# Heat Transfer and Thermodynamics

cmmcnamara
I have a quick question regarding the interrelationship between heat transfer and thermodynamics.

Basically, since temperature as governed by the equations from the study of heat transfer, is neither uniformly distributed (a field) and changes with time (non-equilibrium), how applicable are the results you get from heat transfer back to thermodynamics? Especially considering that many of the equations are developed using energy balance from the first law which assume no work.

I know that heat transfer isn't derived from first principles and is an observational science but seeing that its results contradict the assumptions made by thermodynamic analysis, how trusted/accurate are the results, and since it's investigation have there been any reformulations of thermodynamics which account for it? Or are the violations from heat transfer simply negligible when considering them in thermodynamics?

## Answers and Replies

Mentor
There are no such violations. Heat transfer is an essential component to making thermodynamics work in the real world. Could you explain in more detail the problem you are seeing -- with an example, perhaps?

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cmmcnamara
Let me try and find a specific example but in the mean time, what I suppose my main issue in grasping the compatibility between the two is the idea that thermodynamics works in quasi-equilibrium states while heat transfer obviously shows us that heat transfer rates can not only exist not in equilibrium but can be accelerating or decelerating within a region at a rate which may not even be close to equilibrium. Perhaps I can go find an example which does a better job at explaining my confusion than I can actually word.

Mentor
While that's true, it doesn't mean that one or the other is wrong, it just means they are talking about two different things.

Thermodynamics, for example, discusses the processes involved in a steam engine, including the fact that heat is transferred in the boiler. But the mechanics of how the heat is transferred really aren't that important for thermodynamics.

Mentor
Let me try and find a specific example but in the mean time, what I suppose my main issue in grasping the compatibility between the two is the idea that thermodynamics works in quasi-equilibrium states while heat transfer obviously shows us that heat transfer rates can not only exist not in equilibrium but can be accelerating or decelerating within a region at a rate which may not even be close to equilibrium. Perhaps I can go find an example which does a better job at explaining my confusion than I can actually word.

In analyzing heat transport and other transport phenomena, we virtually always make the implicit assumption for distributed parameter systems that, at each spatial location (i.e., locally), the material is very close to thermodynamic equilibrium, so that it is valid to use thermodynamic functions, such as heat capacity, in modeling calculations. Based on decades of experimental conformation, this assumption has proven to be a very accurate representation of actual physical behavior. See Transport Phenomena by Bird, Stewart, and Lightfoot.

Studiot
I can't imagine why you would think that either heat transfer or work transfer is not part of thermodynamics. Or why the equations of transfer are not derived from the same principles that supplies the first law.

One of the most successful engineering textbooks of all time on the subject is

Engineering Thermodynamics, Work and Heat Transfer, by Rogers and Mayhew.

The title speaks for itself but it certainly provides a fully integrated approach.

I would also endorse Transprt Phenomena as a classic and have recommended it many times here. It is, however, significantly more mathematical than Rogers and Mayhew.

As a further reference the second chapter of Reddy : Applied Functional Analysis and Variational Methods in Engineering is a masterpiece. It is entitled a review of the field equations of engineering and provides a reference for the rest of the book. The chapter contains concise introduction to all the main areas of mechanical science, including thermodynamics, heat transfer and elasticity and their interconnection.

go well

cmmcnamara
In analyzing heat transport and other transport phenomena, we virtually always make the implicit assumption for distributed parameter systems that, at each spatial location (i.e., locally), the material is very close to thermodynamic equilibrium, so that it is valid to use thermodynamic functions, such as heat capacity, in modeling calculations. Based on decades of experimental conformation, this assumption has proven to be a very accurate representation of actual physical behavior. See Transport Phenomena by Bird, Stewart, and Lightfoot.

Ok thank you very much, I'll check that out. Oh yes I do remember Thermo often assumes a "well-mixed" system.

I can't imagine why you would think that either heat transfer or work transfer is not part of thermodynamics. Or why the equations of transfer are not derived from the same principles that supplies the first law.

One of the most successful engineering textbooks of all time on the subject is

Engineering Thermodynamics, Work and Heat Transfer, by Rogers and Mayhew.

The title speaks for itself but it certainly provides a fully integrated approach.

I would also endorse Transprt Phenomena as a classic and have recommended it many times here. It is, however, significantly more mathematical than Rogers and Mayhew.

As a further reference the second chapter of Reddy : Applied Functional Analysis and Variational Methods in Engineering is a masterpiece. It is entitled a review of the field equations of engineering and provides a reference for the rest of the book. The chapter contains concise introduction to all the main areas of mechanical science, including thermodynamics, heat transfer and elasticity and their interconnection.

go well

I'll definitely check those out as well, thank you! And it's not that I don't believe work/heat transfer is not a part of thermodynamics, it surely is. My question was more debating whether the assumptions behind heat transfer theory and the assumptions behind thermodynamics are compatible with one another.

As for the derivations of the transfer equations, I see that the first law is put into effect for the derivation of energy balance for heat transfer equations but not for the derivation of the mechanics behind it. My book states that laws such as Fourier's law are created based on observational evidence and not from first principles.

