Talk:Second law of thermodynamics

Understanding the Second Law and the Clausius Statement

The statement of the Second Law is correctly quoted in the article "Laws of Thermodynamics" as: "The second law of thermodynamics states that in a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems never decreases." That is all that needs to be said, but one must understand that entropy is also affected by changes in any form of internal energy, not just kinetic energy which relates to temperature. For example, when ice melts, water vapor condenses, a ball rolls down a plank, fire burns, chemical or nuclear reactions take place - all are examples of the Second Law operating and increasing entropy. However when the above statement is followed by "A common corollary of the statement is that heat does not spontaneously pass from a colder body to a warmer body" we are restricting the process to one in which the only form of internal energy to change is kinetic energy. This is not what Clausius said: he just referred to some other change occuring, and that change does not have to be work (ie energy) being applied or added. Furthermore, the process does not have to be restricted to an isolated system provided that, if there are other thermodynamic systems changing then these have to be interacting ones if we are to consider the total sum of entropy and how that changes. For example, radiation from the cold atmosphere to the warmer surface is a single one-way process without any other interacting thermodynamic systems, so it must obey the Second Law and thus cannot cause heat from cold to hot unless there are other changes.

The key thing to understand is that the progress towards maximum entropy (sometimes called "Maximum Entropy Production" or MEP) involves unbalanced energy potentials reducing down to zero. For example, in a force field like gravity or centrifugal force (as in a vortex cooling tube) there can be a non-zero temperature gradient parallel to the direction of the force, eg radially in a vortex tube where the helical motion of gas moving down the tube creates colder gas in the central regions and hotter gas in the outer regions, ie a radial temperature gradient. This is the Second Law of Thermodynamics operating. A similar gradient also develops in regard to density in the troposphere, and this also is a result of the Second Law because potential energy is involved. In the absence of other changes that Clausius talked about, let us consider a column of air in the troposphere and assume no phase change or reactions are taking place. This narrows us down to considering just the mean molecular kinetic energy (KE) and the mean molecular gravitational potential energy (PE) and, for there to be no unbalanced energy potentials at maximum entropy (ie thermodynamic equilibrium) then the sum (PE+KE) must be a constant at all altitudes, and so, since PE increases with altitude then KE must decrease, creating the temperature gradient we see in every planetary troposphere. Note that thermodynamic equilibrium does not always necessitate isothermal conditions, ie thermal equilibrium throughout. Both the density gradient and the temperature gradient are the one and the same state of thermodynamic equilibrium. The pressure gradient is a result thereof, not the cause because pressure is proportional to the product of temperature and density by the Ideal Gas Law. This law does not imply, for example, that high pressure will maintain high temperatures. One final note: the state of thermodynamic equilibrium may never be reached in the troposphere, but the Second Law is still operating and creating a tendency for the system to move towards maximum entropy. For more on this read my 2013 paper "Planetary Core and Surface Temperatures" which is on Researchgate, LinkedIn and at https://ssrn.com/author=2627605. Douglas Cotton, Independent Researcher into Atmospheric and Subterrestrial Physics. — Preceding unsigned comment added by 2001:8003:26E2:3300:BC4F:4174:E728:BEF9 (talk) 02:43, 28 October 2022 (UTC)

Footnote: What Clausius first wrote in German in 1854 translated reads: "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time." Note the similar wording in the modern statement (quoted above) that refers to "interacting" systems. The "other change" may not necessarily require addition of energy. For example, after a storm which disturbed the density gradient in the troposphere, gravity will act by redistributing molecules and, in the process, reducing unbalanced energy potentials (that is, increasing entropy) but not supplying energy, which of course gravity, being just a force, cannot do. I would define entropy as "a measure of progress in the reduction of unbalanced energy potentials." With such a definition we can understand the process of "maximum entropy production" which is what the Second Law is all about. -

Douglas Cotton, author of the peer-reviewed paper "Radiated Energy and the Second Law of Thermodynamics" (2012) which explains how Nature ensures that every one-way passage of radiation will obey the Second Law and thus never cause heat from a cooler source to a warmer target. 2001:8003:26E2:3300:AD47:5DA:350A:7A54 (talk) 22:21, 17 November 2022 (UTC)

Removals

I removed the "Generalized conceptual statement of the second law principle" section on the grounds that not everything that managed to get published needs to be included here. This is an article on a standard topic in the physics curriculum and should be based on solid, standard references that indicate what the whole field cares about, not niche perspectives that have yet to gain ascendancy. As StarryGrandma said, we would need sources like review articles [1].

I also trimmed some equations that had been included as images. These were even worse for accessibility purposes than all the other ways of displaying math online and clutter up the page. Equations are content, not decoration. XOR'easter (talk) 21:27, 7 May 2023 (UTC)

@XOR'easter, this is an engineering application of the second law. I found an open source reference that does a literature review in the introduction, starting with one of the Wright papers, and puts it in context:

Shan, Shiquan; Zhou, Zhijun (2019). "Second Law Analysis of Spectral Radiative Transfer and Calculation in One-Dimensional Furnace Cases". Entropy. 21 (5): 461. doi:10.3390/e21050461. PMC 7514951. PMID 33267174.{{cite journal}}: CS1 maint: unflagged free DOI (link)

Entropy's publisher is at least semi-predatory, and the peer-review in its journals can be extremely rapid. The article might not be a reliable secondary source per Wikipedia policies. --Jähmefyysikko (talk) 15:55, 8 May 2023 (UTC)

I wouldn't trust Entropy for these purposes (or for most any other purposes, either). XOR'easter (talk) 16:03, 8 May 2023 (UTC)

Oh yes, MDPI journals. StarryGrandma (talk) 19:31, 8 May 2023 (UTC)

Wiswright, however this is too specialized a topic for a top-level article like this should be. With so many odds and ends in here it seemed OK to leave it in for now. But it should be elsewhere, with some explanation of why entropy has become important in engineering. I understand why for chemistry, and why it isn't used as much in physics and astrophysics. StarryGrandma (talk) 14:50, 8 May 2023 (UTC)

Poorly explained equation sourced from non-standard reference

The paragraph starting Introducing a set of internal variables has multiple problems.

The equation given is poorly explained and introduces the variable $\Xi$ without definition:

$\mathrm {d} S={\frac {\delta Q}{T}}-{\frac {1}{T}}\sum _{j}\,\Xi _{j}\,\delta \xi _{j}$

I gather that $\Xi$ is intended to represent the mean conjugate to $\xi$, but this is not explained. Such material is premature and inappropriate here in any case. What's more, the summation is a "rabbit pulled out of a hat" that beginners reading this page will not understand at all.

Judging by the references given to papers by Pokrovskii at the end of the paragraph, my guess is that this equation and its notation are simply copied from his work. This isn't OK. Furthermore, it's not clear that these publications are authoritative enough to be justified here.

I propose removing this paragraph and its two references. cstark (talk) 09:19, 13 December 2024 (UTC)