfer".
And it goes on to say :-
In common usage, the noun heat has a broader meaning, and can refer to temperature or to the sensation felt when touching or being close to a high-temperature object.[9]
The second section refers to 'a broader meaning'? Um - does this 'broader meaning' have the same definition as the first one then? There is already an extensive disambiguation link Heat
This is confused and confusing, not suitable for an encyclopedia. -- Damorbel ( talk) 19:10, 23 May 2012 (UTC)
Where it has:- they exchange thermal energy
Now going to the article Thermal energy; the very first line has:-
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system temperature
Which is different from the definition in the Heat section which defines heat as 'heat flow', or 'heat transfer' so making a logical impossibility. How can something (heat) be defined by a a qualified version of itself, ('heat flow' etc.) that is a version of itself that is restricted somehow in its meaning? -- Damorbel ( talk) 19:47, 23 May 2012 (UTC)
Of course the heat equation breaks down in gases except where they are held at constant volume. All this is merely a way of saying that you can integrate heat to get internal energy change, when no work is done (this is just conservation of energy), and we call such internal energy changes "thermal energy changes" since they are due to nothing more than heat input, or outflow. With that qualification, which is always understood, what's the big problem? S B H arris 22:41, 26 May 2012 (UTC)
Physicists don't say that heat is convected?! If true, that would explain a lot. More specifically, you would say that heat cannot be advected (like my my examples of bullets and gas streams with no heat-like velocity distributions). Since the diffusion part of convection (whether free or force convection) would presumably still be kosher, leaving simple thermal diffusion left as the only game in town when it comes to heat (radiation is sort of thermal diffusion with photons). It comes to me that perhaps the advective part of "heat transfer" (internal energy transfer) in rheids (fluids) is what is giving us all the problems. Heat transfer by diffusion always proceeds with a nice regular thermal gradient where every little region has nice a definable temperature (that happens in solids, and rheids with no mass-transfer of thermal energy look thermally like solids). In radiation you can talk about an ideal pair of reservoirs with a temperature difference, but that never actually happens in nature. In nature, what actually happens is the skins of all objects immediately equilibrate to the various temperatures that are defined by the various view-factors and conductivities in the system, and then old fashioned solid conduction as per the heat equation happens, after that. So, without advection you can't even set up the problems that are vexing us where heat supposedly "flows" but temperature cannot be defined. So perhaps that is the answer. We've been trying to talk the advection part of convection-heat transfer, and if thermodynamically and in physics that's verbotten, then that is our answer. You can always break up convection into a diffusive part, and an advected part that can be gotten rid of by changing reference frames, and transfers energy between systems by simple kinetic energy without any entropy. That's why it doesn't act like "heat" and why it sometimes has no "temperature." Does a river of liquid helium at 0 K have a temperature? No. But it can transfer energy into a system, simply by striking it and bouncing off. Tell me how much energy it must transfer, and I'll tell you how fast is has to run, in order to strike and heat the second system. Do we call that transfered energy, "advected heat"? No. Or, yes? It has no temperature. There's our problem. Is it heat? S B H arris 00:08, 1 May 2012 (UTC)
BTW, very small low pressure systems as you describe are subject to experimentation all the time (by "small" I mean system dimension < Knudsen 1, else what do you mean by Knudsen number?). In such systems, physicists cheerfully go on measuring heat convection and advection. [1] and temperature also. Are they deluding themselves?
In my helium example, if you stick a thermometer in the flow, it will heat up from something friction-like if the flow is a gas flow at 0 K, although I don't know if there will be frictional heating with actual superfluid helium since there is no friction. How the hell does that work? The molecules have to get around objects, and do they not sometimes strike them and transfer momentum? And if they are moving very rapidly, is this not significant momentum?
Anyway, leaving aside such problems, an engineer would say that the advected portion of heat is simply "thermal energy" that is transported across a boundary by virtue of a macroscopic current, and is no different than tranporting heat by taking a hot solid cube HERE and moving it over into the target system to heat it, THERE. In that case, the "heat" that counts is the one that is left over after you adjust your reference frame, and the kinetic energy of the fluid or the heat-carry solid wouldn't count itself as "heat", but rather energy input by some other form (work, perhaps). A thermometer doesn't see it until it has been transformed in the other system into thermal energy (thermalized) by random impacts there. Again my example of heating a system by firing O K crystal bullets at it and watching them disintegrate and transfer vibrations that end up as temperature increases. If you DEFINE this kinetic energy input as "work" then I'm not heating the system, by definition. But if you don't define it as "work" then I AM heating it, by definition. But doing so without any temperature gradient. Count Iblis above suggests that the idea of temperature gradients in the real world as heat transfer is happening, is a convenient fiction, and isn't true, as it demands a non-continuum picture in which there are little differential volumes, each with a little temperature (a temperature field in time and space) and that this sort of thing has a reality. Whereas, when heat is actually flowing in a solid (the best defined system we have), there actually is no such physical thing. "Temperatures" as we define and idealze them, only "appear" after heat flow has STOPPED (since only then do equilibrated systems where we define T appear-- the best example being a gas where perfect M-B distributions are not seen while heat is flowing through the gas). So that leads to a conundrum of what causes heat to flow while it is actually flowing. I believe I see this point. S B H arris 18:16, 1 May 2012 (UTC)
The heading "physicists don't say that heat is convected?" (NB"?") They would be nuts if they did, they would be right back in the good (old?) (caloric) days where 'heat' was thought to be a fluid and it 'flowed'. Convection, advection, are both forms of mass transport by fluid (gas, liquid) flow; the fluids involved have a temperature thus associated energy also, but it is the mass that flows, not the energy. -- Damorbel ( talk) 08:16, 9 June 2012 (UTC)
Chjoaygame, if you introduce the Knudsen number into a discussion about heat you should give a good explanation why. The Knudsen number is based on a very generally described dimension called "a representative physical length scale". The Knudsen number is the ratio of the mean free path to this "representative physical length scale" which can be the dimension of an orifice through which gas is flowing. One might whish to discuss this, but why in the article about Heat? What is there about Heat that has anything to do with linear dimensions?
