Second Law Of Thermodynamics Research Articles

Infodynamics, Information Entropy and the Second Law of Thermodynamics

Information and Energy are related. The Second Law of Thermodynamics states that entropy continuously increases, applies to changes in energy and heat, but it does not apply to information dynamics. Changes in energy and information are coupled but have completely different dynamics. Infodynamics has made clear that Thermodynamic Entropy and Information Entropy are distinct concepts. Total Energy contains Free Energy and Thermodynamic Entropy, whereas Total Information or Information Entropy contains Useful Information and Noise, both of which may be gained or lost in irreversible processes. Increases in Free Energy of open systems require more Useful Information, reducing or increasing Thermodynamic Entropy. Empirical data show that the more Free Energy is created, the more Useful Information is required; and the more Useful Information is produced the more Free Energy is spent. The Energy – Information relationship underlies all processes where novel structures, forms and systems emerge. Although science cannot predict the structure of information that will produce Free Energy, engineers have been successful in finding Useful Information that increases Free Energy. Here I explore the fate of information in irreversible processes and its relation with the Second Law of Thermodynamics, showing that distinguishing between Thermodynamic Entropy and Information Entropy, and disentangling its interactions, is fundamental in advancing our understanding of thermodynamics of irreversible processes.

Physics-informed data-driven discovery of constitutive models with application to strain-rate-sensitive soft materials

AbstractA novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on strain-rate-sensitive soft materials. This model is based on the viscous dissipation-based visco-hyperelasticity framework where the total stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscous overstress contributions. It is shown that each of these stress components can be written as linear combinations of the components of an irreducible integrity basis. Three Gaussian process regression-based surrogate models are trained (one per stress component) between principal invariants of strain and strain rate tensors and the corresponding coefficients of the integrity basis components. It is demonstrated that this type of model construction enforces key physics-based constraints on the predicted responses: the second law of thermodynamics, the principles of local action and determinism, objectivity, the balance of angular momentum, an assumed reference state, isotropy, and limited memory. The three surrogate models that constitute our constitutive model are evaluated by training them on small-size numerically generated data sets corresponding to a single deformation mode and then analyzing their predictions over a much wider testing regime comprising multiple deformation modes. Our physics-informed data-driven constitutive model predictions are compared with the corresponding predictions of classical continuum thermodynamics-based and purely data-driven models. It is shown that our surrogate models can reasonably capture the stress–strain-strain rate responses in both training and testing regimes and improve prediction accuracy, generalizability to multiple deformation modes, and compatibility with limited data.

Entropy production for diffusion processes across a semipermeable interface

The emerging field of stochastic thermodynamics extends classical ideas of entropy, heat, and work to nonequilibrium systems. One notable finding is that the second law of thermodynamics typically only holds after taking appropriate averages with respect to an ensemble of stochastic trajectories. The resulting average rate of entropy production then quantifies the degree of departure from thermodynamic equilibrium. In this paper we investigate how the presence of a semipermeable interface increases the average entropy production of a single diffusing particle. Starting from the Gibbs-Shannon entropy for the particle probability density, we show that a semipermeable interface or membrane S increases the average rate of entropy production by an amount that is equal to the product of the flux through the interface and the logarithm of the ratio of the probability density on either side of the interface, integrated along S. The entropy production rate thus vanishes at thermodynamic equilibrium, but can be nonzero during the relaxation to equilibrium, or if there exists a nonzero stationary equilibrium state (NESS). We then give a probabilistic interpretation of the interfacial entropy production rate using so-called snapping out Brownian motion. This also allows us to construct a stochastic version of entropy production. Finally, we illustrate the theory using the example of diffusion with stochastic resetting on a circle, and find that the average rate of interfacial entropy production is a nonmonotonic function of the resetting rate and the permeability. Published by the American Physical Society 2024

Entropy generation and heat transfer characteristics in MHD Casson fluid flow over a wedge with viscous dissipation and thermal radiation

