Thermodynamics today | Prof. Adrian Bejan

Reproduced from:

Thermodynamics today

Adrian Bejan

J. A. Jones Distinguished Professor

Duke University

Accepted Manuscript

PII: S0360-5442(18)31389-6

DOI: 10.1016/

Reference: EGY 13357

To appear in: Energy

Received Date: 27 April 2018

Accepted Date: 14 July 2018

Please cite this article as: Adrian Bejan, Thermodynamics today, Energy (2018), doi: 10.1016/j. energy.2018.07.092


  • Why Prof. Szargut’s career had impact on my own career.
  • Review of the current state of thermodynamics.
  • Review of common mistakes and misconceptions in thermodynamics.
  • The graphic evolution of thermodynamics, diagrams and designs.


In this paper I use the example set by Prof. Jan Szargut as point of reference for a brief look at the current state of thermodynamics—the doctrine, its reach and importance. I start with my first encounter with Prof. Jan Szargut in 1979, and I show how his work influenced mine. Next, I review the structure that underpins thermodynamics as a discipline: the laws and the self-standing phenomena that they underpin, and graphic methods that convey these principles. Along the way, I draw attention to a recent trend that is caused by the inflation in scientific publishing due to the internet: the most common mistakes and misconceptions in thermodynamics, and how they are being spread. In sum, this paper is a call to action, to value, improve and defend the science of thermodynamics.

Keywords: Thermodynamics, laws, mechanics, caloric, constructal, evolution, design, discipline.

Professor Szargut

Science is like a civilized territory that improves, prospers and expands because it makes life better for the people who belong to it. It expands as long as it keeps producing useful things, which attract people. The civilized welcome the newcomers—the nobodies—provided that they obey the laws, the discipline. People join because their lives become better that way. To fight the barbarians who pillage on the perimeter is a necessary and unpleasant effort, a nuisance, not the objective. As the defeated barbarians are assimilated and civilized, the civilized territory expands and, as a result, life, peace, movement and freedom flourish. The civilized territory that does not fight the pillagers is destined to disappear along with the good way of life that it was sustaining. Thermodynamics, like all the useful artifacts (e.g., science) produced by the civilized, is no different.

I first met Professor Szargut at the workshop “Second Law Analysis of Energy Devices and Processes”, held on 14-16 August 1979 at The George Washington University, in Washington, D.C., and sponsored by the U. S. department of Energy [1]. I was lucky to be included, because I had just finished my first year as an assistant professor, and my record was relatively unknown. As it turned out, this first workshop of my career was truly formative, for two reasons:

First, it affirmed the importance of ‘correct’ thermodynamics in the pursuit of solutions for the most pressing concerns about energy and the future. The workshop organizers invited as advisers, speakers and participants some of the most authoritative figures in thermodynamics in the U. S. from one or two generations before mine, for example, Joseph Kestin, Edward Obert, Myron Tribus, Richard Gaggioli, Paul Naghdi, and many more. To affirm the importance of correct thermodynamics was a big deal then, on the heels of the 1974 energy crisis, when most of the discussions and solutions were reminiscent of caloric theory, under the guise of a thermodynamics in which the speaker knows only the first law, and speaks of “thermal energy” and “conservation”. As I show here, to affirm the importance of correct thermodynamics is an even bigger deal today.

Second, the organizers had the vision to invite speakers from Europe. This was a rare and positive quality of the workshop, especially on the background provided by the Cold War. Professor Szargut presented a review [2] of the contemporary thermodynamics pursued in Europe, on both sizes of the Iron Curtain. His review also covered the history of thermodynamics, in particular, the history of “second law analysis,” lost work and lost power, which developed in the late 1800s as the Gouy-Stodola theorem, and grew into a field of its own (availability, available work, exergy) in the 20th century.

Professor Szargut’s review opened our eyes to the reality that colleagues in other countries treat and use thermodynamics with care, and consider this doctrine alive, not dead. As I look back, his lecture opened up my own eyes even though (because of my origin) I was familiar with both sides of Europe, the languages and the scientific literature. What I was doing before the 1979 workshop, as a disciple of Keenan’s M.I.T. school of thermodynamics, fused with the field covered in Szargut [2] and the workshop [1, 3], and became my career and books on thermodynamics [4-6]. By the way, in my books I covered not only the topics reviewed in Ref. [2], but also several specific contributions of Professor Szargut and his students [7-10].

