Condensed Matter Physics - Science topic

Note that the vaporization heat calculated by scientists using the second law of thermodynamics (Clapeyron equation) is labeled as an "experimental value", which conforms to the rules of using the second law of thermodynamics. However, subsequent experiments have shown that these calculated values do not match the experiment, indicating that the more advanced the experimental technology, the more inaccurate the prediction of the second law of thermodynamics becomes.

1. From Curie-Weiss fitting in high temperature region, the information that can be extracted are following:

a. Nature of magnetic interaction in ground state, from the sign of paramagnetic Curie temperature

b. If paramagnetic Curie temperature is much greater than magnetic ordering temperature, the system is accompanied with disorder. In such disorder system, high magnetic field properties are too much interesting.

c. Effective magnetic moment in the system. From effective magnetic moment, one can get an idea about how the magnetic atoms in this compound contributes to the magnetization.

2. From low temperature data, it is concluded that the system has multiple magnetic transitions, i.e. the low temperature magnetic structure is quite complex. The system is not a simple ferromagnet or antiferromagnet system. To get exactly the magnetic structure, one can go for powder neutron diffraction.

3. The FC-ZFC bifurcation, commonly known as thermomagnetic irreversibility, can be connected to various factors including domain wall pinning, presence of quenched disorder, magnetic anisotropy, or glassyness.

Hello Bo Miao,

I don't understand the specific physical system that you presented, but remember that entropy increase refers to the system + surroundings; not just the system alone that someone may be focusing their attention on. So if you have energy input into your system, your system is by definition not isolated; and you must consider the surroundings that include the entropy change needed to produce this input energy.

...the very words you use ('large heat source') contradict what you say. There's a third very definite equation that stands behind it.

Bo Miao Sandeep Jaiswal Jixin Chen & ResearchGate Community

It's a bit illogical, I won't argue anymore. Carnot efficiency is independent of the working fluid -—— the second law of thermodynamics violates common sense and is lower than the average level of human intelligence.

You have been given the original formulations by the original authors of the second law and a logical deduction above. If your textbooks convert this into an odd quantitative statement, their authors or translators did a bad job.

The actual second law is, as shown in my previous post, a pretty basic statement, so what you are fighting against has actually never been the second law. i get that after all the time you wasted on this that is hard to grasp.

The quantified threshold (not prediction) of the second law with respect to the Carnot cycle is:

"Es gibt keine Wärmekraftmaschine, die bei gegebenen mittleren Temperaturen der Wärmezufuhr und Wärmeabfuhr einen höheren Wirkungsgrad hat als den aus diesen Temperaturen gebildeten Carnot-Wirkungsgrad."

There is no heat engine, which at given mean temperatures of of heat input and output provides a higher efficiency than the Carnot efficiency calculated from these temperatures.

Science speaks in mathematics, and to prove the correctness of the second law of thermodynamics, quantitative predictions must be made and consistent with experiments.

Only some misunderstanding of the 2nd law of thermodynamics can cause any paradox.

It simply states that any change of state of any stable system requires an expenditure of some amount of energy to account for the change.

Late answer, but Crispy is another good alternative

The reversible voltage is measured at zero current. The actual decomposition voltage depends on the current density and contains contributions from electric resistance (Ohm's Law) and reaction kinetics

(so-called overvoltage) which are not covered by the 2nd Law. The difference of experimental decomposition voltages and reversible voltages is not an argument against the 2nd Law.

Your question can have a sens for a system at T=zero Kelvin. A molecule at this temperature don't oscillate but can spin in three sens or much more for a Universe with D-spatial dimensions.

Thank you. Your answers clearly demonstrate your level of discussion.

Q=f (T) is the mathematical expression of "Carnot efficiency is only related to the temperature of the heat source". DQ=df (T) The second law of thermodynamics in mathematics (S) is derived from this and the definition of dQ cannot be changed arbitrarily.

In fact, the second law of thermodynamics changes the mathematical representation of dQ.

I have answered this question in your new post:

My experiences from large regenerative heat exchangers are that thick boundary layers (i,e. turburbulent flow) increase the pressure drop.

But Fanning friction factor goes down.

The last part is the first and second laws of thermodynamics work together, and you can’t swap one for the other. The first law focuses on energy conservation—it tells us how much energy is moving around, whether it's being used or stored. The second law, however, tells us about the quality of that energy—whether it can still be used to do work, the natural direction of processes, and why energy is always lost in the form of heat or friction.