AbstractThis investigation outlines the significance of MHD Falkner–Skan flow of non‐Newtonian fluid flow over a wedge. To study the non‐Newtonian flow, Casson fluid is taken. Additionally, this study explores heat and mass transport under the influence of viscous dissipation, Joule heating, and thermal radiation. This heat and mass transport investigation is carried out under the influence of thermal and concentration slip factors. Moreover, the entropy generation is also computed using the second law of thermodynamics. A set of nonlinear partial differential equations arises from the mathematical formulation of the problem. Similarity variables are then introduced to achieve a similarity solution. The leading differential equations are solved numerically using the Runge–Kutta‐4 method in conjunction with shooting techniques. Graphical representations are employed to demonstrate the physical significance of relevant parameters. The investigation presents and discusses the impact of various parameters on velocity, temperature, concentration and entropy profiles for three different positions of the wedge: stationary, forward‐moving, and backward‐moving. The main conclusions of the study are as follows: (1) Enhancing the magnetic parameter and wedge angle parameter leads to higher fluid velocity, (2) elevating both the Eckert and magnetic number results in a rapid escalation of fluid energy, (3) Skin friction coefficient increases gradually with an increase in the power law Falkner–Skan parameter.

A Symmetric Form of the Clausius Statement of the Second Law of Thermodynamics.

Bridgman once reflected on thermodynamics that the laws of thermodynamics were formulated in their present form by the great founders of thermodynamics, Kelvin and Clausius, before all the essential physical facts were in, and there has been no adequate reexamination of the fundamentals since. Thermodynamics still has unknown possibilities waiting to be explored. This paper begins with a brief review of Clausius's work on the second law of thermodynamics and a reassessment of the content of Clausius's statement. The review tells that what Clausius originally referred to as the second law of thermodynamics was, in fact, the theorem of equivalence of transformations (TET) in a reversible cycle. On this basis, a new symmetric form of Clausius's TET is proposed. This theorem says that the two transformations, i.e., the transformation of heat to work and the transformation of work from high pressure to low pressure, should be equivalent in a reversible work-to-heat cycle. New thermodynamic cyclic laws are developed on the basis of the cycle with two work reservoirs (two pressures), which enriches the fundamental of the second law of thermodynamics.

Comparative Study of Thermodynamic Performances: Ammonia vs. Methanol SOFC for Marine Vessels

AbstractIn response to escalating environmental concerns and the imperative to institute effective energy management strategies, the pursuit of alternative fuels has emerged as a pivotal endeavor for realizing sustainable energy solutions. Methanol and ammonia have surfaced as particularly promising and environmentally friendly liquid fuels, holding significant potential for aiding in the attainment of decarbonization objectives and addressing global energy requirements. This research proposes and scrutinizes a sophisticated cogeneration system integrating solid oxide fuel cells (SOFCs), gas turbine (GT), steam Rankine cycle, and organic Rankine cycle. Direct utilization of ammonia and methanol as fuel in this intricate system is examined, with the design and modeling facilitated through the utilization of Aspen HYSYS V.12.1. The thermodynamic performance of the proposed system is rigorously assessed by employing the foundational principles of the first and second laws of thermodynamics. The direct SOFCs fueled by ammonia and methanol exhibit notable energy efficiencies of 64.25 % and 58.42 %, respectively. Remarkably, the amalgamated systems showcase heightened energy efficiencies, witnessing a commendable increase of 12.64 % and 10.66 % when powered by ammonia and methanol, respectively, as compared to individual SOFC systems. Examination of exergy destruction reveals the SOFC as the principal contributor, with electrochemical and chemical processes constituting the primary sources of irreversibility. Additionally, explicit values for exergy destruction in the GT, afterburner, and heat exchanger components are provided. A comprehensive parametric study underscores the pivotal role of the fuel utilization factor (Uf), identifying a value of 0.85 as optimal and significantly augmenting the thermodynamic efficiency of the system. This analysis not only substantiates the potential of ammonia and methanol as effective carriers for hydrogen but also underscores the efficacy of waste heat recovery as a viable strategy for enhancing the overall thermodynamic performance of an SOFC system. The findings presented herein contribute valuable insights, paving the way for the strategic utilization of alternative fuels and cogeneration systems in the broader context of sustainable and environmentally conscious energy solutions.