Impact on a young career comes not only from the goodness of the work of his professors’ generation, but also from the goodness of their character. On stage in Washington [2], Szargut impressed everybody with modesty, clarity, conciseness, no nonsense, and deep respect for the science that was created before him, regardless of the nationalities of his predecessors. He was a true scientist, a quiet role model. I heard him several times since then, at ECOS and Gordon conferences, and every time he rose in my esteem. In the following pages, I give a personal account of what I see as the current status of our discipline of thermodynamics.

Distinct phenomena, first principles

What is thermodynamics? As its name indicates, “thermo-dynamics” is the modern science of heat and work and their usefulness, which comes from converting the work (power) into movement (life) in flow architectures that evolve over time to facilitate movement (Figs. 1 and 2). The part of nature that thermodynamics represents is this: nothing moves by itself unless it is driven by power, which is then destroyed (dissipated) during movement.

Figure 1. The evolution and spreading of thermodynamics during the past two centuries (after a drawing made in 1982 [4], p. viii).
Figure 2. The engine and brake flow configuration of nature is represented by the flow of useful energy into the earth (the large rectangle), the partial destruction of this flow in the animate and inanimate engines (the blue disc), followed by the complete destruction of the remaining useful energy stream in the interactions with the environment (the green rectangle) (after a drawing made in 1976 [11], also in Ref. [4], p. 35). In time, all the flow systems exhibit the constructal-law tendency of generating ‘evolving designs’, and this time arrow means less dissipation in the engines and more dissipation in the brakes.

Power means work transfer rate, per unit time. The work transfer can be of several kinds (mechanical, electrical, chemical, magnetic). The name thermodynamics is about power (from dynamis in Greek), and about the movement driven by power, as spelled out by Sadi Carnot in “Reflections on the Motive Power of Fire”.

Nothing evolves unless it flows and has the freedom to change its architecture such that it provides greater and easier access to the available space. Evolution means changes in design that occur in a discernible direction in time, as if oriented toward an objective. Evolution is in the eye of the observer. Evolution is the universal phenomenon that unites the three classes of systems illustrated in Figs. 3-5.

Figure 3. The evolution of design space of power plants, the crest of which is marked by the rising first-law efficiencies of the most efficient models.
Figure 4. The evolution of the design space of power plants, which is bordered from above by the second-law efficiencies of the new models that were adopted.
Figure 5. Few large and many small: the evolution of the hierarchical population of the major airplane models during the 100-year history of commercial aviation [12].

Thermodynamics grew out of engineering from the human urge to have power, to enhance the effect of human effort. From the beginning, this science was about improving a design, which means changing the existing flow configuration of the thermodynamic system. With thermodynamics, humanity made enormous leaps while guided by the ‘objective’ tendency and all its related manifestations and concepts, from cheap power, efficiency and economic sense to sustainability. Thermodynamics itself made steps toward being better, broader and more useful, with new methods and results in its new chapters: exergy analysis, thermoeconomics, entropy generation minimization, and design [4-17].

Design means drawing, an image with message and purpose [18]. Design requires visualization, evolutionary images of macroscopic systems, all flowing and morphing. Design thinking is oriented against reductionism. It is holistic, macro, against the infinitesimal. Flow architecture, evolution (design change) and the future have always been and will continue to be the object of thermodynamics.

Nature impresses and inspires us with changes, behavior, surprises, some good and some bad, all from our point of view. All these are our observations. Observations that are of the same kind and occur in the billions represent one phenomenon. Observations of a second kind represent a second phenomenon, and so on. Each phenomenon is distinct—it is not to be confused or conflated with the second and the third. One phenomenon is a unique, self-standing and universal as a trend (an urge) in nature. The phenomenon of irreversibility (one way flow, from high to low) is not to be confused with ‘what goes up, must come down’ (the conservation of energy in a body thrown upward).

In science, each distinct phenomenon is accounted for by a principle, also known as ‘law’ and ‘first principle’ in scientific publications in English and other modern languages. Like science itself, the concept of principle is primordial, and much older. In Latin and its contemporary descendants, ‘principle’ means ‘first principle’, because princeps means first and foremost, and principium means a beginning, or origin.

Because the phenomenon is self-standing, its principle is self-standing because it cannot be deduced from other principles. Two phenomena, such as irreversibility and energy conservation are summarized as two principles, the second law and the first law. Another phenomenon, such as the evolution of freely morphing flow configuration, is summarized as another principle, the constructal law.

In the creation of thermodynamics, these three phenomena are evident as the origin of the principles that were identified along the way (Figs. 1-5). Principles are necessary in order to compress the volume of observations, and to make the story of science easier to pass on to the next generations. Principles are dependable because they summarize ‘the facts’. To rely on known principles in order to predict how things and behavior should be in nature is to conduct theory.

