Thermodynamic Equations Research Articles

TEOS-10 Equations for Determining the Lifted Condensation Level (LCL) and Climatic Feedback of Marine Clouds

At an energy flux imbalance of about 1 W m−2, the ocean stores 90% of the heat accumulating by global warming. However, neither the causes of this nor the responsible geophysical processes are sufficiently well understood. More detailed investigations of the different phenomena contributing to the oceanic energy balance are warranted. Here, the role of low-level marine clouds in the air–sea interaction is analysed. TEOS-10, the International Thermodynamic Equation of State of Seawater—2010, is exploited for a rigorous thermodynamic description of the climatic trends in the lifted condensation level (LCL) of the marine troposphere. Rising sea surface temperature (SST) at a constant relative humidity (RH) is elevating marine clouds, cooling the cloud base, and reducing downward thermal radiation. This LCL feedback effect is negative and counteracts ocean warming. At the current global mean SST of about 292 K, the net radiative heat flux from the ocean surface to the LCL cloud base is estimated to be 24 W m−2. Per degree of SST increase, this net flux is expected to be enhanced by almost 0.5 W m−2. The climatic LCL feedback effect is relevant for the ocean’s energy balance and may be rigorously thermodynamically modelled in terms of TEOS-10 equations. LCL height may serve as a remotely measured, sensitive estimate for the sea surface’s relative fugacity, or conventional relative humidity.

Thermodynamic Properties and Equations of State for Solid and Liquid Magnesium

Thermodynamic Properties and Equations of State for Solid and Liquid Magnesium

A theoretical equation of state to formulate the melting curve of metals with varying pressure

The objective of this study has been formulate mathematical equations for the melting temperature of metallic solids using various thermodynamics equation of state, specifically those proposed by Modified generalized Lennard – Jones(mGL-J) equation of state (EOS) and Usual-Tait EOS. The derived equations of state establish the relation between pressure, volume, melting temperature, bulk modulus and first-order pressure derivative at zero pressure. These equations of state are used to calculate melting curves for the metallic elements Pd, Cd, Pt, Mn, Au, Al, Zn and Ag up to 30 GPa. The obtained results from Modified generalized Lennard – Jones(mGL-J) equation of state display a significant rise in the melting curve because of a large increase in bulk modulus. The results of mGL-J EOS is the most consistent with the experimental data. The outcomes obtained from Usual-Tait equation of state diverges to a great extent with the experimental melting temperature. The study contributes to a better understanding of the quantitative effect of pressure on the melting temperature of various solids. The derived equations of state are useful to calculate melting temperature at larger pressures.

Correction: Thermodynamic Properties and Equation of State for Alpha-Alumina

Correction: Thermodynamic Properties and Equation of State for Alpha-Alumina

HYGROSCOPIC WATER CONTENT AS AN INDICATOR OF SOIL DISPERSITY:THERMODYNAMIC BASIS AND EXPERIMENTAL VERIFICATION

The adsorption properties of dispersed systems are determined by their surface energy, therefore the indicators of hygroscopy (adsorbed water content) and dispersity (specific surface area of the solid phase) of soils and sediments are in close mutual correlation. This well-known empirical fact received a new fundamental interpretation based on the theory of disjoining water pressure according to Deryagin in the form of a thermodynamic equation connecting the specific surface area, hygroscopic water content of soil samples and the relative humidity of the air in the laboratory room. The theoretical equation allowed us to substantiate the methodology for quantifying the hydrophilic specific surface area of soil samples based on widespread data on their hygroscopy. A comparison of the new method with the standard BET-analysis of the specific surface area, as well as with the previously proposed physically based method for its determining by the slope of thermodynamic water retention curves, showed their statistically reliable agreement in a wide range of estimated specific surface area values from 5 to 340 m2×g-1 for soil samples of different genesis and texture.

Physics-informed deep learning and linear programming for efficient optimization of combined cycle power plants