On the Second Law of Thermodynamics in Continuum Physics

The paper revisits the formulation of the second law in continuum physics and investigates new methods of exploitation. Both the entropy flux and the entropy production are taken to be expressed by constitutive equations. In three-dimensional settings, vectors and tensors are in order and they occur through inner products in the inequality representing the second law; a representation formula, which is quite uncommon in the literature, produces the general solution whenever the sought equations are considered in rate-type forms. Next, the occurrence of the entropy production as a constitutive function is shown to produce a wider set of physically admissible models. Furthermore the constitutive property of the entropy production results in an additional, essential term in the evolution equation of rate-type materials, as is the case for Duhem-like hysteretic models. This feature of thermodynamically consistent hysteretic materials is exemplified for elastic–plastic materials. The representation formula is shown to allow more general non-local properties while the constitutive entropy production proves essential for the modeling of hysteresis.

Dynamic modeling and response characteristics of a solar-driven fuel cell hybrid system based on supercritical CO2 Brayton cycle

This study proposes and evaluates a solar-driven system coupled with a solid oxide fuel cell and the supercritical carbon dioxide cycle, aiming to fully utilize the potential of solar energy while ensuring the safe and stable operation of the energy system. The dynamic mathematical model is established by the lumped parameter method, with a maximum model error of less than 5%. This study analyzes the integrated system based on its harsh off-design conditions, with short-term (in seconds), medium-term (in minutes), and long-term (in hours) dynamic responses. Meanwhile, based on the second law of thermodynamics, a study is conducted on the irreversibility of the operation of heat exchangers. Finally, analyze the mismatch between supply and demand in the time scale caused by solar energy fluctuations. The results show that the system can meet 5 h of hydrogen production work in summer and only 2 and a half hours in winter. The transient entropy generation mainly occurs in the first 5 s, with the highest transient additional entropy generation ratio of 71.7%. The findings of this study provide useful information and a reference for ensuring the safe and flexible operation of renewable power generation systems.

The role of greenhouse gases in radiative equilibrium – Thermodynamic evaluation

Abstract The significance of greenhouse gases for climate change is assessed in the case of carbon dioxide on the basis of thermodynamic data. According to the values of the molar heat capacity, no increased heat-storing property of this greenhouse gas can be determined. The absorption and desorption of infrared radiation by the greenhouse gases is seen as a reversible dynamic process, which on the one hand reduces the IR radiation from the Sun, and on the other hand, delays the re-radiation from the Earth. As converters of heat into IR photons and vice versa, the greenhouse gases play an important role in balancing the radiation. The direction of heat transport in the atmosphere is determined by the 2nd Law of Thermodynamics. The range of IR radiation is determined according to the gradation of air pressure in the atmosphere.

Thermoeconomic analysis and environmental impact assessment of the Akkuyu nuclear power plant

Within the scope of this study, a thermoeconomic analysis was carried out for Akkuyu Nuclear Power Plant (ANPP), the first nuclear power plant of Türkiye. As a result of the analysis, it is aimed to reduce the cost of energy production and prevent thermal pollution at the same time by converting the heat discharged into the environment into useful heat due to the working principle of NPP. Thermodynamic analysis was performed in the Engineering Equation Solver (EES) program using equipment values equivalent to ANPP. Cost analysis was performed using the specific exergy costing (SPECO) method, which is based on the second law of thermodynamics and is the most widely used cost analysis method. The study concludes that the energy efficiency is 35%, while the economic analysis shows that the best case has an exergy efficiency of 68% with a payback period of 7–8 years, and an electricity cost of $0.0196 per kWh. It is possible to use the heat discharged from the plant indirectly in district heating (heating, hot water needs of the lodgings, guesthouses in the facility), greenhouse heating, agricultural drying and heating, considering the geographical conditions and livelihood of the region. Thus, 68% of the waste heat was utilized, the unit cost of the energy produced was reduced and at the same time thermal pollution was reduced at the same rate. The results of the study can contribute to the efforts preventing energy waste, thermal environmental pollution, and reducing greenhouse gas emissions. Additionally, it could aid in the development of more energy-efficient and environmentally friendly power generation systems, including pioneering nuclear power plants in developing countries.