Misconceptions, as ‘new’ science

Sadly, students of science today are not taught any of the above. They are taught other things, some wrong. They are being misled by followers of the believers in the infinitesimal, believers who in their time were themselves lured toward reductionism. All you have to do is read what many anonymous scientists and editors post as “thermodynamics” on wikipedia [19]. They agree with each other. The same group censors (opposes and deletes) the attempts to define, explain and transmit thermodynamics correctly. Thermodynamics used to be brief, simple and unambiguous. Today, confusion reigns in public discourse and scientific papers. The words “thermodynamics” and “entropy” are pasted on new concepts without respect for their proper meaning. Recently, I made an attempt to clarify this situation [20-22], so here are a few excerpts:

We are often told that nature is complicated. Not if you see nature from thermodynamics! Nature is the simplest thought imaginable, because she (natura) consists of only two systems, your system (the portion selected by you, the observer, for contemplation) and the rest, the environment, which is also selected by you. Nature, system and environment are in the eye of the observer.

Process means the change in the state of the thermodynamic system. State is the collection of numerical values that represent the system features, which are called properties.

If your chosen system generates power in order to move through its environment, then the world that you contemplate behaves as an engine & brake whole (Fig. 2), that is an engine that is dissipative (irreversible) by its very nature. Through movement, the brakes dissipate the power generated by the engines. Others may contemplate other systems that generate power and movement (waterfalls, animals, atmospheric and oceanic currents). For all the thinkers together, the same world as yours is an endless collection of intertwined (embedded) engine & brake flow systems.

We are often told that nature is nondeterministic. Not if you see nature in the crystal ball called science! With science, we know in advance how nature will be. Science is the human contrivance (the add-on) that enables all of us to anticipate the future, to move more easily—economically, safely, farther, longer in time—during our lifetime flow on the earth’s surface (cf. Fig. 2). Science evolves because we—the human and machine species—evolve. With the science of today we are better movers than yesterday. When I was a student, predicting the weather two days ahead of time was guess work. Today we know what the weather will be next week, everywhere on the globe.

We are often told that disorder is increasing. No, because observed is also the opposite, which is the ubiquitous phenomenon of design birth and evolution in nature. Order is in the eye of the observer. Where many see the trivial (diversity), few see the subtle (order, organization, principle). Many attribute ‘disorder’ to the second law. That is false. The second law says nothing about “disorder”; review Clausius and Kelvin’s statements:

Clausius: No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.

Kelvin: Spontaneously, heat cannot flow from cold regions to hot regions without external work being performed on the system.

These famous statements should remind us that a new law does not have to be stated in mathematical terms. The second law of thermodynamics was stated in words, as a mental viewing, not in mathematical code. The mathematical inequality came later, when Clausius (not Boltzmann) invented the property called ‘entropy’. Like any other law of physics, the second law of thermodynamics is a concise statement of a distinct universal tendency (one phenomenon) in nature. That tendency is irreversibility, the fact that everything by itself flows one way, from high to low.

Measurable is the change in the entropy inventory of a special closed system selected for a particular measurement. Entropy change from state 1 to state 2 is the name for the integral of δQ/T during a specially selected ‘reversible’ process from state 1 to state 2, where δQ is the infinitesimal flow of heat from the environment to the system during the process, and T is the temperature (kelvin) of the system boundary, at the spot crossed by δQ. A reversible heating process is so special (and not real) that at any time between state 1 and state 2 the system is isothermal and in equilibrium with its environment, which is the heat source.

What can also be measured is the entropy that is generated by an unambiguously defined system during an unambiguously described process. For example, if the system functions as an engine—receiving net heat transfer and transferring net work to the environment—then by calculating the theoretical work output in the reversible limit, and measuring the actual work output, which is always smaller than the theoretical work output, one can calculate the difference (the theoretical minus the actual) and divide it by the thermodynamic temperature of the environment: the result is the entropy generated during the process, e.g., cycle or steady-state operation. This calculation is the Gouy-Stodola theorem [2, 4, 21], which is a theorem (not a law) because it is deduced from the first law and the second law, combined [21]. The entropy generated by a refrigeration system can be measured similarly, as the positive difference between the actual power requirement and the theoretical (reversible limit) power requirement, divided by the thermodynamic temperature of the ambient.