You write "An example where temperature cannot be defined is in a very dilute gas" This a rather controversial statement since, if a collection of molecules is sufficiently dense to be called a gas, then it must also be able to have a defined temperature. Further, if the 'pressure' is reduced to the point where the molecular interaction is effectively absent then the individual molecules still have an energy thus they must also still have a temperature (see ' Boltzmann constant').-- Damorbel ( talk) 09:03, 9 June 2012 (UTC)
It is going too far to try to say what is the everyday use of the word heat. The attempt that was made was faulty, and gave no suitable dictionary reference. It is enough to say what is covered in the present article. Chjoaygame ( talk) 07:09, 26 May 2012 (UTC)
Dear colleagues:
I am considering three things:
I would like to have consenses before I modify the Article as I want to avoid that we will edit our texts in the Article over and over again, thus confusing the readers.
I would greatly appreciate your opinion.
The proposed new section would have the title Heat or heat flow? and read as follows:
In thermodynamics heat is not a function of state but a process parameter. In order to understand the implications of this statement let us look at two bodies a and b at temperatures Ta and Tb and with internal energies Ua and Ub. Suppose Ta > Tb. We connect them for some time by a heat-conducting wire with negligible heat capacity. During this time heat flows from the warm body to the cold body given by
Initially the temperatures are Tai and Tbi and the corresponding internal energies are Uai and Ubi. (The final state gets lower index f.) The total amount of heat transferred from a to b is Q = Ubf - Ubi = -(Uaf - Uai). The net result of the process is that the internal energy of a has decreased and the internal energy of b has increased.
The fact that heat is not a function of state means that the heat Q was nowhere before the process and it is nowhere after the process. Heat is only a meaningful concept when it flows. In other words: heat flow is the basic concept and not heat. Of course one can integrate the heat flow over time and obtain a certain quantity of heat, but there is no region in space where the heat is “stored”. In daily life one would say that heat is stored in body b, but thermodynamically this is incorrect. No object is capable of storing heat. In this sence the term heat capacity, which plays a central role in thermodynamics, is misleading.
Also in other fields of thermodynamics the term heat is used in a confusing if not incorrect way. Look at the famous experiment of Joule in which he determined the so-called mechanical equivalent of heat. He used a falling weight to spin a paddle-wheel in an insulated barrel of water. Through the paddle the water is brought into turbulent motion and comes to rest after some time. Joule observed that the temperature of the water has increased, but the potential energy of the weight is not converted into heat. It has increased the internal energy of the water. Thermodynamically never in this experiment heat is involved. The water with the paddle form an adiabatic system.
A similar argument leads to the conclusion that power is more realistic than work. In order to emphasize that heat flow and power are the basic thermodynamic properties it is better to express the laws of thermodynamics in terms of time derivatives so, for closed systems,
where P is the power applied to the system, and
where is the rate of entropy production.
The fact that heat flow is the basic quantity and not heat implies that we need a definition for heat flow rather than for heat. This would sound somehow like: heat flow is a flow of energy through matter driven by a temperature gradient. Microscopically the energy flow is due to the fact that the atoms, coming from a high-temperature region, pass a surface with a higher energy than the atoms coming from a low-temperature region. Based on this picture the coefficient of thermal conductivity can be derived with the kinetic theory of gases. [1]
Adwaele ( talk) 12:42, 1 June 2012 (UTC)
You have some solid points. "Heat" Q (in joules) is actually the time integral of heat flow dQ/dt. But the terms heat and heat flow (which really should be in units of power) are used synonymously, since heat is always flowing, so one gets away with it. But it's confusing to the student. And doing the integral makes it look as though the heat-power that has passed through the time-integrated is a quantity of heat energy that still resides someplace, whereas (as you point out) it is gone (and now is internal energy). You summed it up as it went past, but it passed into nowhere, and disappeared qua heat! Leaving only a total integrated (entropy*temperature) TdS, as its proxy. S B H arris 18:00, 1 June 2012 (UTC)
First a trivial comment. Rather than saying that heat flow is a process parameter, I would prefer to say that it is a process variable or a process quantity. To be explicit, I think it right in general to say that heating refers to process rather than to state.