Efficient operation of combined cycle power plants (CCPP) involves solving mixed-integer nonlinear optimization problems, constrained by thermodynamic differential equations, thermal constraints, and temporal dependencies between variables. The optimization problem aims to maximize profit for day-ahead operation by minimizing short-term and long-term costs, and accounting for volatility in ambient conditions and energy price. In operational terms, the challenge lies in developing an efficient and robust optimization algorithm capable of determining optimal values for thousands of temporal variables. It must also have the capacity to evaluate a multitude of scenarios encompassing various weather and market conditions. To address this challenge, this paper proposes a hybrid optimizer that utilizes deep learning models trained on historical operational data of a real CCPP, along with a surrogate physics-driven piecewise-linear model of CCPP, to determine the optimal values of thousands of control setpoints, with strong temporal co-dependencies, within a two-minute runtime required by industry constraints. A multi-resolution architecture is proposed to efficiently implement this optimizer. The algorithm sequentially solves the problem in coarse and fine resolutions to accelerate convergence. Final results are checked for feasibility using pre-trained deep learning models, ensuring accuracy and validity. The study shows that the proposed model provides comparable results to the exact solution while reducing computational costs, up to 95%. This research has practical implications for power plant system operators, as well as traders and dispatchers, enabling them to make optimal decisions for day-ahead contracting purposes and CCPP operation in a reasonable time, ultimately leading to more efficient and cost-effective power plant management. Furthermore, the methodology introduced in this work could potentially be extended to other industrial applications that require large-scale, complex optimizations, where the precise governing principles of a process can be approximated by piecewise-linear functions.

The thermal perception of outdoor urban spaces in a hot arid climate: A structural equation modelling (SEM) approach

Human thermal comfort is linked to multi-sensory attributes and psychological cognition besides the influence of prominent meteorological parameters. To date, even the most advanced thermal comfort models like UTCI consider the interaction between human and external surroundings to be a heat transfer problem applying thermodynamic equations in the derivation behind thermal comfort indices. Machine learning (ML) models offer the advantage of improving the accuracy of predictor variable, but they fail to determine the relationship between the independent variables and data-driven prediction models. Structural Equation Modelling (SEM), an advanced modelling technique, can expose all hidden relationships among variables using latent variables while not being data-driven like ML. This study aimed to develop a structural framework which systematically explains these relationships and quantify the effects of 24 variables on outdoor thermal comfort using SEM due to its ability to represents the response of the dependent variable to a unit change in an explanatory variable. The method employed 635 structured interviews, observations, and wide-ranging micrometeorological measurements conducted concurrently in three Pedestrianized urban alleys in Cairo. The model statistically confirmed the hypothesis that overall thermal comfort in urban spaces is significantly influenced by multiple factors. Of these, background microclimatic conditions had the greatest relevance and certain urban features the least. 1 unit increase microclimate leads to a change in thermal comfort by 0.423 and 0.349 in summer and winter, respectively. In terms of thermal perception, the model shows that individuals are willing to tolerate a wider range if certain urban features are present such as shaded seating opportunities. These outcomes may aid to provide important guidance for urban designers to enhance thermal perception in urban streets.

Experimental (ρ,P,T) data of H2 + CH4 mixtures at temperatures from 278 to 398 K and pressures up to 56 MPa

The blending of hydrogen and natural gas (H2-NG) has emerged as a crucial and cost-effective means for processing hydrogen fluids through natural gas networks thereby aiding transition to net-zero energy. Nonetheless, the effective adaptation of H2-NG mixtures, especially up to 20% hydrogen concentrations, to existing natural gas distribution and storage facilities relies heavily on a comprehensive understanding of their thermophysical properties. We measured densities of three binary mixtures of hydrogen and methane (xH2 = 0.0532, 0.0858, and 0.2031) at temperatures between 278 and 398 K, and pressures up to 56 MPa using a vibrating tube densimeter (VTD). The VTD was calibrated using H2 and H2O. The measured densities were in reasonable agreements with the predictions of two thermodynamic equations of states (EoSs), Multi-Fluid Helmholtz Energy Approximation (MFHEA) and Peng-Robinson (PR). The average absolute relative deviation (AARD) for the measured density against the predictions of the PR EoS are 1.07%, 1.09%, and 0.89% for xH2 = 0.0532, 0.0858, and 0.2031 mol fractions respectively. While the AARD for the measured density against the predictions of MFHEA EoS are 0.16%, 0.16%, and 0.32% for xH2 = 0.0532, 0.0858, and 0.2031 mol fractions respective. The MFHEA EoS, which has the structure of GERG-2008, has better agreements with our density data than the PR EoS. The relative high deviations with PR EoS results from the PR's simple structure making it deficient in calculating thermal properties of natural gas in saturated-liquid and homogeneous states. In addition, the uncertainty of the measured density was determined, and the experimental data were compared with available literature data. Finally, the compressibility factor (Z), speed of sound (w), specific heat capacity at constant volume (CV), and specific heat capacity at constant pressure (Cp) were obtained from the experimental results and were compared with the predictions of MFHEA EoS. This work provides accurate density and other thermophysical data useful for engineering/process designs and modelling of H2 and natural gas systems thereby enhancing energy transition strategy.