To measure entropy as it is being generated (produced) is not to engage in ‘name dropping’, to impress an audience that, although science loving and educated, is not acquainted with the word entropy. To measure entropy is deathly essential for our own evolutionary design and survival as the “human & machine” species [20, 23, 24]. The contrivances that we study by invoking thermodynamics, from power plants to water falls, windmills and domesticated animals, are our add-ons. They make each of us bigger, more complex and immensely more powerful than our naked bodies. Contrivances are human. They are the add-ons that enhance the effect (the impact) of human effort (from the Greek word míchaní). Contrivance is the historic and most general meaning of the word ‘machine’ today. Contrivances make our life movement (Fig. 2) more efficient, farther on earth, and with longer time.

Many confuse the second law with the notion that in a box filled with identical particles the assembly tends toward a larger number of probable states, from which the claim that the second law is probabilistic. This is the core idea of statistical mechanics, which is a self-standing and younger field, much narrower than thermodynamics. Why narrower, because to assume a swarm of particles in a closed box is to throw away the “any system” power of thermodynamics. The “any system” is the most general system, while the box with bouncing invisible particles is the extremely special, the local, the extremely particular system with a configuration that is chosen.

Even in an isolated system that proceeds toward death according to the second law, the natural emergence of ‘order’ and evolution is plain to see. Think of an isolated system initially filled nonuniformly with fluid (high pressure on one side of a partition, and low pressure on the other side), and you will recognize the birth of macroscopic organization, flow structure and evolution (turbulence, jets, eddies). Think of an isolated system containing initially two bodies, one with positive charges and the other with negative charges. On the way to its second-law death, the isolated system impresses us with lightning, which is a macroscopic phenomenon of flow organization and evolution. This is contrary to claims that the second law accounts for evolution. The evolution phenomenon is accounted for by the constructal law, not by the second law.

The reductionism hidden in the isolated box with numerous identical particles has attracted many. For example, some physicists (e.g. Refs. [19] and [25]) view the evolution of big living things (animals) on Earth as those particles in that box, each individual capable of existing in more probable and less probable “microstates”. What about the food, fuel, power, engine-like design, size, shape, diversity, locomotion, flow path and evolution of each of these “particles”? This makes no sense. Clearly, those who know only the recent (statistical thermodynamics) believe that they can shoe-horn the old and the macro (all of nature, rivers, celestial bodies, animals, engines) into their micro probabilistic narrative. That is wrong, and the confusion does not stop there.

We are also told that all living forms conduct some sort of computation (sic) as a crucial component of their adaptive potential [26]. A recent review paper [27] teaches the three faces of entropy which do not include the original entropy of Clausius (that one is reduced to a single line in the Introduction: “an extensive property that links temperature with heat,” which is a statement that I do not recognize).

A science book [28] defines thermodynamics this way: “Thermodynamics is the mathematical physics of gases” (p. 200), which is unrecognizable. The book also teaches that the second law of thermodynamics “states that, in a closed system, entropy (S) is always steady or increasing” (no, that happens in an adiabatic closed system, not in any closed system). The quotation continues: “Thermodynamic entropy is, roughly speaking, a measure of how disordered a system is. A system that starts out in an ordered, uneven state—say a hot region next to a cold region—will always tend to even out, with heat flowing from the hot area to the cold area until evenly distributed.” This long quotation illustrates the shoe-horning of reality into the narrow (micro, disorder) paradigm. The writer (a math professor) misrepresents the macro process from nonequilibrium (‘uneven’) to equilibrium (‘even’) into a fictitious story about order and disorder. Why fictitious, because ‘uneven’ does not mean ‘order’. The uneven initial state in this process can be any system in any nonequilibrium state, such as a body of fluid in highly turbulent flow, a system that most people would recognize as chaotic, disorganized, not ‘order’.

We are often told that the laws of thermodynamics hold only for closed systems. This is not true. The laws of thermodynamics are universally valid, for any system, closed or open, isolated or not, steady or unsteady. The confusion is understandable because during the birth of thermodynamics from the union of the ‘heat’ and ‘work’ lines (Fig. 1) the system that preoccupied the minds of the pioneers was a closed system: a heat engine operating in cycles or in steady state, while in communication with an environment that has two distinct parts, one hot the other cold, the fire and the atmosphere. The laws were generalized for open systems during the second half of the 1800s, chiefly because of the advances in locomotive and power plant evolution.

None of the advances made in the technologies that generate and use power today would have been possible without the correct application of the laws of thermodynamics to systems that are modeled as open and time dependent, which is the most general model, the “any system” object of thermodynamics.

We are often told that the laws of thermodynamics pertain to equilibrium states. This is contradicted by the presence of the inequality sign in any mathematical restatement of the second law, which refers to the universal tendency of irreversibility in all the flows, inside the system and between system and environment. Flows happen because they are driven by temperature and pressure differences, and because systems with differences are not in equilibrium. They are not in the dead state. On the contrary, most of the systems modeled after nature and analyzed in science are in live states [20], with flows, configuration and freedom to change. The arrow of time is painted visibly on live phenomena: the evolution of flow organization throughout nature, animate and inanimate.