Second, a cautious whisper. I feel that it may be going overboard with zeal to insist officiously that heat only flows. It is wise and correct in a certain sense. But to insist on it to an extreme puts many respectable and established and otherwise-reliable thermodynamic sources in the wrong, when they talk about processes of heat production, meaning tranformation of other kinds of energy into internal energy in ways that can be made to increase temperature, such as friction and viscosity. This is verging on admitting something for the phrase 'thermal energy', but perhaps not too much, when the phrase is said to refer to state and not process. I am cautious about making this comment, fearing of course that it might provoke zealots of correct thinking to admonish me with severe strictures of rectitude. I think some more thought about this may be in order. Chjoaygame ( talk) 21:15, 1 June 2012 (UTC)
This reminds me that I must fix the thermal energy article, which states that thermal energy is a state variable. Nonsense! Except in the limit that no chemical or PV work is done, so that a change in thermal energy becomes a change in internal energy, which is a state function. Otherwise the difference between constant pressure and constant volume heat capacities (which are different for every substance, even if good approximations) show clearly that temperature is path-dependent, and thus so is thermal energy or "heat content." You can get an object to the same temperature in two ways (for example), using two different total amounts of heat dumped into it, if you let it do PV work to get to the state in one case, but not in the other. So δW = 0 and no change in chemical potential and so on, must be specified before we talk of thermal energy in any such fashion. And then indeed, "thermal energy" (an idealized quantity in the limit of no other energies that are reversibly turned into heat at the same time) is that component of internal energy that can be extracted by a temperature gradient. But if you don't make δW = 0, you can, by fiddling with work or other internal heat/chemical potential sources, extract any number of differert amounts of thermal energies from the same object, in passing to a given lower temperature (or to absolute zero, for that matter). If you do so, that makes thermal energy content inherrently ridiculous. S B H arris 21:49, 1 June 2012 (UTC)
I am having difficulty with the arguments presented in this article. The problem arises because of the idea that heat is the motion fof particles (see kinetic theory) which describes exactly how the temperature of (and energy in) materials is related to the motion of the particles that make up the materials contradicts most of what is described in this article. Additionally kinetic theory explains how heat is transferred between samples of material, something this article does not explain.
Can anybody please explain the difference? -- Damorbel ( talk) 20:30, 12 June 2012 (UTC)
The whole point of thermodynamics is to describe a macroscopic object in terms of a few variables. Suppose e.g. that you want to give a complete description of the center of mass motion of balls that can collide with each other. You are not interested how the atoms inthe balls behave, just how the balls will move. Then what is the most minimalist description that is still correct? The equations you get from conservation of momentum involve inly the center of mass motion. But the conservation of energy equation contains both the center of mass energy and the internal energy. If you ignore the fact that center of mass energy can get transferred to internal energy, you are not going to see the balls come at rest ever. It is this transfer which is heat.
So, the very reason heat appears, is precisely because you chose not to keep a certain number of variables explicitely in your equations, you don't want to bother about the zillions of microscopic variables. But because energy can leak into those varables and you need to work with conservation of energy, you need to account for that. The moment you add more variables so that you can keep track of smaller details of the system, heat becomes the energy transfer to the other degrees of freedom that are not captured by your variables. And if you describe the system in terms of all the 10^23 degrees of freedom, there is no heat anymore. All enegy transfer is then described by work. The thermodynamic description then gives an exact description of the physical system, the entropy of the system is then always identical to zero. Count Iblis ( talk) 20:26, 13 June 2012 (UTC)
This article must decide on the definition of heat. Is heat to be defined as energy (Joules) or energy transfer (Watts - Joules per second)?
"Heat is primarily defined as energy transfer by conduction or...". Thus Joules per second; so nothing to do with the energy (Joules) in the motion of particles? Are you sure? -- Damorbel ( talk) 08:21, 2 July 2012 (UTC)
Chjoaygame, your note (on your last contribution) says "Heat or heat transfer?: no need to decide; both are useful" sums up the whole article. 'Both being useful' is not an argument for treating them as being the same, it is just like treating electric charge and current as the same, do you do that? If you are not aware of the difference then I suggest you do a little personal research. -- Damorbel ( talk) 05:35, 5 July 2012 (UTC)
The comment(s) below were originally left at Talk:Heat/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Very important article, but it lacks references Snailwalker | talk 00:05, 21 October 2006 (UTC) |
Substituted at 20:12, 26 September 2016 (UTC)
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This whole "continuous process description" (within a conventional thermodynamical treatment) is a red herring you continue to raise. For quasistatic changes this is possible, but thermodynamics can in some cases also be used to compute the outcome of processes that are not quasistatic. Also for these cases, one can (in principle) define heat and work, and actually calculate them in some of such cases easily (e.g. the free expansion case is a rather trivial example). In general, this is a complicated matter, because in general you then do have to consider the real dynamics of the system, so you do have to give a "continuous process description", but this will be based on the real dynamics of the system, not on some efective thermodynamic description involving generalized forces.
In Reif's quantum mechanical picture, this is evident, he introduces the Hamiltonian of the system and says that the mean energy of the ensemble after the change is well defined given how the external parameters are changed. There is nothing to argue about that, if you have an initial condition for the ensemble, each ensemble member is in some well defined quantum state, and the time dependence of the external parameters is defiend, then the Schrödinger equation fixes the final state for each ensemble member and hence the mean energy change of the ensemble.
This means that you have to consider the dynamics of the system in terms of the molecules that make up the system. Obviously, that's not very practical to do exactly, but one can introduce stastistical methods that work well, see e.g. the last few chapters of the book by Reif.
