Reasoning and Logical Proofs of the Fundamental Laws:
“No Hope” for the Challengers of the Second Law of Thermodynamics

Milivoje Kostc, Department of Mechanical Engineering, Northern Illinois University, DeKalb, IL 60115, USA

Entropy 2023, 25(7), 1106; https://doi.org/10.3390/e25071106  * NASA ADS * Google Scholar * Semantic Scholar: Figures and Tables [More here or Download PDF (39 pp.)]

* Browse Figures * Published: 24 July 2023. This article belongs to the Special Issue:
Exploring Fundamentals and Challenges of Heat, Entropy, and the Second Law of Thermodynamics: Honoring Professor Milivoje M. Kostic on the Occasion of His 70th Birthday)

Abstract
This comprehensive treatise is written for the special occasion of the author’s 70th birthday. It presents his lifelong endeavors and reflections with original reasoning and re-interpretations of the most critical and sometimes misleading issues in thermodynamics—since now, we have the advantage to look at the historical developments more comprehensively and objectively than the pioneers. Starting from Carnot (grand-father of thermodynamics to become) to Kelvin and Clausius (fathers of thermodynamics), and other followers, the most relevant issues are critically examined and put in historical and contemporary perspective. From the original reasoning of generalized “energy forcing and displacement” to the logical proofs of several fundamental laws, to the ubiquity of thermal motion and heat, and the indestructibility of entropy, including the new concept of “thermal roughness” and “inevitability of dissipative irreversibility,” to dissecting “Carnot true reversible-equivalency” and the critical concept of “thermal-transformer,” limited by the newly generalized “Carnot-Clausius heat-work reversible-equivalency (CCHWRE),” regarding the inter-complementarity of heat and work, and to demonstrating “No Hope” for the “Challengers” of the Second Law of thermodynamics, among others, are offered. It is hoped that the novel contributions presented here will enlighten better comprehension and resolve some of the fundamental issues, as well as promote collaboration and future progress.

Keywords: fundamental laws; second law of thermodynamics; Carnot cycle; reversible equivalency; exergy; entropy generation; thermal roughness; thermal friction irreversibility; thermal transformer; virtual thermal particles 

“If your theory is found to be against the second law of thermodynamics, I give you no hope; there is nothing for it but to collapse in deepest humiliation”.—Arthur Eddington 

Impasse: “Perhaps, after all, the wise man’s attitude towards thermodynamics should be to have nothing to do with it. To deal with thermodynamics is to look for trouble”. 

Anecdotal Laws of Thermodynamics (LT) [bracketed terms added]:♦[0LT]: You must play the game [equilibrium]. ♦[1LT]: You can’t win [conservation]. ♦[2LT]: You can’t break even [dissipation]. ♦[3LT]: You can’t quit the game [0 K impossible].—Thermodynamics-WikiQuote  

“The Second Law of thermodynamics can be challenged, but not violated—Entropy can be decreased, but not destroyed at any space or time scales. […] The self-forced tendency of displacing nonequilibrium useful-energy towards equilibrium, with its irreversible dissipation to heat, generates entropy, the latter is conserved in ideal, reversible processes, and there is no way to self-create useful-energy from within equilibrium alone, i.e., no way to destroy entropy”.—[2LT.mkostic.com].

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Table of Contents (Outline)

        Abstract

1. Introduction

2. Ubiquity and Conjugation of “Energy Forcing and Displacement” 

3. Reasoning Logical-Proofs of the Fundamental Laws

4. Ubiquity of Thermal Motion and Heat“, Thermal-Roughness,” and Indestructibility of Entropy [4.1. Ubiquity of Thermal-motion, Thermal-energy and Heat, Temperature and Entropy; 4.2. Thermal particles, “Thermal Virtual-particles,” and “Thermal-moles” or Dimensionless entropy; 4.3. Thermal-energy is a Distinguished part of Internal-energy - “Pond analogy” demystified; 4.4. "Thermal-Roughness" Ubiquity, and Inevitability of Thermal-Friction; 4.5. Inevitability and Conjugation of Work-dissipation and Entropy-generation - "Planck's increase in entropy without dissipation" challenged; 4.6. Irreversibility of Entropy-generation and Indestructibility of Entropy - Essence of the 2LT ]

5. Carnot Maximum Efficiency, Reversible Equivalency, and Work Potential [5.1. Carnot Cycle Maximum Efficiency: Proof by Contradiction-Impossibility; 5.2. Carnot Cycle, Carnot Efficiency, and Carnot Equality (CtEq); 5.3. Carnot “Reverse-cycle” and Thermodynamic “Reversible Equivalency”; 5.4. Work-potential, Formation-work, and Exergy]