Entropy generation analysis and thermal synergy efficiency in the T-shaped micro-kenics

In this work, three different twist angles of a micro helical insert in a T-shaped are studied numerically in order to evaluate the laminar steady flow behavior of Newtonian fluid in chaotic geometry. In the geometries under consideration, thermal mixing behavior is carried out using fluids having two distinct input temperatures. Under the influence of chaotic advection and low rates of Reynolds number, the second law of thermodynamics is controlled in terms of the entropy generation caused by hydrodynamic and thermal processes. The governing equations are numerically solved using the CFD Fluent code. Thus, the micromixer's configuration demonstrated a very significant improvement in mixing degree while minimizing friction and thermal irreversibilities. The synergy coefficient, which depicts the link between velocity and heat transfer in angle form, is analyzed and the results are provided.

New models of d-dimensional black holes without inner horizon and with an integrable singularity

Theoretically, it has been proposed that objects traveling radially along regular black holes (RBHs) would not be destroyed because of finite tidal forces and the absence of a singularity. However, the matter source allows the creation of an inner horizon linked to an unstable de Sitter core due to mass inflation instability. This inner horizon also gives rise to the appearance of a remnant, inhibiting complete evaporation. We introduce here a d-dimensional black hole model with Localized Sources of Matter (LSM), characterized by the absence of an inner horizon and featuring a central integrable singularity instead of an unstable de Sitter core. In our model, any object tracing a radial and timelike world-line would not be crushed by the singularity. This is attributed to finite tidal forces, the extendability of radial geodesics, and the weak nature of the singularity. Our LSM model enables the potential complete evaporation down to r h = 0 without forming a remnant. In higher dimensions, complete evaporation occurs through a phase transition, which could occur at Planck scales and be speculatively driven by the Generalized Uncertainty Principle (GUP). Unlike RBHs, our model satisfies the energy conditions. We demonstrate a linear correction to the conventional area law of entropy, distinct from the RBH's correction. Additionally, we investigate the stability of the solutions through the speed of sound.

Entropy and the Limits to Growth.

In its business-as-usual scenario, the 1972 Club-of-Rome report-The Limits to Growth-describes the collapse of the world economy around the year 2030, either because of the scarcity of natural resources or because of pollution. Mainstream economists, the high priests of secular societies, condemned it fiercely. Their gospel of perpetual economic growth, during which technological progress would solve all problems, promises a bright future for all mankind. On the other hand, engineers, natural scientists, and mathematicians realized that the breakdown scenario is due to the inclusion of the First and the Second Law of Thermodynamics in the Club-of-Rome's world model. According to these laws, nothing happens in the world without energy conversion and entropy production. In 1865, Rudolph Clausius, the discoverer of entropy, published the laws as the constitution of the universe. Entropy is the physical measure of disorder. Without a proper understanding of energy and entropy in the economy, all efforts to achieve sustainability will fail.