Mentor
Ok thank you very much, I'll check that out. Oh yes I do remember Thermo often assumes a "well-mixed" system.

I'll definitely check those out as well, thank you! And it's not that I don't believe work/heat transfer is not a part of thermodynamics, it surely is. My question was more debating whether the assumptions behind heat transfer theory and the assumptions behind thermodynamics are compatible with one another.

As for the derivations of the transfer equations, I see that the first law is put into effect for the derivation of energy balance for heat transfer equations but not for the derivation of the mechanics behind it. My book states that laws such as Fourier's law are created based on observational evidence and not from first principles.

Fourier's law is definitely derived from first principles; note the it contains the heat capacity within the determination of the thermal diffusivity.

I think that paraphrasing your original question would be: How can a parcel of material be considered to be at thermodynamic equilibrium, and how can I use the thermodynamic equilibrium functions for the material, if there are temperature gradients present in the parcel, or if the parcel is being deformed. After all, both these factors constrain the number of quantum states available to the parcel, so that it can not exhibit the most probable distribution of quantum states (required for thermodynamic equilibrium)? The answer is that it has been found in practice these constraints on the distribution of quantum states typically do not have a significant effect on the properties.

As far as the derivation of the mechanics equations is concerned, follow Studoit's suggestion to check out Transport Phenomena. There is a connection between the mechanical energy balance equation and the thermodynamic energy balance equation that you need to look at. Transport Phenomena specifically addresses this.

Chet

Homework Helper
I have a quick question regarding the interrelationship between heat transfer and thermodynamics.

Basically, since temperature as governed by the equations from the study of heat transfer, is neither uniformly distributed (a field) and changes with time (non-equilibrium), how applicable are the results you get from heat transfer back to thermodynamics? Especially considering that many of the equations are developed using energy balance from the first law which assume no work.
Thermodynamic states are equilibrium states. Thermodynamics deals with changes between such states.

Thermodynamics does not deal with the state of a system that is not in equilibrium, ie. the actual states of a system during an irreversible process. Therefore, in thermodynamics one does not analyse the physical process of heat transfer in a non-equilibrium process. There is no scientific theory, as far as I am aware, that even attempts to deal in a comprehensive way with the analysis of non-equilibrium thermodynamic processes. It is too complicated.

AM

Mentor
Thermodynamic states are equilibrium states. Thermodynamics deals with changes between such states.

Thermodynamics does not deal with the state of a system that is not in equilibrium, ie. the actual states of a system during an irreversible process. Therefore, in thermodynamics one does not analyse the physical process of heat transfer in a non-equilibrium process. There is no scientific theory, as far as I am aware, that even attempts to deal in a comprehensive way with the analysis of non-equilibrium thermodynamic processes. It is too complicated.

AM

Try Googling non-equilibrium thermodynamics and see all the many books and encyclopedia listings that are returned. de Groot's work was published over 50 years ago.

Studiot
Thermodynamics does not deal with the state of a system that is not in equilibrium,

There is one notable exception in classic thermodynamics.

Whilst the pressure, temperature etc is often undefinable in a system the volume is nearly always definable, whether the process is reversible or irreversible.

Homework Helper
Try Googling non-equilibrium thermodynamics and see all the many books and encyclopedia listings that are returned. de Groot's work was published over 50 years ago.
I didn't say that no one has tried to analyse a non-equilibrium thermodynamic process. I just said that there was no comprehensive theory for analysing non-equilibrium thermodynamic process as there is for (equilibrium) thermodynamics. I may have overstated it a bit in saying that there had been no attempt at such a theory.

That is my impression. This quote from the forward to W. Muschik, 'Six Lectures on Fundamentals and Methods. Aspects of Non-Equilibrium Thermodynamics (1990)' seems to support my impression:
W. Muschik said:
"Until today there is no basis of non-equilibrium thermodynamics commonly accepted. This is due to the fact that there does not exist a natural extension of thermostatics to a non-equilibrium theory, so that different schools arose using different fundamentals for developing their non-equilibrium concepts. "

The author of this paper published in 2009 by the Royal Society of Chemistry (P. Attard, "The second entropy: a general theory for non-equilibirum thermodynamics and statistical mechanics", Annu. Rep. Prog. Chem., Sect. C, 2009, 105, 63–173) seems to share a similar view:
P. Attard said:
"Whereas the fundamentals of the equilibrium theory are complete and attention is nowadays focussed on applications, even the most basic requirements of a non-equilibrium theory have yet to be established. For example, there is currently nothing comparable to the Helmholtz free energy for a non-equilibrium system, and there is no consensus on a variational principle for time-dependent systems that is the equivalent of the maximization of ordinary entropy that underlies equilibrium thermodynamics (see below). Further, although the Boltzmann probability distribution provides the foundation of equilibrium statistical mechanics, (it is the summit, according to Feynman),12 no comparable probability distribution exists for non-equilibrium systems (see also below). Given the importance of time-dependent phenomena, there have been many efforts to construct a comprehensive non-equilibrium theory. That these three most basic requirements have yet to be consensually established strongly suggests some fundamental misconception, inappropriate starting point, or missing element. "

AM