So, it is still well defined in principle. Reif claims on page 71 that despite the complicated nature of this, it can be readily measured, giving some examples. Count Iblis ( talk) 16:00, 29 April 2012 (UTC)
I refer to Pippard, A.B. (1957/1966), Elements of Classical Thermodynamics, reprinted with corrections, Cambridge University Press, London. Pippard 1957 is listed in Reif's 1965 longer bibliography at the end of his book but is not suggested in the shorter reading lists at the ends of the chapters. Pippard 1957 is listed by Buchdahl 1966 in his bibliography of ten references. Pippard 1966 is listed in Callen 1985 in his list of six books on thermodynamics on page 485, with the comment: "A scholarly and rigorous treatment." Callen 1960 occurs in several of Reif's 1965 end-of-chapter suggested reading lists.
I will not try here to summarize Pippard. Enthusiastic editors may like to read what he says. Chjoaygame ( talk) 20:13, 1 May 2012 (UTC) Chjoaygame ( talk) 20:38, 1 May 2012 (UTC)
Let's discuss here this issue raised by SBHarris above in more detail. We know that we can avoid having to consider this by focussing on initial and final states that are in thermal equilibrium with well defined temperatures. If the work done by the system is known (and it is well defined in princile as pointed out in the book by Reif), then the heat absorbed follows from the First Law (which is thus taken the definition of heat). Then during the heat flow, a simple thermodynamic description isn't available, except in the quasistatic limit.
But we are not satisfied with this and we want to dig deeper. We should be able to bring two objects with different temperatures into contact with each other and see that the temperatures come closer to each other until they become equal and thermal equilibrium is reached. And this is precisely when heat flows between the systems. However, during this process the systems are not in thermal equilibrium, so you could question if ou could assign temperatures when the process of heat transfer is going on. Now, we know that in practice, there isn't much of a problem here, you can measure temperatures when heat transfer is going on. So, under not too extreme circmstances, we should be able to define temperatures.
Suppose then that during the process of heat transfer one object has temperature of T (in some sense). Without making that precise at this moment, we should note the following. If we were to interrupt the flow of heat (put an insulator between the two objects and let the object reach internal thermal equilibrium), then we could see a difference. In case of the heat flowing between the objects, there is obviously a flux of energy from the object, which is absent in the case of full internal thermal equilibrium.
If the object is a gas in a box, and we focus on a point inside the box, close to the boundary, then the moleculs there have a certain velocity disribution. In case of thermal equilibrium, there is no net transport of energy; the velocity distribution is Maxwellian. When the two objects are in thermal contact, there is a net flux of energy that moves thoough the box. This means that the velocity distribution is not of a purely Maxwellian form. We can understand this as follows.
When the two objects are in thermal contact, we have conduction of heat from one object to another and in a first approximation, you can describe this situation using time dependent temperatures, but if we want to take into account that the objects themselves have to conduct heat internally, then the objects not being in thermal equilibrium can to first approximation be described as there being local thermal equilibrium. So, to a good approximation we should have a Maxwellian velocity distribution where the temperature is position dependent.
Now, this is still not yet consistent with heat being conducted through the gas to the boundary of the box. Because we still have have a Maxwellian velocity distribution at every point, and then the flux of energy is exactly zero. However, once we take into account the finite mean free path of molecules in the gas, this changes things. If you imagien a plane parallel to the boundary of the box just inside the box, and look at the flux of kinetic energy of molecules that in both directions (left to right or vice versa). If we assume to first approximation that the velocity distribution is Maxwellian, then the fact that the molecules originate from one mean free path in one direction or the other, makes a difference. The flux from the two directions do not cancel, one flux is from a Maxwell distribution at a slightly higher temperature than the other. So, we then have net flux of energy toward the boundary of the box.
The velocity distribution is then not precisely Maxwellian due to molecules traveling finite distances, and that then yields the non-zero flux of heat. This is then not a fully self-consistent way of looking at things, because we started with assuming that you do have a position dependent Maxwellian distribution and we end up with something slightly different. Of course, a purely Maxwellian distribution does not yield a nonzero energy flux, so however one arrives at this conclusion, the end result is that the flow heat is related to local termal equilibrium breaking down; the velocity distribution is not purely Maxwellian.
That's why saying that mere temperature differences explain heat flow is not sufficient. In terms of the two boxes this is analogous to saying that if you have just two objects at a different temperature, no heat will flow unless you bring them into thermal contact. But the act of doing that leads to non-equilibrium in the objects themselves. Before you brought the objects into thermal contact, the non-equilibrium of the two objects with each other could be described exactly with assigning two different temperatures to the objects. Bring them into thermal contact and this exact description will break down. And as I explained above, you can look at what happens inside the objects, exact local thermal equilibrium in an object is not sufficient to capture the heat flow.
Count Iblis ( talk) 23:10, 28 April 2012 (UTC)
When no work flows between systems (one system doesn't do work on the other) then conservatin of energy demands conservation of heat. So it's easy to fall into the trap of simplifying things, by picking systems in which no work done is done between systems. The problem (as noted below) is that in advection of heat, there is advection of mass, which amounts to bouncing some masses off another system, much like throwing rocks or shooting bullets at it. That's kind of like work. This is transfer of energy by the kinetic energy of the bulk flow (bulk current of advection), but there is not necessarily any entropy involved at the input, so it's a funny type of energy transfer. My example is a river of liquid helium at 0 K (helium is a liquid even at 0 K) which I can run into a test system (like it strike and splash off the face of your perfect cube, which is at some temp) at the speed of sound, or however fast you like, and thereby "heat up" (or add energy to) the second system (the cube), up to any temperature you like (until its atoms have the same kinetic energy as the helium atoms, energy will flow into the system I'm "heating"). But is it art? Is this process "heating"? Does it "count"? It's advective. It's kinetic. But where is my input temperature? S B H arris 00:19, 1 May 2012 (UTC)
Count Iblis writes above at 00:05, 16 April 2012: "Work is always well defined (being the change in internal energy due to the change in external parameters), heat transfer is thus also always well defined."