A facile design of porous heat sink optimized thermodynamically for thermo-hydraulic performance

Implementing active cooling through micro-channel heat sinks integrated with printed circuit heat exchangers demands a simultaneous enhancement of thermal and hydraulic performance, all while avoiding complex designs for ease of fabrication. We propose a porous wall embedded double-layered micro-channel heat sink, aiming to decrease the necessary pumping powers while maintaining a minimal impact on the heat transfer rate. Additionally, this design simplifies geometric complexities, enhancing ease of fabrication. We assessed the feasibility of different porous embedded double-layered micro-channel heat sink configurations by evaluating their thermal and hydraulic performance. Our analysis uniquely integrates the principles of the second law of thermodynamics with traditional first law analysis, providing novel insights into heat sink design. We discovered that configuring porous walls solely in the top layer of the double-layered micro-channel heat sink is the only viable option. Furthermore, our analysis reveals that embedding porous walls exclusively in the top layer reduces irreversibility due to frictional losses by 9.13 %, with a slight increase in irreversibility due to heat transfer by 1.55 %, in comparison to the solid double-layered micro-channel heat sink at a flow rate of 1000 ml/min. Moreover, at the same flow rate, compared to configuration with porous walls in both layers, the top layer configuration exhibits improved thermal performance by 17.28 %. Next, we demonstrate that while the first law analysis indicates the viability of the top porous configuration, the second law analysis limits its viability to a certain coolant flow rate range. Finally, we optimize the heat sink design and coolant flow rates, proposing a viable design by simply incorporating porous walls in only the top layer of double layered micro-channel heat sink, which otherwise proved to be non-viable.

System-bath correlations and finite-time operation enhance the efficiency of a dissipative quantum battery

The reduced state of a small system strongly coupled to a thermal bath may be athermal and used as a small battery once disconnected. The unitarily extractable energy (a.k.a. ergotropy) will be negligible if the disconnecting process is too slow. To study the efficiency of this battery, we consider the cycle of disconnecting, extracting, and connecting the battery back to the bath. Efficiency, i.e. the ratio between ergotropy and connecting plus disconnecting work, is a function of disconnecting time. We consider the Caldeira–Leggett model of a quantum battery in two scenarios. In the first scenario, we assume that the discharged battery is uncorrelated to the bath when connecting back and find that the efficiency peaks at an optimal disconnecting time. In the second scenario, the discharged battery is correlated to the bath, and see that the optimal efficiency corresponds to an instantaneous disconnection. On top of these results, we analyze various thermodynamic quantities for these Caldeira–Leggett quantum batteries and express the first and second laws of thermodynamics for the cycles in simple form despite the system-bath initial correlations and strong coupling regime of the working device.

Performance improvement of a rotating gas separator for electrical submersible pump considering entropy generation method

The utilization of Electrical Submersible Pumps (ESPs) stands as one of the foremost methods in artificially extracting oil, primarily within the oil industry. Under typical conditions, the pump encounters a two-phase flow of oil and gas. Should the gas phase within this mixture surpass an acceptable threshold, it can lead to a significant decline in performance and inflict detrimental damage upon the pump. To address this issue, the incorporation of a gas separator unit, one of the pivotal components within ESPs, is imperative at the pump's inlet section. Enhancing the gas separator unit holds paramount importance for ensuring pump safety and optimizing performance, particularly in wells with elevated gas contents.The conventional approach to calculating hydraulic losses in turbomachinery, relying on pressure drop calculations, often falls short in pinpointing the precise locations of losses. This paper delves into enhancing gas separator performance by augmenting gas separation efficiency through the application of the entropy generation method and leveraging the second law of thermodynamics. To achieve this, pivotal entropy-generating geometrical parameters of the gas separator were identified as the design variables necessary for forming the Taguchi sample space. Numerical simulations were conducted utilizing steady three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations for incompressible fluid flow, coupled with a turbulence model. Results indicate that the gas separation efficiency (GSE) of the initial model surged from 45.6% to 88% in the improved sample, albeit with a concurrent rise in entropy generation rate (EGR) from 209 W/K to 243.1 W/K. To establish a more comprehensive criterion for analysis, the ratio of GSE to EGR was employed as an objective function. This ratio quantifies the efficiency of gas separation per unit of energy loss, and it escalated from 0.218 in the primary sample to 0.362 in the improved sample, representing a 66% increase. This signifies that despite simultaneous increases in EGR and GSE, the rate of energy loss per unit of gas separation has diminished. Furthermore, the heightened EGR in the improved sample can be attributed to an increase in total volume, leading to an expanded contact surface area and consequently an elevation in total entropy. This investigation underscores the advantages of the entropy generation method, particularly in delineating the precise location and magnitude of energy dissipation within the rotating gas separator.

