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Needs some sort of organization and simplification 185.11.18.46 (talk) 07:40, 7 August 2022 (UTC)
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)
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)
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