Count Iblis makes a fundamental mistake of simple physics in writing that comment.
In physics, change in internal energy is not well defined by change in external parameters alone. Also needed for a calculation of the change of internal energy is information about a non-deformation variable, such as pressure, or, dare I say it, temperature. The distinction between work and heat needs even more. For its calculation, it needs also the record of the course of the values of the conjugate generalized forces belonging to the external parameters.
Probably Count Iblis has made this fundamental mistake in simple physics because he has been muddled by reading the angel of muddle, Reif 1965. Count Iblis' mind is full of stories about quantum mechanical Hamiltonians, told by Reif 1965, that get him into muddles like this. Reif 1965 is full of hubris about how clever he is with his better way of teaching physics, but look at the result in this case!
Count Iblis writes also above at 15:32, 16 April 2012: "If you can't define heat in general (i.e. during non-equilibrium conditions), then you have a huge problem, because we all know that heat flows during non-equilibrium conditions."
One cannot be sure exactly what Count Iblis means by this loosely worded comment, but it looks hard to separate it from a statement that heat is convected during non-equilibrium conditions. Synthesizing this comment of his with his above fundamental mistake in simple physics, it seems likely that Count Iblis is making the fundamental mistake of thinking that because a body has a high density of internal energy, and some of its components are moving, that this constitutes heat transfer. With all respect to engineering terminology, physicists do not say that heat is convected. They say that internal energy is convected, but the above comment by Count Iblis looks hard to distinguish from a statement that heat is convected, though his comment is loosely worded and its precise meaning is indeterminate. More muddle probably arising from an overdose of Reif 1965. Chjoaygame ( talk) 08:28, 30 April 2012 (UTC)
In physics, heat is dealt with mostly by thermodynamics.
Thermodynamics is built on the distinction between heat and work. If work can be defined for a process, then heat is also defined for it. The modern approach to thermodynamics describes processes as passages between states, and for the states, it defines internal energy and entropy. Temperature is a necessary consequence. No temperature means that there must be something wrong with either energy or entropy; entropy is the weak point, because it needs the definability of work and heat. No temperature therefore logically requires no distinction between heat and work; that means no thermodynamic macroscopic description.
What about the statistical definition of entropy? It is the amount of information needed to take you from the macroscopic thermodynamic description to the microscopic description. You need the macroscopic description in order to define the entropy by the statistical definition. No macroscopic thermodynamic description implies no entropy by the statistical definition.
There are various axiomatic schemes for the macroscopic thermodynamic description. The Carathéodory one is considered by many to be the most mathematically elegant. But it contains the same physics as the other schemes; it differs only in the mathematical structure. The insistence on excluding temperature from the definition of heat is for mathematical elegance, not for any sound physical reason. Actually Carathéodory himself in his own scheme defines temperature but does not define heat at all. One wonders then why it is so burningly important for some that heat should be defined without reference to temperature.
On the other hand, admitting empirical temperature and constructing the other concepts from it has a good intuitive as well as physical basis. There are those who hate that thought. That's a good part of why they like to insist on the exclusive dominance of the Carathédory–Born approach that, in some form or other, dominates many, but not all, modern texts. Chjoaygame ( talk) 06:06, 4 May 2012 (UTC)
I refer to Landsberg, P.T. (1961), Thermodynamics with Quantum Statistical Illustrations, Interscience, New York, volume 2 of the series edited by I. Prigogine, Monographs in Statistical Physics and Thermodynamics. This is one of the ten general references named by Buchdahl 1966. Landsberg also wrote another book (1978) listed by Callen 1985 in his bibliography for statistical mechanics, entitled Thermodynamics and Statistical Mechanics, Oxford University Press, Oxford UK, ISBN 0–19–851142–6, which has Chapter 1, pages 1–4, copied with hardly any changes from §1 of Chapter 1 of the 1961 book.
Landsberg is a Carathéodory man to his finger tips, with much attention to finer mathematical matters.
In Chapter 2, on page 6 of the 1978 book he allows two systems, specified by sets of independent variables {x1} and {x2}, to interact thermally till they reach thermal equilibrium. Then he writes: "Thus thermal equilibrium is specified by a relation f12({x1},{x2}) = 0 . This relation is assumed to be unique in the sense that, if all but one variable is known, f = 0 determines the remaining variable uniquely. This remaining variable is in fact a measure of the temperature."
Landsberg is recognizing that Carathéodory's non-deformation variable "is in fact a measure of [empirical] temperature". Carathédory does not mention this in so many words, but just goes on to develop absolute thermodynamic temperature before introducing the word temperature. But his systems already have empirical temperatures existing in their presupposed physical constitution.
From this I infer that Landsberg explicitly recognizes the existence of empirical temperature as presupposed for the definition of thermal interaction leading to thermal equilibrium. This is in agreement with the view of Kittel & Kroemer 1980.