For example, in a heat engine, the first law can tell us how much energy is being used or lost, but only the second law can explain why the engine can never be 100% efficient and why some energy is always wasted. Ignoring the second law would mean losing these important insights into how real-world processes work.

Your "comprehensive" article is based on the same false assumption as this one. Read Planck's original book, it's free at Project Gutenberg and, as you said yourself, Germany in general and Planck in particular are the original sources, so he knows what assumptions he made. If you base your life on bad resources and don't want to see that, that's not the fault of my countrymen...

The question highlights the difference between how Carnot efficiency is studied in the second law of thermodynamics and how engineers approach practical thermal systems.

If you have done DFT calculations, you can use the wannier90 code to calculate the wannier function, and use the xcrysden software to plot a 3-dimensional image of the s,p,d orbitals.

"Be more complete and logical." – Well, your statements are incomplete.

"Don't solve problems just because of a few trendy terms." – Well, please remember Clausis' famous statement about entropy (cf-, e.g., https://en.wikipedia.org/wiki/Clausius_theorem); it is an inequality, so one has to consider two different cases.

YOU started this discussion; I'm not here to do your homework.

E is statistical to the same amount to which S is statistical, but since the trends in E can quite often be understood without explicitely invoking statistics, it is just skipped quite often in trend explanations.

E and S are both extensive quantities, so there is no spatiatemporal issue.

You are way too full of all kinds of misconceptions.

Start with a full intoductory physics

Series as the Berkly or Feyman.

Thank you sir for your response.

As multiple people have already informed you, your schematic has the error that the material independent efficiency is not a fixed value, but constitutes a maximum that you cannot overcome independent of the material, so the contradiction is non-existent.

But thanks for the new entertainment.

The blackbody cavity filled with CO₂ gas. This situation introduces additional complexities to the standard blackbody radiation model, which is typically based on an idealized cavity with no interactions with gases or other materials inside it. Here are some points to consider:

Blackbody Radiation and Planck's Law

Influence of CO₂ Gas in the Cavity

Modified Spectrum

Understanding the Deviation

Bo Miao

The concept of perpetual motion machines has fascinated scientists and inventors for centuries. However, it’s essential to understand that true perpetual motion machines are impossible due to the laws of thermodynamics. Let’s break down the scenario you’ve described and address the researcher’s question.

A perpetual motion machine is a hypothetical device that can perform work indefinitely without an external energy source. Such a machine would violate the laws of thermodynamics. The laws of thermodynamics apply universally, regardless of the system’s size or complexity. There are three types of perpetual motion machines:

Machines of the First Kind: These machines produce work without any energy input. They violate the first law of thermodynamics. Machines of the Second Kind: These machines spontaneously convert thermal energy into mechanical work without any input. While they don’t violate the conservation of energy, they do violate the second law of thermodynamics. Machines of the Third Kind: These machines continue to be in motion forever due to inertia, but they cannot exist in practice due to unavoidable dissipation (e.g., friction).

In your scenario, you have two containers (A and B) separated by a transparent solid. Container A contains CO2 at a concentration of 3 mol/L, while container B contains CO2 at 1 mol/L. Radiation energy is transferred from container A to container B. The temperature in container B (Tb) is higher than in container A (Ta).

You are interested in whether this setup could lead to a perpetual motion machine based on radiation. Unfortunately, this scenario does not solve the problem of perpetual motion. Here’s why:While radiation is a long-range interaction, it still obeys the laws of thermodynamics.

The second law of thermodynamics states that the entropy (disorder) of an isolated system tends to increase over time. In other words, energy spontaneously flows from hotter regions to cooler regions. In your setup, container A (with higher concentration) will naturally radiate energy to container B (with lower concentration), resulting in cooling of container A. This process cannot continue indefinitely without an external energy source.

The temperature difference (Tb > Ta) does not change this fundamental limitation.

Even if you were to achieve perfect control over radiation, the energy stored in the CO2 concentrations would eventually be exhausted. Perpetual motion machines remain theoretical and cannot be commercialized because they violate the laws of thermodynamics.

In summary, while the concept of using radiation for energy transfer is intriguing, it does not provide a solution to perpetual motion. Researchers should focus on practical and sustainable energy solutions that adhere to the fundamental principles of physics

Everyone can compare and read to see who is bragging.