People like to talk about the principle of entropy increase. There is no such principle, and whether the entropy (or some other property) of your system increases depends on how you select your system. This misconception is due to the (correct) notion that for a closed system that cannot experience heat transfer with its environment (called adiabatic, a very special kind of closed system) the second law states that the system entropy inventory (a property) must increase in time, while ‘any’ change occurs inside the system. An even more special closed system that is adiabatic is an isolated system (closed, no heat transfer and no work transfer).

Because of the second law statement for such special cases, many believe that the second law accounts for organization, evolution, life, death, and the arrow of time. This is false. The second law says nothing about architecture, design (contrast, black lines on white background [18]), evolution (design change) and the time arrow of evolution (design change). Review the Clausius and Kelvin statements of the second law. The second law is the law of physics of the natural phenomenon of irreversibility, nothing more, and nothing less.

We often hear that the organization that we see all around is governed by a maximum or minimum principle. This contradicts language and logic, not just thermodynamics. Minimizing entropy generation cannot be the same as maximizing entropy generation, and minimizing flow resistance cannot be the same as maximizing flow resistance. Because of the word “entropy” in such claims, many believe that the second law covers entropy generation minimization and maximization, which is false. Reis [29, 30] has shown that these contradictory statements of extremum and optimality are consequences of the constructal law. Entropy and entropy generation are eminently different concepts. Entropy is a function of state, while entropy generation is not [21].

Models and drawings

From its inception, thermodynamics was communicated by means of models and drawings, which continue to dominate the textbooks today. A new subject comes with new terms and concepts, and because it is new it is more difficult to convey than older subjects with established terminologies and mathematics. ‘Teach the simplest first’ is the wise way to convey any subject, not just the newest and the most subtle.

The simplest is called ‘model’, which is defined as a simplified facsimile of a physical object that was observed before the model was conceived, drawn and built. We saw this in the memoir of Sadi Carnot [31], where the real thing (the steam engine), which was invading the continent from Britain, was reduced to one cylinder filled with an ideal gas and fitted with one piston, and no mathematics. This model and its cyclical functioning as an engine were described mathematically and graphically (in diagrams) ten years later by Émile Clapeyron [32], and by many other authors since. Clapeyron is the artist who drew (three times!) the famous Carnot cycle as a curvilinear parallelogram.

The chief attraction in this gallery of models and drawings is the engine (Fig. 6), now called power plant (read again: power, not work, and not ‘energy’ per unit time), which appears in an unending sequence of configurations that promise higher efficiencies than their precursors. Figure 6 is the 1977 temperature-heat (T-Q) diagram [33, 34], which has been used ever since in many applications [4, 5]. Refrigeration plants (Fig. 7) are the second attraction in this exhibit, and so on. The book of thermodynamics is an illustrated story of the evolution of design (drawings) even though from the 1850s onward the two principles (the first law and the second law) did not command in any way that design and evolution should happen. What was missing as a principle then became the constructal law today (Fig. 1).

Figure 6. The 1977 temperature-heat (T-Q) graphic method for power generation [4, 5, 33, 34].
Figure 7. The 1988 exergy wheel diagram for a vapor-compression refrigeration cycle [5].

The value of the simplest did not go away as the subject matured. My view of this continuing stream of science-art creation is colored by my penchant toward making drawings [33-39]. That is why the samples that I exhibit in Figs. 6-14 are from my time and peer reviewed publications. The captions of these figures paint the big picture to which they belong: evolution in nature (Fig. 1).