Comparative study of combustion processes generated by the use of different fuels: energy and exergy analysis

Through energy and exergy analysis, the present work revisits the combustion processes generated using different fuels (CH4, C3H8, H2, LPG, Natural gas and Biogas) under the same operating conditions. First, numerical computations, in which the turbulent dynamic k-ϵ model coupled with a probability density function (PDF) approach together with different sub-models that ensure the reliability of the results, are used. Then, the First and Second Laws of thermodynamics are applied to all fuel combustion cases considered previously to predict the energy loss, exergy destruction and their corresponding efficiencies. Next, variations in the air factor, the air inlet temperature and the fuel inlet temperatures are considered to analyse the response of combustion system performance as well as energy and exergy losses for the different fuels under investigation. The results show an amelioration of combustion parameters for the mixture of fuel and air using values of λ greater than 1. Also, the preheating of the inlet air temperature has a positive effect on energetic parameters. However, preheating the inlet fuel does not take a considerable role in the efficiency amelioration and loss reduction of the combustion system. It further turns out that biogas features higher energy efficiency compared to other fuels, at approximately 89.64%, while hydrogen fuel exhibits higher exergy efficiency at around 78.70% followed by biogas with 74.96%.

Casimir–Onsager matrix for weakly driven processes

Modeling of physical systems must be based on their suitability to unavoidable physical laws. In this work, in the context of classical, isothermal, finite-time, and weak drivings, I demonstrate that physical systems, driven simultaneously at the same rate in two or more external parameters, must have the Fourier transform of their relaxation functions composing a positive-definite matrix to satisfy the Second Law of Thermodynamics. By evaluating them in the limit of near-to-equilibrium processes, I identify that such coefficients are the Casimir–Onsager ones. The result is verified in paradigmatic models of the overdamped and underdamped white noise Brownian motions. Finally, an extension to thermally isolated systems is made by using the time-averaged Casimir–Onsager matrix, in which the example of the harmonic oscillator is presented.

Thermodynamic performance investigation of environmentally friendly working fluids in a geothermal integrated pumped thermal energy storage system

Abstract Among the available energy storage technologies, pumped thermal energy storage (PTES) is emerging as a potential solution for large-scale electrical energy storage with no geographical limitations and high roundtrip efficiencies. However, PTES requires a low-cost, high-temperature heat source to achieve reasonable roundtrip efficiencies. Moreover, organic Rankine cycle-based PTES systems require high-performance and environmentally friendly working fluids. In this study, the thermodynamic performance of a geothermal integrated PTES system using environmentally friendly working fluids is investigated. The mathematical model of the geothermal integrated PTES system is developed using the first and second laws of thermodynamics and implemented in Engineering Equation Solver (EES). With the developed model, the thermodynamic performance of the PTES system for different working fluids, including Butene, cyclopentane, iso-butane, R1233zd(E), R1234ze(Z), R1224yd(Z), HFO1336-mzz(Z), R365mfc, n-hexane, and n-pentane was investigated. For geothermal fluid outlet temperatures between 60°C and 120°C and geothermal fluid inlet and outlet temperature differences across the evaporator between 20°C and 60°C, the net power ratio i.e., the ratio of the electrical energy discharged to the electrical energy used to run the charging cycle, is between 0.25 and 1.40. This shows that the system has the potential to give back more than 100% of the electrical energy used during charging under certain conditions. High net power ratios are obtained for a combination of high source temperatures and low geothermal fluid inlet and outlet temperature differences.

A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism.

We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure-property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius-Duhem inequality. The kinetic framework employs a stress-strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model's results showing good correlations.