6. Thermal Transformers: Carnot–Clausius Heat–Work Reversible Equivalency (CCHWRE) [or Carnot–Clausius Equality (CCE) for short]: 6.1. Thermal Transformers and CCHWRE; 6.2. Proof of Ideal-gas Equation-of-state and CCHWE [or CCE for short] Confirmation; 6.3. Reversible-cycles are 100%-efficient: Carnot-efficiency is essentially the “Measure of Heat-WP or Exery - "Carnot's efficiency misplaced (more)” ]

7. “No Hope” for the Challengers of the Second Law of Thermodynamics [7.1. “Perpetual-Motion Watch” Deceptive Example; 7.2. Three “Primary Deception structures” of hypothetical violation of the 2LT; 7.3. “Experimental test of a Thermodynamic-paradox” Demystified ]

8. Conclusions

         Appendix A. Outline: Reasoning Fundamental Laws and “No Hope” for the 2LT Challengers

       Appendix B. Thermal-Transformer and Temperature-Oscillator: Dynamic and Structural Quasi-Equilibriums (including “Persistent-Currents Quasi-Equilibrium”)

       References and Notes 

[...] The fundamental Laws of Thermodynamics (LT) are the fundamental laws of nature, and they are considered to be axiomatic and experiential without proof, as never experienced otherwise, or as self-evident postulates. Due to the very complex micro- and macro-structures and their intricate interactions, it would be impossible to deterministically prove the Laws, but they could be reasoned logically, and their general validity inferred in principle, as it will be deduced here. 

[...] The two fundamental Laws of Thermodynamics (1LT and 2LT) are believed to be empirical and axiomatic without proof. However, they are mechanistic in nature and in principle are more general consequences of the Newtons’ law of motions, see Figure 1. The three Newton’s Laws (NL) of forces and motions are holistic in a sense that the 2NL of motion is also the 3NL of action–reaction equality when the inertial forces are included, and the 1NL of inertia is a special case of the 2NL when external forces are balanced (zero). 

[...] It may be deduced that, due to equality of acting and reacting forces along the same mutual displacement, the energy transferred by acting-force displacement must be equal to the energy of the opposing, reacting-force displacement—that is, the interactively displaced (or transferred) energy from acting to reacting particle or body will be conserved. In the absence of the opposing reaction forces, there will be no energy transfer. This will be true in general since all elementary and/or bulk interactions are additive, regardless of complexity of system structure or types of interactions (also forced fields could be represented by relevant “equivalent particles,” such as photons, etc.). 

[...] Furthermore, it is reasoned here that the energy directional transfer (2LT) is due to a particle or body forcing action onto another particle or body resisting to change its existential “inertial-state”, by equal reacting force in opposite direction (the 3NL) along a mutual displacement.

[...] Therefore, during the mutual (shared and equal) displacement, the acting body will be transferring its energy onto the reacting body, the two being the same, in principle, the product of equal action and reaction force (including process inertial forces) and equal mutual displacement. Therefore, the directional energy transfer and dissipation (2LT) and energy conservation (1LT) are consequences of the fundamental Newton’s Laws of mechanics, and not merely empirical as commonly postulated, see Figure 1 and Equations (1) and (2) [in here]. 

[...] Key Point 8. The forced-displacement interaction is a process of energy transfer from the acting particle (or body) with higher energy density onto a reacting particle (or body) of lower energy density (i.e., energy intensity, see Table 1), displacing (transferring) its energy during the interaction, i.e., diminishing its energy (figuratively “decelerating” its structure) while increasing energy of the reacting body (figuratively “accelerating” its structure) until the energy densities (or intensities) are equalized when mutual self-sustained equilibrium is achieved.

[...] In addition to reasoning the physical concepts of the 1LT and 2LT Laws, further inferences and/or reasoning proofs for new or newly re-interpreted concepts are also offered throughout, i.e.,: “Thermal Virtual-particles” and “Thermal-moles” as dimensionless entropy (Section 4.2); Heat–work energy “Pond analogy” misconception (Section 4.3); Ubiquity of “Thermal-roughness & thermal-friction” (Section 4.4); Inevitability and Conjugation of Work-dissipation and Entropy-generation (proving the Planck’s statement to be misplaced, Section 4.5); Carnot Equality (Section 5.2); "Thermal transformer" concept and "Carnot–Clausius Heat–Work Reversible Equivalency  [or Carnot–Clausius Equality (CCE) for short]" (CCHWRE or CCE for short, Section 6.1); Proof of Ideal gas state (Section 6.2); Reversible Cycle efficiency is perfect (100%) and essentially “measure” the Work-Potential or Exery of heat source (Section 6.3); Primary “2LT Deception structures” (Section 7.2); “Thermodynamic paradox” demystified (Section 7.3); among others.

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