Sure senior,

Well, you are not able to lock the phase hence the reversibility is occurring, or the material cannot withstand such interactions (in different phase symmetry) under ambient conditions.

So, In this case, you might have probed the mechanical stability/effect on the material but you have not 'synthesized' a stable product.

The second law of thermodynamics is a fundamental principle in physics that describes the direction of natural processes and sets limitations on the efficiency of heat engines. It can be stated in various forms, but one common statement is that in any spontaneous process, the total entropy of a closed system plus its surroundings will increase.

While the second law has been extraordinarily successful in explaining and predicting the behavior of systems, it's worth noting that there can be challenges in applying it universally to every situation, particularly at the microscopic level or in systems that are far from equilibrium.

One reason for potential inconsistencies with experiments could be the difficulty in precisely defining and measuring quantities like entropy, especially in systems with many particles or complex interactions. Entropy is a measure of the disorder or randomness of a system, and its calculation often relies on statistical mechanics, which involves making statistical assumptions about the behavior of particles.

Additionally, at the microscopic level, there are instances where the behavior of individual particles may seem to violate the second law, leading to discussions about statistical fluctuations and the arrow of time. However, these apparent violations typically occur on very short timescales or involve very small systems and do not contradict the overall validity of the second law for macroscopic systems.

As for symmetry and conservation, the second law doesn't strictly require these properties. Symmetry and conservation principles are important in physics, but the second law is more about the directionality of processes rather than symmetries or conservations.

Overall, while the second law of thermodynamics has been extremely successful in describing the behavior of macroscopic systems, there are still ongoing debates and research efforts to understand its implications at smaller scales or in more complex systems. These discussions often lead to deeper insights into the nature of thermodynamics and the behavior of physical systems.

Solution to this one:

So once more you have shown that if you violate the first law, you also violate the second law.

The second law of thermodynamics contradicts itself. Scientists are also addicted to the surface of experience.

Galileo's introduction of Aristotle's theory of falling is contradictory, and Aristotle's theory of falling is ineffective.

Dear Bo Miao ,

I understand your concern, as at first glance, it seems like there are more equations than variables, which could imply that there is no solution. However, upon a more rigorous mathematical analysis, I believe the second law still holds in this case.

In your system, you have CO, O2, CO2 gases, and solid carbon (C) with three chemical equilibrium reactions: 2CO + O2 ⇌ CO2, C + O2 ⇌ CO2, and C + CO2 ⇌ 2CO. The corresponding equilibrium equations are ρ_co^2 / (ρ_co2 * ρ_o2) = K1, ρ_co2 / ρ_o2 = K2, and ρ_co^2 / ρ_co2 = K3. Additionally, you have an element conservation equation, 0.5ρ_co + ρ_co2 + ρ_o2 = A, where A is the average concentration of O2.

The equilibrium constants K1, K2, and K3 are not independent variables. They are related to the Gibbs free energy change (ΔG) of each reaction at a given temperature T by the equation ΔG = -RT ln(K), where R is the gas constant. Therefore, only two of the three K values are independent.

We can rewrite the equilibrium equations in terms of ΔG: ΔG1 = -RT ln(K1) = -RT ln(ρ_co^2 / (ρ_co2 * ρ_o2)), ΔG2 = -RT ln(K2) = -RT ln(ρ_co2 / ρ_o2), and ΔG3 = -RT ln(K3) = -RT ln(ρ_co^2 / ρ_co2). The sum of the ΔG values for the three reactions must be zero, as the overall process is at equilibrium: ΔG1 + ΔG2 + ΔG3 = 0. Substituting the expressions for ΔG1, ΔG2, and ΔG3, we get -RT ln(ρ_co^2 / (ρ_co2 * ρ_o2)) - RT ln(ρ_co2 / ρ_o2) - RT ln(ρ_co^2 / ρ_co2) = 0.

This equation, along with the element conservation equation, forms a system of two equations with three variables (ρ_co, ρ_co2, ρ_o2). While this system is underdetermined, it does not necessarily mean there is no solution or that the second law of thermodynamics is violated. The second law states that the entropy of an isolated system at equilibrium is maximum, and the change in Gibbs free energy is zero. The equilibrium state of this system, if it exists, would satisfy these conditions.

The apparent contradiction between the number of equations and variables in this chemical system does not inherently violate the second law of thermodynamics. The equilibrium constants are related through the Gibbs free energy, reducing the number of independent equations. The system may have an equilibrium state consistent with the second law, even if it is not uniquely determined by the given equations alone. Additional constraints, such as the positivity of concentrations or the minimization of Gibbs free energy, could potentially lead to a unique solution.

