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Results for “thermodynamic entropy”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Adaptation of Wallace's approach to the specific heat of elemental solids with significant intrinsic anharmonicity, particularly the light actinide metals

The quasiharmonic approximation is the most common method for modeling the specific heat of solids; however, it fails to capture the effects of intrinsic anharmonicity. In this study, we introduce the “elastic softening approximation,” an alternative approach to modeling intrinsic anharmonic effects on thermodynamic quantities, which is grounded in Wallace's thermodynamic framework that tracks entropy changes resulting from the continuous change (e.g., softening) of phonons as a function of temperature. A key finding of our study is a correlation between Poisson's ratio and the differential rate of phonon softening at finite frequencies, compared to lower frequencies relevant to elastic moduli measurements. We observe that elemental solids such as α -Be, diamond, Al, Cu, In, W, Au, and Pb, which span a wide range of Poisson's ratios and exhibit varying degrees of intrinsic anharmonicity, consistently follow this trend. When applied to α -U, α -Pu, and δ -Pu, our method reveals unusually large anharmonic phonon contributions at elevated temperatures across all three light actinide metals. These findings are attributed to the unique combination of enhanced covalency and softer elastic moduli inherent in the actinides, potentially influenced by their 5 f -electron bonding. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗
DOE OSTI2026

Working Fluid Characterization and Performance Assessment of Subcritical Organic Rankine Cycles Based on the Lee–Kesler Approach for Energy Recovery

Here, a generalized model using the Lee–Kesler approach based on the corresponding states principle is developed to assess the performance of subcritical Organic Rankine Cycles operating with different working fluids. Each fluid is characterized by five parameters: the acentric factor, critical temperature, critical pressure, molar mass, and the ideal-gas ratio of specific heats at the critical temperature. The model was developed using the compressibility factor modified version of the Benedict–Webb–Rubin equation proposed by Lee and Kesler and the enthalpy and entropy functions to calculate thermodynamic state properties. The model was validated by comparing the results calculated with the model and working fluid thermodynamic properties obtained with the CoolProp database. This comparison was conducted for 91 working fluids, obtaining a relative error below 5% for 88 out of the 91 fluids (∼97%). A generalized parametric study was conducted to determine the influence of the pinch point and each fluid parameter on the performance of Organic Rankine Cycle (ORC) systems. It was found that efficiency increases with critical temperature, ideal-gas ratio of specific heats at the critical temperature, and acentric factor, reaching up to 13%. The developed model enables the evaluation of ORC system performance for existing working fluids. It also allows the formulation and evaluation of new fluids to enhance the performance of the ORC while retrieving energy from any kind of source; and likewise, the methodology can be applied to other power generation cycles.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A Comparison of Order-Disorder in Several Families of Cubic Oxides

Order-disorder on both cation and oxygen sites is a hallmark of fluorite-derived structures, including pyrochlores. Ordering can occur on long- and short-range scales and can result in persistent metastable states. In various cubic oxide systems, different types of disorder are seen. The purpose of this paper is to review and compare the types and energetics of order-disorder phenomena in several families of cubic oxides having pyrochlore, weberite, defect fluorite, perovskite, rocksalt, and spinel structures. The goal is to better understand how structure, composition, and thermodynamic parameters (enthalpy and entropy) determine the feasibility of different competing ordering processes and structures in these diverse systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1972

Computer program for natural gas flow through nozzles

Subroutines, FORTRAN 4 type, were developed for calculating isentropic natural gas mass flow rate through nozzle. Thermodynamic functions covering compressibility, entropy, enthalpy, and specific heat are included.

Johnson, R. C.↗
NASA NTRS1994

Heat release effects on the instability of parallel shear layers

The influence of time-dependent heat addition on the linear instablity of shear layers is of considerable interest in understanding the dynamic behavior of reacting flows and combustion-turbulence interactions. The approach is based upon the Bernoulli enthalpy aeroacoustics theory, which utilizes the specific enthalpy and specific entropy as the primary thermodynamic variables. In addition, velocity oscillations are split into Helmoholtz decomposition theorem.