I claim that it is also in agreement with a natural reading of Reif 1965. For example, Reif 1965 on page 94 writes: "Let us now discuss in greater detail the thermal interaction between two macroscopic systems A and A′. We shall denote the respective energies of these systems by E and E′." I observe that E and E′ are non-deformation variables of Carathéodory and thus qualify as empirical temperatures. It is evident that, in their very essence, Reif's macroscopic systems are such that temperature is definable for them. The issue is not whether Reif has mentioned this at any particular stage of his presentation. The issue is as to the physical character of his systems, whether or not temperature is definable for them. It is. Chjoaygame ( talk) 07:15, 6 May 2012 (UTC)
I think that this section can and must be improved:
Please agree or disagree with this point of view.
( Adwaele ( talk) 09:40, 18 May 2012 (UTC)).
I agree with your criticism. There is no notice given there in the article that it is intended there that the process shall be at constant pressure. Chjoaygame ( talk) 10:26, 20 May 2012 (UTC)
I agree that the notation δWboundary and δWother needs clarification, as well as a reliable source. Chjoaygame ( talk) 10:29, 20 May 2012 (UTC)
I don't find the present statements about this to be objectionable. Chjoaygame ( talk) 10:31, 20 May 2012 (UTC)
It be possible for a statement like this to appear in the article:-
"The SI unit of heat is the Joule. Heat can be measured with a calorimeter, or determined indirectly by calculations based on other quantities, relying for instance on the first law of thermodynamics"?
It is a statement of what heat is, devoid of any reference to temperature!
Is there a reliable source for it? Otherwise it should go. -- Damorbel ( talk) 16:01, 23 May 2012 (UTC)
The opening section has:-
Because it is by definition a transfer of energy, heat is always associated with a process of some kind, and "heat" is used interchangeably with "heat flow" and "heat transfer".
And it goes on to say :-
In common usage, the noun heat has a broader meaning, and can refer to temperature or to the sensation felt when touching or being close to a high-temperature object.[9]
The second section refers to 'a broader meaning'? Um - does this 'broader meaning' have the same definition as the first one then? There is already an extensive disambiguation link Heat
This is confused and confusing, not suitable for an encyclopedia. -- Damorbel ( talk) 19:10, 23 May 2012 (UTC)
Where it has:- they exchange thermal energy
Now going to the article Thermal energy; the very first line has:-
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system temperature
Which is different from the definition in the Heat section which defines heat as 'heat flow', or 'heat transfer' so making a logical impossibility. How can something (heat) be defined by a a qualified version of itself, ('heat flow' etc.) that is a version of itself that is restricted somehow in its meaning? -- Damorbel ( talk) 19:47, 23 May 2012 (UTC)
Of course the heat equation breaks down in gases except where they are held at constant volume. All this is merely a way of saying that you can integrate heat to get internal energy change, when no work is done (this is just conservation of energy), and we call such internal energy changes "thermal energy changes" since they are due to nothing more than heat input, or outflow. With that qualification, which is always understood, what's the big problem? S B H arris 22:41, 26 May 2012 (UTC)
Physicists don't say that heat is convected?! If true, that would explain a lot. More specifically, you would say that heat cannot be advected (like my my examples of bullets and gas streams with no heat-like velocity distributions). Since the diffusion part of convection (whether free or force convection) would presumably still be kosher, leaving simple thermal diffusion left as the only game in town when it comes to heat (radiation is sort of thermal diffusion with photons). It comes to me that perhaps the advective part of "heat transfer" (internal energy transfer) in rheids (fluids) is what is giving us all the problems. Heat transfer by diffusion always proceeds with a nice regular thermal gradient where every little region has nice a definable temperature (that happens in solids, and rheids with no mass-transfer of thermal energy look thermally like solids). In radiation you can talk about an ideal pair of reservoirs with a temperature difference, but that never actually happens in nature. In nature, what actually happens is the skins of all objects immediately equilibrate to the various temperatures that are defined by the various view-factors and conductivities in the system, and then old fashioned solid conduction as per the heat equation happens, after that. So, without advection you can't even set up the problems that are vexing us where heat supposedly "flows" but temperature cannot be defined. So perhaps that is the answer. We've been trying to talk the advection part of convection-heat transfer, and if thermodynamically and in physics that's verbotten, then that is our answer. You can always break up convection into a diffusive part, and an advected part that can be gotten rid of by changing reference frames, and transfers energy between systems by simple kinetic energy without any entropy. That's why it doesn't act like "heat" and why it sometimes has no "temperature." Does a river of liquid helium at 0 K have a temperature? No. But it can transfer energy into a system, simply by striking it and bouncing off. Tell me how much energy it must transfer, and I'll tell you how fast is has to run, in order to strike and heat the second system. Do we call that transfered energy, "advected heat"? No. Or, yes? It has no temperature. There's our problem. Is it heat? S B H arris 00:08, 1 May 2012 (UTC)
BTW, very small low pressure systems as you describe are subject to experimentation all the time (by "small" I mean system dimension < Knudsen 1, else what do you mean by Knudsen number?). In such systems, physicists cheerfully go on measuring heat convection and advection. [1] and temperature also. Are they deluding themselves?
In my helium example, if you stick a thermometer in the flow, it will heat up from something friction-like if the flow is a gas flow at 0 K, although I don't know if there will be frictional heating with actual superfluid helium since there is no friction. How the hell does that work? The molecules have to get around objects, and do they not sometimes strike them and transfer momentum? And if they are moving very rapidly, is this not significant momentum?