Thermodynamic Evaluation of Low-GWP and Environmentally Friendly Alternative Refrigerants

Refrigerant systems, crucial for modern life, are increasingly important due to their environmental impact and rising energy costs, with their advancement influenced by social life evolution and widespread use in homes and buildings. A systematic search using thermodynamic models identified 48 possible ternary mixtures and 5 pure refrigerants. These combinations, based on thermodynamics, could provide energy savings, paving the way for real-world testing and definitive conclusions, not yet studied in literature. REFPROP refers to the reference fluid properties program, developed by NIST version 9.0 for 2010, is a program for calculating the thermodynamic and transport properties of industrially important fluids and their mixtures. This program was used to evaluate the refrigerant properties in different mixing ratios. Then, using the MATLAB version of 2020 apparatus to arrange and solve all the variables to generate the results under set boundary conditions, all the characteristics were incorporated into thermodynamic equations. when compared to R134a, the results demonstrated that mixtures of natural refrigerants usually have acceptable thermal performance; these mixtures may be recommended as suitable replacements for refrigeration and air conditioning systems because they are environmentally harmless and have a low GWP.

A Novel Designation of Solid Oxide Fuel Cell-Integrated System Using LPG as Fuel for Marine Vessels

A Novel Designation of Solid Oxide Fuel Cell-Integrated System Using LPG as Fuel for Marine Vessels

The absorption effect and mechanism of graphene oxide removal from aqueous solution by basalt stone power

Graphene oxide (GO) is a novel carbon material utilized extensively for diverse industrial applications. When exposed to environmental elements like sunlight and chlorination, GO can undergo a series of physical and chemical transformations, and its presence in water and the environment can endanger ecosystems. Therefore there is a need for methods that can effectively remove GO from water. Accordingly, we delve into the efficacy of basalt stone powder (BSP) as an adsorption medium for purifying aqueous solutions of GO. We examine the impact of various experimental parameters—namely pH, initial solution concentration, adsorbent mass, contact duration, and ambient temperature—on GO adsorption, employing the method of controlled variables. The adsorption efficacy is notably influenced by the pH level. At an acidic pH of 3, an initial GO concentration of 80 mg/L, an adsorbent dosage of 50 mg, and a temperature of 303 K (approximately 30 °C), the adsorption removal efficiency reaches an impressive 99 %, boasting a maximum adsorption capacity of 112 mg/g. Dynamically, the adsorption kinetics align most closely with a pseudo-first-order model, achieving equilibrium after 24 h. Thermodynamic analyses reveal that the Langmuir isotherm model most accurately describes the adsorption behavior, indicating an enhancement in BSP's adsorption capacity for GO as temperature rises. Based on thermodynamic equations, the adsorption of GO onto BSP is deduced to be a spontaneous process. Our findings illustrate BSP's considerable potential in the treatment and removal of GO from water, and therefore it may prove useful in environmental remediation efforts.

A novel designation of LNG solid oxide fuel cells combined system for marine application

This paper presents a pioneering multigeneration system for marine vessel applications, involving the integration of solid oxide fuel cells (SOFCs) fueled by liquefied natural gas (LNG), coupled with LNG cold energy utilization cycles and exhaust gas heat recovery systems. The system comprises a tandem arrangement of organic Rankine cycle (ORC) and trans-critical carbon dioxide cycle (TCO2), specifically engineered to harness the cold energy released during LNG regasification process. The elevated temperature exhaust gases emanating from the SOFC are efficiently recuperated through a series of components including a gas turbine (GT), regenerative, steam Rankine cycle (SRC), and waste heat boiler (WHB). The proton exchange membrane fuel cells (PEMFC) is designed to enhance the overall operational flexibility and responsiveness of the multigeneration system. The Aspen Hysys V12.1 is used to simulate the propose system and numerical method is employed to parameter optimize of system. The first and second laws of thermodynamics are applied to establish the thermodynamics equations and calculated the system performances. The described system is estimated to obtain energy efficiency of 69.32 % and exergy efficiency of 33.85 %. The high-temperature exhaust gas harvesting integrated systems are sufficiently generated 2091.24 kW which accounted 35.49 % of entire power generate. Furthermore, the parametric researches are implemented to examine the influence of current density, β values to the performance indicators of systems. The WHB is designed to generate 1081 kg/h of superheated vapor at 170 °C and 405 kPa for various purposes of seafarers and equipment's onboard ship. The economic feasibility is performed to view the possibility of investment, maintenance cost and payback period for the described system.