Figure 8. 1974 model for illustrating the irreversibility of heat transfer through the insulation of a refrigeration machine [13]. The opportunity to extract work (power) from the heat flow is located in the detail on the right side of the drawing. The compartment in which entropy is being generated is separate, in the detail on the left.
Figure 9. 1976 model for illustrating the destruction (loss) of useful work (power) during heat transfer across a finite temperature difference [11], also in Ref. [4]. This mental viewing is the basis for the physics of flow and movement in nature (Fig. 2).
Figure 10. 1976 model [4, 11] of why the performance of a real engine should be inferior to that of an engine imagined in the reversible limit. The imperfection of the real engine (the dashed-line system) is isolated in the heal-leak detail on the left side. The remainder of the model, on the right side, captures the operation in the reversible limit.
Figure 11. 1982 model [4] of a real engine operating between a high-temperature system (TH) and the ambient (TL). The engine system is viewed as a sandwich of three subsystems: two temperature gaps (TH – THC and TLC – TL), each crossed by heat flow, and the remainder that is free of irreversibility.
Figure 12. 1984 model that reveals the dissipative engine responsible for ‘free’ or ‘natural’ convection [5]. The turning fluid volume is the thermodynamic system. The system is an engine coupled to a brake, which dissipates the power generated by the engine. The heat input comes from the left (the hot wall), and the same heat current is rejected 100% to the cold fluid reservoir to the right. The rejected heat current is the sum of the heat current rejected by the engine and the heat current rejected by the brake that dissipates the power generated by the engine. This model is a consequence of the 1976 drawing shown in Fig. 2.
Figure 13. 1988 model showing why the performance of a refrigeration system (the large rectangle) with heat leak from ambient (T0) to the cold zone (TL) is inferior to that of the same system in the reversible limit [5]. Throughout Figs. 8-12, note the graphic identification of each locus of imperfection (irreversibility), and the separation of this feature from the remainder of the system, which is modeled as perfect, i.e., irreversibility free.


Figure 14. 1988 drawings showing the evolution of the configuration of steam-cycle power plants [5, 38]. Compare the evolution of the architecture (top) with the evolution of the cycle traced by the working fluid on the T-s diagram (bottom). The arrow of time points tothe right, toward greater efficiency, because of the increasing gap between the average high and low temperatures experienced by the working fluid. These drawings underpin (and illustrate most succinctly) what went on in the constitution of the power-plant contrivances during their evolution in Figs. 3 and 4.

The simplest drawings that have been adopted have three features that make them realistic enough and useful as communicators of scientific knowledge. They illustrate flows, irreversibility, and opportunities (freedom) to change the drawing, to make it better. These features are evident in all the samples exhibited here. The flows are heat interactions, work interactions and streams of fluid. The irreversibility is placed by the artist in a special organ, which is distinct from the rest. In that organ heat flows across finite temperature differences, fluid flows across finite pressure differences, and so on. That organ accounts for the thermodynamic imperfection—the irreversibility—of the whole object that is being modeled. Features such as temperature and pressure levels, sizes of diameters of pipes and heat transfer surfaces, and time intervals (rhythms) of process execution are free to change and to be discovered. Why, because the whole enterprise of modeling is dedicated to discovering the features that, if changed, would make the whole drawing better.

Mistakes in modeling happen, and this is normal, it’s not a big deal. In fact, mistakes are useful and educational after they are identified and corrected. Science is self-correcting, after all [22]. Damaging is when the mistake is repeated intentionally by its original authors and associates, in tendentious publications that continue long after the mistake has been corrected. It seems that the purpose of such publishing is to persuade the readers that more papers prove the correctness of the original mistake. It is as if science is about counting votes. Science is not democracy. This kind of publishing is false science. The Tower of Babel that ensues is a threat to the discipline, the next generation, and the integrity of science [40-44]. Here are two examples:

First, the power plant model of Fig. 11 was proposed independently by several authors, whose work is reviewed in Refs. 6, 21 and 45. For example, in Ref. 4 (p. 146) it was used in the first consideration of the problem of allocating a finite area among the two heat exchangers, which is the main purpose of the model. Novikov [46] had only the hot-end heat exchanger in the model. Chambadal [47] had a combustion chamber in place of a postulated high temperature source of heat. Curzon and Ahlborn [48] included both heat exchangers but made the unrealistic assumption that the heat input arriving from high temperature is free to vary, i.e., infinitely plentiful, coming from a high temperature reservoir. This assumption is not realistic for terrestrial power plants, because on earth there is only one temperature reservoir (the atmosphere). Unlike the ambient, ‘fire’ is expensive, not free, as was pointed out in Refs. [6], [21], [45] and [49]. Criticism of this line of work was also provided by Gyftopoulos [50, 51] and Moran [52]. In spite of these corrections, publishing based on the model of Ref. [48] continues unabated under new labels such as finite-time and endoreversible thermodynamics.

Second, there are papers now that claim an “analogy” between heating a solid body (heat transfer) and charging an electrical capacitor (work transfer). Examples are discussed most recently in Refs. [34, 36]. The analogy (named ‘entransy’ by its adepts) is false science, as was proven by many independent authors [53-61]. Charging a capacitor is not analogous to heating a body. Charging a capacitor is analogous to stretching a spring, because both processes are driven by work input. Work must be done to stretch the spring and to move charge between the plates of the capacitor. The elongation of the spring, and the separation of charges between plates (voltage, spacing) are macroscopic features of configuration, design.