Anyway, leaving aside such problems, an engineer would say that the advected portion of heat is simply "thermal energy" that is transported across a boundary by virtue of a macroscopic current, and is no different than tranporting heat by taking a hot solid cube HERE and moving it over into the target system to heat it, THERE. In that case, the "heat" that counts is the one that is left over after you adjust your reference frame, and the kinetic energy of the fluid or the heat-carry solid wouldn't count itself as "heat", but rather energy input by some other form (work, perhaps). A thermometer doesn't see it until it has been transformed in the other system into thermal energy (thermalized) by random impacts there. Again my example of heating a system by firing O K crystal bullets at it and watching them disintegrate and transfer vibrations that end up as temperature increases. If you DEFINE this kinetic energy input as "work" then I'm not heating the system, by definition. But if you don't define it as "work" then I AM heating it, by definition. But doing so without any temperature gradient. Count Iblis above suggests that the idea of temperature gradients in the real world as heat transfer is happening, is a convenient fiction, and isn't true, as it demands a non-continuum picture in which there are little differential volumes, each with a little temperature (a temperature field in time and space) and that this sort of thing has a reality. Whereas, when heat is actually flowing in a solid (the best defined system we have), there actually is no such physical thing. "Temperatures" as we define and idealze them, only "appear" after heat flow has STOPPED (since only then do equilibrated systems where we define T appear-- the best example being a gas where perfect M-B distributions are not seen while heat is flowing through the gas). So that leads to a conundrum of what causes heat to flow while it is actually flowing. I believe I see this point. S B H arris 18:16, 1 May 2012 (UTC)
The heading "physicists don't say that heat is convected?" (NB"?") They would be nuts if they did, they would be right back in the good (old?) (caloric) days where 'heat' was thought to be a fluid and it 'flowed'. Convection, advection, are both forms of mass transport by fluid (gas, liquid) flow; the fluids involved have a temperature thus associated energy also, but it is the mass that flows, not the energy. -- Damorbel ( talk) 08:16, 9 June 2012 (UTC)
Chjoaygame, if you introduce the Knudsen number into a discussion about heat you should give a good explanation why. The Knudsen number is based on a very generally described dimension called "a representative physical length scale". The Knudsen number is the ratio of the mean free path to this "representative physical length scale" which can be the dimension of an orifice through which gas is flowing. One might whish to discuss this, but why in the article about Heat? What is there about Heat that has anything to do with linear dimensions?
You write "An example where temperature cannot be defined is in a very dilute gas" This a rather controversial statement since, if a collection of molecules is sufficiently dense to be called a gas, then it must also be able to have a defined temperature. Further, if the 'pressure' is reduced to the point where the molecular interaction is effectively absent then the individual molecules still have an energy thus they must also still have a temperature (see ' Boltzmann constant').-- Damorbel ( talk) 09:03, 9 June 2012 (UTC)
It is going too far to try to say what is the everyday use of the word heat. The attempt that was made was faulty, and gave no suitable dictionary reference. It is enough to say what is covered in the present article. Chjoaygame ( talk) 07:09, 26 May 2012 (UTC)
Dear colleagues:
I am considering three things:
I would like to have consenses before I modify the Article as I want to avoid that we will edit our texts in the Article over and over again, thus confusing the readers.
I would greatly appreciate your opinion.
The proposed new section would have the title Heat or heat flow? and read as follows:
In thermodynamics heat is not a function of state but a process parameter. In order to understand the implications of this statement let us look at two bodies a and b at temperatures Ta and Tb and with internal energies Ua and Ub. Suppose Ta > Tb. We connect them for some time by a heat-conducting wire with negligible heat capacity. During this time heat flows from the warm body to the cold body given by
Initially the temperatures are Tai and Tbi and the corresponding internal energies are Uai and Ubi. (The final state gets lower index f.) The total amount of heat transferred from a to b is Q = Ubf - Ubi = -(Uaf - Uai). The net result of the process is that the internal energy of a has decreased and the internal energy of b has increased.
The fact that heat is not a function of state means that the heat Q was nowhere before the process and it is nowhere after the process. Heat is only a meaningful concept when it flows. In other words: heat flow is the basic concept and not heat. Of course one can integrate the heat flow over time and obtain a certain quantity of heat, but there is no region in space where the heat is “stored”. In daily life one would say that heat is stored in body b, but thermodynamically this is incorrect. No object is capable of storing heat. In this sence the term heat capacity, which plays a central role in thermodynamics, is misleading.
Also in other fields of thermodynamics the term heat is used in a confusing if not incorrect way. Look at the famous experiment of Joule in which he determined the so-called mechanical equivalent of heat. He used a falling weight to spin a paddle-wheel in an insulated barrel of water. Through the paddle the water is brought into turbulent motion and comes to rest after some time. Joule observed that the temperature of the water has increased, but the potential energy of the weight is not converted into heat. It has increased the internal energy of the water. Thermodynamically never in this experiment heat is involved. The water with the paddle form an adiabatic system.
A similar argument leads to the conclusion that power is more realistic than work. In order to emphasize that heat flow and power are the basic thermodynamic properties it is better to express the laws of thermodynamics in terms of time derivatives so, for closed systems,
where P is the power applied to the system, and
where is the rate of entropy production.