Numerical investigation in effects of refrigerants’ thermodynamic properties on performance of supersonic ejector

ABSTRACT Using zeotropic mixtures with unique temperature glide characteristics as the working medium in heat-driven ejector refrigeration system will potentially reduce the irreversible losses in heat exchange process. However, the intrinsic link between the pure/mixture refrigerants’ thermophysical properties and the entrainment performance of supersonic ejector has not yet been elucidated. In this study, a novel ejector CFD model is established by coupling the real-gas thermodynamic equation and species transport equation, then the relationships between thermophysical properties of pure/mixture refrigerants and ejector’s dimensionless operational parameters were thoroughly investigated. The results indicated that the ejector expansion ratio rises as primary flow inlet temperature or refrigerant’s normal boiling point increases, while the dimensionless parameters of primary nozzle are relatively insensitive to the variation of primary flow inlet temperature and refrigerant’s boiling point, resulted in changes of supersonic jet expansion behaviour. Moreover, the specific volume and adiabatic index change characteristics resulted in minor fluctuations of primary nozzle’s dimensionless parameters. When the bubble point temperature is fixed at 30℃ in the condenser, the saturated vapor/liquid phase pressure glide characteristics of R600a/R1234ze mixture may lead to an increasement of ejector’s compression ratio.

Parametric energy optimization of a ventilated facade with windows in Mediterranean climates

Ventilated facades are an effective passive measure to improve the energy performance of buildings in warm and temperate climates such as the Mediterranean. However, although in the Mediterranean sociocultural context the use of windows is widespread, there is a lack of energy analysis of ventilated facades in combination with windows. This is due to the lack of accurate simulation tools to evaluate the energy performance of this combination because of its complex thermodynamics, which, among other issues, requires three-dimensional computational fluid dynamic tools. In this work, a parametric energy analysis of the design parameters of a ventilated façade with window openings has been performed using a three-dimensional numerical model developed by the authors that combines turbulent Navier–Stokes thermodynamic equations for air with a set of differential equations for the envelope temperatures. The results of the analysis showed the potential of the opaque ventilated façade (OVF) with windows when applied to the rehabilitation of energetically obsolete facades, achieving a remarkable reduction in heat flux with respect to these facades, a reduction that reaches 32% for the yearly heat flux when using the optimal configuration found.

Structural Realism About the Free Energy Principle, the Best of Both Worlds

AbstractThere are realist and antirealist interpretations of the free energy principle (FEP). This paper aims to chart out a structural realist interpretation of FEP. To do so, it draws on Worrall’s (Dialectica 43(1–2): 99–124, 1989) proposal. The general insight of Worrall’s paper is that there is progress at the level of the structure of theories rather than their content. To enact Worrall’s strategy in the context of FEP, this paper will focus on characterising the formal continuity between fundamental equations of thermodynamics—such as Boltzmann’s equation and Gibbs’s equation—on the one hand, and Friston’s characterisation of FEP on the other. Lack of a universal consensus on the physical character of entities that feature in thermodynamics, information theory and FEP notwithstanding, I argue that there is structural continuity and unity at the level of mathematical equations that regiment entropy, information and free energy. The existence of such structural continuity and unity provides grounds for structural realism about FEP.

Classical stochastic approach to quantum mechanics and quantum thermodynamics

We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component φ j of the wave vector is understood as a stochastic complex variable whose real and imaginary parts are proportional to the coordinate and momentum associated with a degree of freedom of the underlying classical system. From the classical stochastic equations of motion, we derive a general equation for the covariance matrix of the wave vector, which turns out to be of the Lindblad type. When the noise changes only the phase of φ j , the Schrödinger and the quantum Liouville equations are obtained. The component ψ j of the wave vector obeying the Schrödinger equation is related to the stochastic wave vector by |ψj|2=⟨|ϕj|2⟩ .

Assessing energy fluxes and carbon use in soil as controlled by microbial activity - A thermodynamic perspective A perspective paper

Soil organic matter (SOM) plays a central role for both the C cycle and soil functions. Plants provide the input and heterotrophic (micro)organisms are essential for the turnover. Microbial metabolism links matter and energy fluxes and generates the highest energy turnover dynamics in SOM because the organisms need both energy and matter for maintenance and growth. In this perspectives paper, we evaluate the knowledge on thermodynamic approaches potentially applicable to study the turnover of organic matter in the soil system. Thermodynamics is essential for understanding organic matter turnover in soil as turnover and storage are controlled by the energy supply to, and consumption by, microbes. Instead of just comparing the heat of combustion of compounds without considering microbial anabolism, we need to apply conventional thermodynamic state variables that can be either estimated using established thermodynamic equations, or measured empirically in soil. In particular, we can follow and quantify overall changes of enthalpies by calorimetry. Here, we suggest to apply a thermodynamic concept with the related experimental approaches of calo(respiro)metry and turnover mass balances including biomass formation. This enables us to better interpret and understand the highly variable carbon use efficiency (CUE) in a multi-substrate system such as soil and to relate this to energy use efficiency (EUE). Combining the experimental measurements of the thermodynamic state variables with mass turnover data allow prediction of whether compounds can be metabolized with energy delivery to microorganisms, or be thermodynamically stabilized under the respective redox and electron acceptor conditions. Energy balancing shows how much energy is actually used and retained in the soil, how much is emitted as heat, and how much may be stabilized due to endergonic turnover reactions. Thermodynamic stabilization should therefore be considered as basic stabilization process for organic compounds in soil.