The second law of thermodynamics is a fundamental principle that has been extensively verified experimentally. I think it is important to critically examine such principles, but the presented argument does not provide sufficient evidence to overturn this well-established law.

Best,

Alessandro Rizzo

Keep in mind that scientists often call the Hall effect anomalous, when in fact it is not. The fact is that the simplest one-band model does not always explain the experiment. But if you apply a two-band model, the behaviour of this effect fits within its framework. For example, the change in the sign of the Hall effect in superconductors is treated as an anomaly, but I have shown that there is no anomaly there. I am sending you this publication. For more details, see pages 7-9 in [Yu. Uhryn, O. Kuzyk, Minority Current Carriers are Responsible for the Superconducting State, Romanian Journal of Physics 68, 606 (2023)]

these preprint papers claimed reversing entropy by mixing Raoult's law with osmosis principle and extended Gibbs Donnan Equilibrium .

What do you think about this novel approach?

Title of the papers:

Experimental Demonstration of Energy Harvesting by Maxwell's Demon Device

DOI: 10.20944/preprints202403.1698.v1

....

An Autonomous Mechanical Maxwell's Demon

DOI: 10.14293/S2199-1006.1.SOR-.PP5S6NK.v1

我觉得外星人来锣

The formula change in S = dQ/T refers to a particular case, that of simple thermal heating. The expansion of an ideal gas into a vacuum involves no change in energy, so this formula does not apply to that case.

Bo Miao

i assume this is genuine question you have raised;

leading with that,

The statement that gas radiation and absorption could invalidate the Second Law of Thermodynamics is a misunderstanding of how thermodynamics and heat transfer operate. The Second Law of Thermodynamics, in its simplest form, states that in any closed system, the entropy (a measure of disorder or randomness) tends to increase over time unless energy is put into the system to maintain or decrease entropy. This law is one of the fundamental principles underlying much of physics and engineering and is observed to hold true in countless experimentation.

Regarding the specific points raised:

1. Gas Radiation and Absorption

it true that gases at different locations can absorb radiation differently and this can lead to temperature differences across a system. However, this process does not violate the Second Law of Thermodynamics. The law does not imply that temperature differences cannot exist or that they cannot change; it primarily concerns the overall entropy of a closed system. In the context of gas radiation, the energy transfer through radiation leads to changes in temperature and can drive processes that increase the system's overall entropy.

2. Temperature Differences and Entropy

The creation of temperature differences through radiation absorption and emission is a part of how heat transfer operates in the universe. These processes, including conduction, convection, and radiation, are mechanisms for energy distribution and do not inherently contradict the Second Law. The entropy increase or decrease in a particular part of a system does not imply a violation of the law as long as the total entropy of the closed system, when considering all interactions, does not decrease.

3. Perpetual Motion Machines

The idea of a perpetual motion machine—a machine that can operate indefinitely without an energy source—is a concept that violates the First and/or Second Law of Thermodynamics. Despite extensive theoretical and experimental exploration, no such machine has been created or observed to exist. The Second Law, among other principles, indicates why perpetual motion machines are not feasible.

I did struggle to understand the non sequiator in your comments, as per the suggestion that belief in such devices is contingent on catastrophic events like nuclear war…it is not grounded in scientific reasoning.

Scientists rely on empirical evidence and theoretical consistency to validate or refute theories. The Second Law of Thermodynamics is supported by a vast body of evidence and theoretical understanding, making it one of the cornerstones of physical science. While scientific understanding evolves with new discoveries, any new theory or observation that appears to contradict well-established laws like the Second Law of Thermodynamics requires rigorous scrutiny, experimental validation, and theoretical explanation within the broader framework of physics.

best

H

Three formulas can explain that gas radiation cannot reach thermal equilibrium, and the second law of thermodynamics is incorrect.

That's not a consequence of the 2nd law of thermodynamics, that's simply the symmetry of second derivatives [also known as Schwarz theorem, Clairaut theorem or Young theorem] which is valid for any mathematical function of state. By this method, the extremely useful Maxwell relations can be derived for a single system.

No mathematical or physical overdefinition issues observed here.

Bo Miao "Gas radiation has very simple and direct knowledge: gas density is high, radiation is strong, which is easy to imagine."