Heat transfer and work transfer are eminently different. They are not analogous. This is why thermodynamics emerged as a new science (Fig. 1). Had work transfer and heat transfer been analogous, the caloric line would have been absorbed into the older line, mechanics, not thermodynamics. Mayer and Joule discovered the equivalence between the respective units of measurement of work and heat, not the analogy between work and heat. Equivalence means equal valence, strength, value, weight, etc., as in 1 kg of meat versus 2.2 lbm of cheese, not the analogy of meat and cheese. Mayer and Joules’ predecessors knew the difference between working and heating, and between macroscopically identifiable energy change (kinetic, gravitational potential) and not identifiable (internal energy). As shown in Ref. [22], the heat-work analogy is a mistake as egregious as claiming an invention of a perpetual motion machine.

“Beware of false knowledge; it is more dangerous than ignorance.”
George Bernard Shaw

Writings fly, laws remain

Thermodynamics is not a mantra, and neither is the constructal law. Figure 1 makes very clear the evolutionary being of this science. Indeed, in the twenty years since its arrival [62, 63], the field of “physics of life and evolution” that was defined by the constructal law is growing in many directions, all good, including some that propagate under new names that tend to obscure the oneness of the phenomenon and the origin of the principle.

For example, antifragility [64] is defined as “the resilient resists shocks and stays the same; the antifragile gets better”. From the point of view of the constructal law, the system gets better because it is a live flow system with freedom to morph in the evolutionary direction traced by the law. Others use terms such as heterogeneity and complexity, which would be appropriate for the still (dead) image of a configuration, but miss the new physics, which is the evolution phenomenon, the natural evolutionary tendency of flow of configuration, the freely morphing of all configurations in a discernible direction in time, the time arrow of nature [65]. Very recent work with the same objective is described [66] as “dissipation-driven adaptation of abiogenesis” (for the translation of that, view Fig. 2: it means the evolution of non bio flow systems that dissipate power as they flow and morph with freedom).

In 2013, Pross and Pascal [67] proposed that “a general theory of evolution may be expressed as follows: All stable (persistent) replicating systems will tend to evolve over time towards systems of greater DKS.” Their DKS is shorthand for “dynamic kinetic stability,” which in the terminology of thermodynamics means “flow system.” Their stable DKS means steady flow, and “stable” sounds scientific because there is a stability principle in thermodynamics (based entirely on the first law and the second law and nothing more). These word matches are crowned by the use of the words “evolve” and “persistent,” which reveal that their authors’ version of evolution has a lot in common with the constructal law statement of 1996, in which the verbs to evolve and to persist define life as physics. Unlike the constructal law, which is about all physics, Pross and Pascal limit themselves to biological systems.

In 2014, Georgiev et al. [68] proposed “to account for the phenomenon of self-organization based on a principle of increased physical action, which provides a means to define what exactly organization is and how it is achieved and measured.” They define “physical action” as the energy and time necessary for motion. Put together, these words convey a message that matches the constructal law: the evolution of flow organization leads to easier flowing (which when the driving force is fixed, means increased flow, or movement). Georgiev et al. use the word “action,” which sounds scientific because it reminds us of the 1700s and mathematics, analytical mechanics and variational calculus. In 2000, I drew attention to history and “action” in the last paragraphs of my book “Shape and Structure, from Engineering to Nature” [23], where I wrote:

“Performance improvement, or optimization, is an old idea and an even older natural phenomenon. It has been with us throughout the history of engineering. Its reach, however, is much broader and more permanent: everything exhibits it. We can be sure that the performance of power plants—the performance of man, really—will continue to improve in time, in the same way that, in time, the rainfall will generate a more effective (dendritic) flow structure. Examples of geometric maximization of performance are everywhere, in the optimal folding of protein structures, the optimal configuration of reversed-field pinch plasma, the geometrical control of catalysis, adsorption and multiphase processes, the electromigration of metals, and geochemical patterns. Geophysicists and physiologists are converging on the conclusion that the optimization of performance has been the generating mechanism for geometric form in all plants, animals, and inanimate flow structures.

If this phenomenon is so old and prevalent, then what is new? New is the streamlining of its study into a single principle, which is self-standing, a law. This was my objective in this book. Most of this work could have been done one or two centuries ago, before thermodynamics. The geometric minimization of resistances to heat and fluid flow could have been accomplished based on Fourier’s heat transmission and the hydrodynamics of Bernoulli, Poiseuille, and Darcy. It is a mystery that this was not done then, because that period was still influenced by Leibnitz’s, Maupertuis’, and Castigliano’s intuition that, of all possible processes, the only ones that actually occur are those that involve minimum expenditure of “action”. Instead, modern physics embarked on a course tailored to the principle of infinitesimal local effects. Constructal theory is a jolt the other way, a means to rationalize macroscopic features, objective, and behavior.”