The fact that heat flow is the basic quantity and not heat implies that we need a definition for heat flow rather than for heat. This would sound somehow like: heat flow is a flow of energy through matter driven by a temperature gradient. Microscopically the energy flow is due to the fact that the atoms, coming from a high-temperature region, pass a surface with a higher energy than the atoms coming from a low-temperature region. Based on this picture the coefficient of thermal conductivity can be derived with the kinetic theory of gases. [1]
Adwaele ( talk) 12:42, 1 June 2012 (UTC)
You have some solid points. "Heat" Q (in joules) is actually the time integral of heat flow dQ/dt. But the terms heat and heat flow (which really should be in units of power) are used synonymously, since heat is always flowing, so one gets away with it. But it's confusing to the student. And doing the integral makes it look as though the heat-power that has passed through the time-integrated is a quantity of heat energy that still resides someplace, whereas (as you point out) it is gone (and now is internal energy). You summed it up as it went past, but it passed into nowhere, and disappeared qua heat! Leaving only a total integrated (entropy*temperature) TdS, as its proxy. S B H arris 18:00, 1 June 2012 (UTC)
First a trivial comment. Rather than saying that heat flow is a process parameter, I would prefer to say that it is a process variable or a process quantity. To be explicit, I think it right in general to say that heating refers to process rather than to state.
Second, a cautious whisper. I feel that it may be going overboard with zeal to insist officiously that heat only flows. It is wise and correct in a certain sense. But to insist on it to an extreme puts many respectable and established and otherwise-reliable thermodynamic sources in the wrong, when they talk about processes of heat production, meaning tranformation of other kinds of energy into internal energy in ways that can be made to increase temperature, such as friction and viscosity. This is verging on admitting something for the phrase 'thermal energy', but perhaps not too much, when the phrase is said to refer to state and not process. I am cautious about making this comment, fearing of course that it might provoke zealots of correct thinking to admonish me with severe strictures of rectitude. I think some more thought about this may be in order. Chjoaygame ( talk) 21:15, 1 June 2012 (UTC)
This reminds me that I must fix the thermal energy article, which states that thermal energy is a state variable. Nonsense! Except in the limit that no chemical or PV work is done, so that a change in thermal energy becomes a change in internal energy, which is a state function. Otherwise the difference between constant pressure and constant volume heat capacities (which are different for every substance, even if good approximations) show clearly that temperature is path-dependent, and thus so is thermal energy or "heat content." You can get an object to the same temperature in two ways (for example), using two different total amounts of heat dumped into it, if you let it do PV work to get to the state in one case, but not in the other. So δW = 0 and no change in chemical potential and so on, must be specified before we talk of thermal energy in any such fashion. And then indeed, "thermal energy" (an idealized quantity in the limit of no other energies that are reversibly turned into heat at the same time) is that component of internal energy that can be extracted by a temperature gradient. But if you don't make δW = 0, you can, by fiddling with work or other internal heat/chemical potential sources, extract any number of differert amounts of thermal energies from the same object, in passing to a given lower temperature (or to absolute zero, for that matter). If you do so, that makes thermal energy content inherrently ridiculous. S B H arris 21:49, 1 June 2012 (UTC)
I am having difficulty with the arguments presented in this article. The problem arises because of the idea that heat is the motion fof particles (see kinetic theory) which describes exactly how the temperature of (and energy in) materials is related to the motion of the particles that make up the materials contradicts most of what is described in this article. Additionally kinetic theory explains how heat is transferred between samples of material, something this article does not explain.
Can anybody please explain the difference? -- Damorbel ( talk) 20:30, 12 June 2012 (UTC)
The whole point of thermodynamics is to describe a macroscopic object in terms of a few variables. Suppose e.g. that you want to give a complete description of the center of mass motion of balls that can collide with each other. You are not interested how the atoms inthe balls behave, just how the balls will move. Then what is the most minimalist description that is still correct? The equations you get from conservation of momentum involve inly the center of mass motion. But the conservation of energy equation contains both the center of mass energy and the internal energy. If you ignore the fact that center of mass energy can get transferred to internal energy, you are not going to see the balls come at rest ever. It is this transfer which is heat.
So, the very reason heat appears, is precisely because you chose not to keep a certain number of variables explicitely in your equations, you don't want to bother about the zillions of microscopic variables. But because energy can leak into those varables and you need to work with conservation of energy, you need to account for that. The moment you add more variables so that you can keep track of smaller details of the system, heat becomes the energy transfer to the other degrees of freedom that are not captured by your variables. And if you describe the system in terms of all the 10^23 degrees of freedom, there is no heat anymore. All enegy transfer is then described by work. The thermodynamic description then gives an exact description of the physical system, the entropy of the system is then always identical to zero. Count Iblis ( talk) 20:26, 13 June 2012 (UTC)
This article must decide on the definition of heat. Is heat to be defined as energy (Joules) or energy transfer (Watts - Joules per second)?
"Heat is primarily defined as energy transfer by conduction or...". Thus Joules per second; so nothing to do with the energy (Joules) in the motion of particles? Are you sure? -- Damorbel ( talk) 08:21, 2 July 2012 (UTC)
Chjoaygame, your note (on your last contribution) says "Heat or heat transfer?: no need to decide; both are useful" sums up the whole article. 'Both being useful' is not an argument for treating them as being the same, it is just like treating electric charge and current as the same, do you do that? If you are not aware of the difference then I suggest you do a little personal research. -- Damorbel ( talk) 05:35, 5 July 2012 (UTC)
The comment(s) below were originally left at Talk:Heat/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Very important article, but it lacks references Snailwalker | talk 00:05, 21 October 2006 (UTC) |
Substituted at 20:12, 26 September 2016 (UTC)