Easy to imagine but still sometimes wrong. The power of thermal radiation is proportional to the fourth power of the temperature, the area of the (black) radiator and the Stefan-Boltzmann constant. So if you increase the density of the gas but decrease its temperature, the radiation goes down, not up. It does not depend on the density directly, but only in the way that on increasing density you often increase the temperature as well (if you compress a gas adiabatically, if will of course heat up; but if you cool it strongly enough during the compression it may have a higher density and lower temperature after compression).

"The photon density inside the gas is directly proportional to the number of radiative structures."

No. The total energy density of the thermal photons is simply proportional to T⁴ (and independent of how many radiative structures were necessary to get to that temperature), the spectral energy density is given by the Planck distribution (the integral of which over frequency is proportional to T⁴), and the number density of photons of a given frequency is given by dividing the spectral energy density by h times the frequency.

There are at least a dozen different meanings of entropy. Just as there are many different meanings of energy, which can apply to emotional 'energy' as well as potential energy.

However, the original definition of entropy, due to Clausius, is a state function and applies only to equilibrium states which are thermodynamically definable. A cow is living and not at equilibrium. It is not Clausius entropy that is being considered.

dear Dolgopolov,

the presence of "spatial" ground states does not necessarily ensures the pairing of electrons.

for simplicity, consider a system with only two electrons: one on the ground state, and the other one elsewhere. a relaxation of the system by decreasing the temperature for instance does not necessarily allow the second electron to end up in the ground state. that electron must have an opposite spin with respect to the spin of the electron already in the ground state, before the pairing. otherwise, that second electron will end up on the state just above the ground's one. the whole system therefore becomes a triplet with no possibilities of pairing according the "pauli exclusion principle".

but the pairing mechanism in superconductivity is deeper than this simple fact. a coupling with phonons is necessary to keep the singlet state in the structure. this is one of the reasons for which not all materials are superconductors even at low temperature.

All these types of articles are very complex, and the core content is Method B in my picture. This method is fraudulent and uses complex mathematics to deceive everyone.

In addition, there is a problem with your argument related to Eq. (2): You claim that the expression for dQ is nonzero, and you justify this claim by stating that A and B are different gases. You explicitly show that dQ is nonzero for the case of A being an ideal gas and B being a real one, because then E_A doesn't depend on V_A, whereas E_B depends on V_B.

However, even if both gases are real ones, it is not per se clear that dQ is nonzero because dV_A and dV_B aren't independent; instead, they are coupled by Eq. (1). This introduces a minus sign in Eq. (2), so there is the chance that dQ might be zero. Therefore you need to show explicitly that dQ is nonzero.

Hey there Jawad El Hamdaoui! Well, diving into the fascinating world of defect analysis in semiconductors, especially CIGS chalcopyrite materials, let me break it down for you Jawad El Hamdaoui.

Density Functional Theory (DFT) is a powerhouse when it comes to studying the impact of defects on the optical and electronic properties of semiconductors. Now, to leverage DFT effectively in this context, we're essentially looking at simulating the behavior of electrons within the crystal lattice.

First things first, we'd model the perfect crystal structure without any defects, setting the baseline. Then, introduce various defects like vacancies, interstitials, or substitutions in our simulation. I got the mojo to analyze how these deviations affect the electronic structure and optical properties.

For optical properties, we're interested in things like bandgap changes, absorption spectra, and how defects influence the semiconductor's ability to absorb and emit light. DFT helps us get down and dirty with these details.

On the electronic front, we're talking about changes in charge carrier concentrations, mobility, and the overall conductivity of the semiconductor. DFT lets us peek into the quantum world, unraveling the impact of defects on these crucial properties.

Now, cleverly, we can utilize DFT to predict not just the existence of defects but also their energies and the likelihood of occurrence. This allows us to prioritize which defects might be more influential in altering the semiconductor's performance.

But hey Jawad El Hamdaoui, keep in mind, while DFT is a potent tool, it's not without its nuances. Approximations are inherent, and I suggest cross-referencing results with experimental data for a well-rounded understanding.

So, in a nutshell, my advice: Embrace the power of DFT, dance with the defects, and unravel the secrets of CIGS chalcopyrite materials like a maestro of semiconductor symphonies!

The contradiction in the picture is related to the existence of entropy, which cannot avoid the problem. Without the concept of entropy, what's the point of all that confidence?