Efficient and selective absorption of NH3 by supramolecular OHP[5]-based ternary deep eutectic solvents

Developing an efficient absorbent for selective ammonia capture is of significant importance in the recovery and utilization of ammonia resources. Herein, a series of supramolecular-based ternary deep eutectic solvents (DESs) was designed and prepared using per-hydroxy pillar[5]arene (OHP[5]) and ethylamine hydrochloride as the key components. It is found that the supramolecular-based ternary DES EaCl-Gly (1:2)-6% OHP[5] could be employed as an efficient absorbent for reversible absorption of NH3. The NH3 uptake capacity reached 2.39 mmol/g and 10.84 mmol/g at 298.2 K under the pressure of 10 kPa and 100 kPa, respectively. Meanwhile, a higher NH3/CO2 selectivity (84) was obtained at 298.2 K and 100 kPa owing to the low solubility of CO2 in EaCl-Gly (1:2)-6% OHP[5]. The results of 1H NMR and FTIR spectra further clarified the absorption mechanism of NH3 by EaCl-Gly (1:2)-6% OHP[5]. Accordingly, the chemical absorption and physical dissolution capacity of NH3 in EaCl-Gly (1:2)-6% OHP[5] were calculated on the basis of isotherm data and thermodynamic equations. This study offers a promising application of pillar[5]arene to form supramolecular-based DESs for efficient NH3 absorption.

A possible thermodynamic definition and equation of state for a model of political election cycles.

This work demonstrates how a simulation of political discourse can be formulated using variables of the agents' behaviors in a simulation, as thermodynamic variables. With these relations the methodology provides an approach to create a correspondence between the variables of an agent based social system and those of a thermodynamic system. Extended from this observation, diagrams akin to a P-V diagram for gases can be created for this social system. The basic thermodynamic variables of temperature, pressure and volume are defined from a system of agents with political and non-political actions engaged in simulated political discourse. An equation of state is defined for the simulated political phenomenon. Through this equation of state the full thermodynamic map of the system is presented under a P-V diagram with isothermal and isentropic lines, which is able to represent the political situation of the system at each point of time. The classic election cycle that takes place can be represented on this thermodynamic map (corresponding to an Otto cycle). This provides a possibility for researching macroscopic social cycles as a thermodynamic/informational cycle as the traces on the thermodynamic map show similarities to an Otto cycle. Such a formulation reinforces the endeavours of social physics to view social phenomena with physical principles.

Use the Thermodynamic State Equations to Analyze the Non-ideality of Gas Mixtures

The assessment of gas behavior in chemical engineering systems necessitates a profound understanding of thermodynamic principles that govern the interactions among the components within a given system. To this end, the deviation from ideality in a single gas or gas mixture is associated with the disparity between the actual behavior of the gas or gas mixture and the behavior anticipated by the ideal gas model. This study is aimed at scrutinizing the deviation from ideal behavior in a gas mixture composed of CH4 and CO2. The analysis employs the cubic equations of state: Van Der Waals, Soave-Redlich-Kwong, and generalized Virial equations, truncated to the third term. These equations are widely recognized for their utility in characterizing substance behavior under specific thermodynamic conditions. The investigation involves an evaluation of the mixture's behavior by assessing variations in the compressibility factor concerning pressure, volume, and pressure, using a thermodynamic calculator at 296.15 K and 15 bar. The findings of this study reveal the prevalence of attractive intermolecular forces at higher pressures and repulsive interactions at lower pressures. An analogous examination of the effect of altering the composition of CH4 was undertaken using the Soave-Redlich-Kwong equation, which incorporates parameters allowing for an evaluation of the impact of molecule size and intermolecular interactions within the mixture. Furthermore, experimental data were employed to validate the results obtained in this study. Consequently, it can be inferred that these equations provide insight into the influence of pressure on molecular interaction forces, encompassing repulsive and attractive forces, which in turn can define the new volume of a real system. Thus, based on the corroboration established herein, these equations demonstrate a high degree of consistency and applicability, thereby expanding the realm of thermodynamic inquiry.