There are many more examples, all from physics, which is the establishment that is now starting to catch up with (and claim) the physics of evolution, life and design that morphs with freedom. Marletto [69] calls it “constructor theory”, which is very close to constructal theory, in substance and title. Materials science is in the news with “active matter” [70], which is another name for “live system” (with flows, morphing while driven by power), which the constructal law field recognized [71] as the opposite of the “dead system” that was used for 100 years in thermodynamics.

Wissner-Gross and Freer [72] describe intelligent behavior as a way to maximize the capture of possible “future” histories of a particular system. This is the same as the constructal law: evolution to greater access to future configurations of movement in space and time, which is the definition of “future”. These examples illustrate the trend to express the life-as-physics idea in a language that sounds more mathematical and more scientific to the reader.

Jaffe and Febres [73] call “synergy” the creation of a whole that is greater than the sum of its parts. Synergy, the word, is certainly not that. The name for that phenomenon is construction with purpose (as in ‘constructal’), or design, contrivance, organ, organization, purpose, direction, machine, etc. The dictionary definition of ‘synergy’ is static, descriptive, not about change and the time arrow of change. It is not about ‘creation’, which is dynamic, evolutionary, morphing with direction, objective, and purpose, and which is predictive if the constructal law is invoked. The key words in the constructal law are two: ‘evolve’ (that’s flow design change in a discernible direction over time, toward easier flow access), and ‘constructal’, which comes from construere in Latin.

The examples discussed up to this point represent science and how it is emerging, overlapping, and spreading. The next example is about a different kind of science, overlap, and spreading:

Authors from P. R. China [74] used the constructal law of Refs. [62, 63], but instead of “constructal” they chose to name it “bionic principle”. Why create the confusion? To benefit whom? For a detailed comparison of Refs. [74] and [63] see Ref. [56]. More recently, these authors honored their name with the symbol G for their own quantity in thermodynamics [75], with disregard for the symbol G that represents Gibbs free energy, and also with disregard for J. W. Gibbs who did not name the free energy (at constant T and P) after himself. Indeed, as I asked in Refs. [34, 36], for whose benefit is such confusion being generated and propagated?

What is to be done

Improve and defend science. Teach thermodynamics and the meaning of its concepts correctly. Why, because they are good, useful and, until better ideas arrive, true.

Science evolves, as an add-on to the evolving human & machine species. What works is kept as an add-on to the architecture that was flowing before. What is false is swept aside, and forgotten. This is the evolutionary ‘morphing’ design that science is.

The science that stays is the science that is useful to people. This truth is worth contemplating, because most of our contemporaries in science have difficulty with the concept of usefulness (objective, purpose, function, design, evolution), even though they themselves rely on it permanently, in thought and way of life.

Clausius wrote in 1851: “I believe, nevertheless, that we ought not to suffer ourselves to be daunted by these difficulties; but that, on the contrary, we must look steadfastly into this theory” [76]. This quote is particularly timely today as we are facing a situation very similar to the one faced by Clausius. To account for the phenomenon of irreversibility, Clausius had to formulate a second principle, the second law of thermodynamics, in addition to the first law for the conservation of energy. Today the new principle is evolution of design (Fig. 1), and the new concept that this principle defines is objective, purpose, life, evolution, or direction of evolutionary changes (cf. Ref. [23], p. xix).

Science is self-correcting. This key truth of science needs to be broadly communicated to all, not only to those who intentionally propagate errors that have been corrected.


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One thought on “Thermodynamics today | Prof. Adrian Bejan

  1. Interestingly energy is not just about temperature. Kelvins law is incorrect, because energy does flow to higher temperatures from low, because otherwise there would not be such a thing as a flame, or the sun.

    You might call this inverted entropy.
    So thermodynamic law only covers half the spectrum.
    Energy & time theory is about time spins containing gravity/ and free energy which does not, but is the fastest one like the speed of light.
    This system understanding for instance has a greater parallel with electricity than with temperature/ although temperature can be an entanglement or a result of it.
    Electricity also is related to gravity, although this is hardly unferstood by man.

    The new energy/ time theory which is unknown to science so far is the universal theory and embodies all of this: to explain evolution processes and future, also containing at the same time parallel inverted relations and explaining quantum mechanics. Which in life is not an exeption at all, but standard.

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