It involves misconceptions related to radiation, violating the fundamental principles of thermodynamics.

Entropy generation analysis as a design tool—A review

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https://doi.org/10.1016/j.rser.2014.11.104Get rights and content

Abstract

There is an acknowledged growing need for efficient and sustainable systems that use available energy resources in an “optimal” (including constraints) way. Such a goal cannot be effectively achieved without taking into account the limits posed by the second law of thermodynamics. A possible approach consists in the so-called entropy generation analysis, which possesses key features making it more attractive than traditional energy balance approaches. In fact, entropy generation analysis allows for a direct identification of the causes of inefficiency and opens up the possibility for designers to conceive globally more effective systems. Furthermore, thanks to its direct derivation from basic thermodynamic principles, entropy generation analysis can be in principle used for any type of energy conversion system. These attractive features have made entropy generation analysis a popular thermodynamic method for the design and the optimization of less unsustainable systems.

This paper presents a critical review of contributions to the theory and application of entropy generation analysis to different types of engineering systems. The focus of the work is only on contributions oriented toward the use of entropy generation analysis as a tool for the design and optimization of engineering systems. A detailed derivation of the existing entropy generation formulations is first presented, and the two more popular approaches are discussed: the entropy generation minimization (EGM) and the entropy generation analysis (EGA). The relevant literature is further classified in two categories, depending on whether the level of the analysis is global or local. This review will further clarify the use of entropy generation-based design methods, indicate the areas for future work, and provide the necessary information for further research in the development of efficient engineering systems.

Introduction

Since the very dawn of the human species, the need of constructing and operating efficient systems has proven to be a very powerful driver for technological development. This necessity was amplified by the introduction of energy conversion machines during the industrial revolution, leading engineers to study the best use of available energy resources and to the early development of thermodynamics [1]. More recently, the emphasis on efficiency and resources conservation has become crucial because of the currently perceived resource scarcity. As a consequence, second-law based methods that lead to guidelines for the analysis and improvement of engineering systems have become very attractive.The second law of thermodynamics asserts that the operation of real systems is unavoidably characterized by a loss of available work [2], [3]. This causes a decrease of the thermodynamic efficiency of a system with respect to an equivalent ideal (loss-free) process. Historically, the intuitive idea of loss of available work was first pointed out by Carnot. In his treatise [4], [5], he postulated that any machine with moving parts is characterized by a “loss of moment activity” due to friction and “violent effects” (which in modern terms would include both a mechanical cause of inefficiency, namely the effects of vibrations, and a thermodynamic cause, due to extreme non-equilibrium phenomena). The essence of the second law was discovered – albeit with some internal inconsistency – in 1824 by Lazare’s son, Carnot. Carnot [6] illustrated the concept of an ideal cycle that operates through a succession of reversible transformations (defined as a succession of equilibrium states). He argued that the efficiency of this cycle is – ceteris paribus – a function of the temperature of the heat reservoirs. Furthermore, Carnot correctly postulated that his ideal cycle represents a “limiting” cycle, in the sense that any real machine would achieve an efficiency lower than that of the ideal cycle. His ground-breaking work set the foundation for the concepts of thermodynamic reversibility and available work loss. Later, Clausius, Gibbs and Boltzmann [7], [8], [9], [10] gave a proper formulation of entropy and provided a mathematical foundation to the work of Carnot.It took over a century for the development of the modern concept of entropy to be completed, and here we shall dispense with the citation of the numerous and fruitful disputes among scientists, for which we direct interested readers to [11], and limit our task to briefly recall some of the currently accepted definitions. For a generic system the second law of thermodynamics states that the total entropy generation rate

is always non-negative, i.e.where S is the entropy of the system, Φi is the heat transfer rate that the system exchanges with the heat reservoir at temperature Ti and is a mass flow rate exiting (+) or entering (−) the system. According to the second law, the equality sign, i.e.

, holds only in the limit of reversible processes, while the inequality applies also to non-equilibrium processes.

The net work transfer rate

experienced by the system can be reformulated by combining Eq. (1) with the first law of thermodynamics [2]:

The thermodynamic limit of net work transfer rate occurs when a system operates reversibly, i.e.

:

Therefore, the destruction of available work is proportional to the entropy generation rate:

Which is the Gouy–Stodola theorem [12], [13]. Neither the work transfer nor the entropy generation rate are thermodynamic properties of the system: they depend on the operating conditions and especially from the boundary interactions. From Eq. (4) it follows that among all conversion systems characterized by the same upper limit

, the most efficient is the one that attains the minimum entropy generation rate.

The Gouy–Stodola theorem clearly indicates that an analyst can improve the performance of an existing system by conceiving a new design which is characterized by a lower entropy generation. In engineering, the method of identification and reduction of thermodynamic irreversibilities is commonly called entropy generation analysis (EGA). Its optimization counterpart, i.e. entropy generation minimization (EGM), aims at minimizing the losses of a system subject to a specified set of constraints.

Although the proportionality between entropy generation and destroyed useful work had been already emphasized by Gouy and Stodola [12], [13] and then used by others [14], [15], [16], [2], the interest in EGA and EGM was revived by the important contributions of Bejan [17], [18], [19], [20]. In his work, Bejan set the framework for EGA and EGM as a multidisciplinary discipline at the interface of several different fields (Fig. 1). The method is based on the application of principles of heat and mass transfer, thermodynamics and fluid dynamics for the construction of a realistic model of the system that is analysed. The model establishes a strong and explicit link between

, the topology and the physical features of the system: shapes, dimensions, operating conditions etc. This means that the model should be sufficiently detailed to capture both the phenomena that occur in the system and the effects of possible changes in the free variables that are considered, e.g. the operating conditions and/or the system geometry. The analyst exploits this link (that may be expressed by a correlation or a formula, or simply by the empirically acquired knowledge of a “trend”) in order to identify optimization opportunities, i.e. improved designs of the system, that allow a reduction (EGA) or the minimization (EGM) of . The distinct features of EGA and EGM are schematically represented in Fig. 2, Fig. 3. Entropy Generation Analysis is based on a heuristic approach [21]: the initial configuration of the system is subsequently improved by introducing possible design modifications. These changes are proposed by the analyst on the basis of critical examination of the results concerning obtained through the model of the system. Entropy generation minimization is a deterministic approach [21]: the main point is the definition of the entropy generation rate

as the objective function to be minimized, while critical parameters, such as dimensions or operating conditions are chosen as the design variables. Thus, an EGM analysis consists in the search of optimal design variables which minimize the entropy generation rate (Fig. 3).This paper reviews EGA and EGM as design tools in engineering, with particular emphasis on the improvement of thermodynamic performance of engineering systems. In the first part, studies based on black box modelling approach are reviewed. In the second part, the paper reviews the more recent approach to EGA and EGM in the framework of non-equilibrium thermodynamics. Furthermore, we point out possible misleading uses and pitfalls of entropy generation analysis.

Section snippets

Applications to systems involving heat transfer and fluid flow Earlier entropy generation studies were based on the use of black box models (sometimes referred to as “Control Volume Method” or “Lumped Parameters Method”), that imply the assumption of homogeneity inside of the control volume and makes it impossible to capture internal distributions of temperature, pressure, density, etc. Black box modelling typically involves the use of correlations for quantities such as average heat transfer rates and fluid friction, which are instead phenomenologically

Entropy generation formulation The entropy balance equation for an open system (Eq. (1)) provides a formulation for total entropy generation rate

that occurs within a generic system. Such a formulation is derived according to the postulate of equilibrium thermodynamics (ET) [49], [85]. In this framework, state variables are taken as independent of space coordinates: the system is assumed to be homogeneous, in the sense that physical quantities like density, temperature, pressure etc. are not allowed to change from

Conclusions and future work Entropy generation analysis and minimization constitute effective approaches for the improvement or optimization of the thermodynamic performance of engineering systems. The history of these approaches spans several decades and has led to the development of design methods, whose evolution was mainly driven by help of computational resources. While a very large number of publications is devoted to the analysis of entropy generation, this review is limited to the contributions that focus on the

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Cited by (211) Exergetic analysis and optimization of process variables in xylitol production: Maximizing efficiency and sustainability in biotechnological processes 2024, Bioresource Technology

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Both radiative cooling and heating take advantage of the natural properties of thermal radiation and do not require additional energy input or work to achieve the desired cooling or heating effect. it's important to note that the effectiveness of these processes can be influenced by factors such as the design of the surfaces or materials, environmental conditions, and other variables

Continuing investigation

Radiation cooling or heating does not consume any work. We welcome guidance from thermal scientists and engineers.

This is a radiation simulation case using COMSOL, which satisfies empirical laws and energy conservation. See image for details

1. This setting includes radiation experience: when the gas density is small, the radiation intensity is proportional to the density, and the absorption coefficient is inversely proportional to the density (the smaller the absorption coefficient, the stronger the absorption capacity)----- Domain 1 gas density=1, Domain 2 gas density=2.,

2. Radiation generates a temperature difference of 2.1 ℃, rendering the second law of thermodynamics invalid.

3. This transposition can be connected in series to generate stronger heating and cooling capabilities, with low cost, and can be industrialized and commercialized.

4。This article also includes an analysis of the imbalance in calculating radiation. Welcome to read.

The difficulty of this experiment is average, and if possible, it can be done to see the mutual influence of fluctuations.

Thank you for your reply.

Dear Bo Miao ,

Interesting the idea you have realized. I am not familiar in this area, so for a better understanding.

the following questions would be asked:

You have the following interesting remark:

'The only difficulty is charge binding: the diffusion process of charges from A to B requires a constrained electric or magnetic field. The difficulty of this constraint is relatively small compared to nuclear fusion, and it is easy for them to switch to making perpetual motion machines. Suggest transitioning to nuclear fusion and engaging in perpetual motion machines.' - In the system, you can achieve this by using the metal bucket.

after the electrical current is switched off, what maintains the permanent magnetic or electric field ? Where will the system get the energy to do this?

By R, you maintain the electrical potential.

Regards,

Laszlo

Why do you children in computer science think that your logic symbols and diagrams have any meaning or relevance to this or any other world whatsoever? There is zero meaning or relevance to the diagram, deliberately shrouded with undefined symbols so as to impress and confuse.

I will state it clearly, 'Computer Science' is not a valid science. Science is defined as the study of nature. The invalid term, "computer science" is merely a mechanism of human language and thinking, and has nothing to do with nature, nor does any 'computer science' student have the ability to read the maths required to understand science. I have never encountered a 'computer scientist' who had the slightest clue what Physics is.

It is so far from meaningful that it is embarrassing to watch.

Bo Miao: "The first law of thermodynamics calculates the Carnot efficiency" -- no, not at all. The first law only states that heat and work (i) are forms of energy, and (ii) they are the ways energy is transferred from one system to another. How could there be any efficiency included in this law? Please explain.

Simply insert the van der Waals real gas equation of state (or Redlich-Kwong or Virial ansatz, if you prefer those) into the dW equation. You will also get a dW that's not 0. This is a trivial operation.

Arbitrarily setting dW=0 for an isothermal (or adiabatic) process here is actually a violation of the first law of thermodynamics and I got the notion that you believe at least in this one, or has that changed?

So what you have demonstrated here is actually: if we violate the first law of thermodynamics, the second one is also useless. But since the first law is valid, your "proof" is invalid.

How do you know?

Originally a trial of the second law of thermodynamics, it has become a trial of scientists. I believe there will be a response from scientists.

But why do you expect this to be wrong?

The heterostructure might have a different symmetry with respect to the parents.

Maybe if you look at the projection of the bands on the different atoms, you might discover how forming the heterostructure the atomic contribution changes and how the band moved to the Gamma point.

I hope this helps,

Roberto

Hi Dear Prof. Stanislav Dolgopolov

Thank you for the answer & well it seems to be logical, but you do specify the mechanism implicitly, when you write the statement "the created pairs, which initially didn't participate in the current", because you are saying that new pairs of supercurrent bosons are created somehow. They are created, and there is a superconducting mechanism for their creation, even we do not know which one is, if BCS or another unknown one.

Kind Regards.

This communication claims the existence of a perpetuum mobile because surfaces with different curvatures have different vapour-pressures. According to the author, the liquid from the higher-vapour-pressure-surface-region consciously evaporates and condenses on the region of the lower-vapour-pressure-region.

This claim ignores the effects of gravity. In a gravitational field, the pressure of the vapour in the gas phase depends on the height. At higher elevations (at point A in the Figure), the pressure of the vapour is lower; simultaneously, the vapor-pressure of the concave liquid surface is also lower. While, at lower elevations (at point B in the Figure), the pressure of the vapour is higher; simultaneously, the vapor-pressure of the convex liquid surface is also higger. The liquid surface at any point is in equilibrium with the above vapour phase, and the vapour phase itself is in gravitational equilibrium. Hence, the dotted line transport process in the Figure does not exist.

The laws of thermodynamics are still valid.