Hegde, U.↗
NASA NTRS2004

Application of Simulated Annealing and Related Algorithms to TWTA Design

Simulated Annealing (SA) is a stochastic optimization algorithm used to search for global minima in complex design surfaces where exhaustive searches are not computationally feasible. The algorithm is derived by simulating the annealing process, whereby a solid is heated to a liquid state and then cooled slowly to reach thermodynamic equilibrium at each temperature. The idea is that atoms in the solid continually bond and re-bond at various quantum energy levels, and with sufficient cooling time they will rearrange at the minimum energy state to form a perfect crystal. The distribution of energy levels is given by the Boltzmann distribution: as temperature drops, the probability of the presence of high-energy bonds decreases. In searching for an optimal design, local minima and discontinuities are often present in a design surface. SA presents a distinct advantage over other optimization algorithms in its ability to escape from these local minima. Just as high-energy atomic configurations are visited in the actual annealing process in order to eventually reach the minimum energy state, in SA highly non-optimal configurations are visited in order to find otherwise inaccessible global minima. The SA algorithm produces a Markov chain of points in the design space at each temperature, with a monotonically decreasing temperature. A random point is started upon, and the objective function is evaluated at that point. A stochastic perturbation is then made to the parameters of the point to arrive at a proposed new point in the design space, at which the objection function is evaluated as well. If the change in objective function values (Delta)E is negative, the proposed new point is accepted. If (Delta)E is positive, the proposed new point is accepted according to the Metropolis criterion: rho((Delta)f) = exp((-Delta)E/T), where T is the temperature for the current Markov chain. The process then repeats for the remainder of the Markov chain, after which the temperature is decremented and the process repeats. Eventually (and hopefully), a near-globally optimal solution is attained as T approaches zero. Several exciting variants of SA have recently emerged, including Discrete-State Simulated Annealing (DSSA) and Simulated Tempering (ST). The DSSA algorithm takes the thermodynamic analogy one step further by categorizing objective function evaluations into discrete states. In doing so, many of the case-specific problems associated with fine-tuning the SA algorithm can be avoided; for example, theoretical approximations for the initial and final temperature can be derived independently of the case. In this manner, DSSA provides a scheme that is more robust with respect to widely differing design surfaces. ST differs from SA in that the temperature T becomes an additional random variable in the optimization. The system is also kept in equilibrium as the temperature changes, as opposed to the system being driven out of equilibrium as temperature changes in SA. ST is designed to overcome obstacles in design surfaces where numerous local minima are separated by high barriers. These algorithms are incorporated into the optimal design of the traveling-wave tube amplifier (TWTA). The area under scrutiny is the collector, in which it would be ideal to use negative potential to decelerate the spent electron beam to zero kinetic energy just as it reaches the collector surface. In reality this is not plausible due to a number of physical limitations, including repulsion and differing levels of kinetic energy among individual electrons. Instead, the collector is designed with multiple stages depressed below ground potential. The design of this multiple-stage collector is the optimization problem of interest. One remaining problem in SA and DSSA is the difficulty in determining when equilibrium has been reached so that the current Markov chain can be terminated. It has been suggested in recent literature that simulating the thermodynamic properties opecific heat, entropy, and internal energy from the Boltzmann distribution can provide good indicators of having reached equilibrium at a certain temperature. These properties are tested for their efficacy and implemented in SA and DSSA code with respect to TWTA collector optimization.

Radke, Eric M.↗
DOE OSTI2021

Operational Limits of Redox Metal Oxides Performing Thermochemical Water Splitting

Solar thermochemical hydrogen production is an attractive technology that stores intermittent solar energy in the form of chemical bonds. Efficient operation requires the identification of a redox-active metal oxide (MO x ) material that can achieve high conversion of water to hydrogen at minimal energy input. Water splitting occurs by consecutive reduction and reoxidation reactions of MO x . MO x is reduced to MO x-δ and, in the second step, is reoxidized by water recovering the initial MO x and generate H 2 . The material must reduce at temperatures achievable in concentrated solar receiver/reactors, while maintaining a thermodynamic driving force to split water. At equilibrium, extent of reduction depends on temperature and oxygen partial pressure, and in this analysis, a set of thermodynamic properties, namely, enthalpy and entropy of oxygen vacancy formation, is sufficient to represent MO x . Herein, a method to easily classify materials based on these thermodynamic properties under any condition of oxygen partial pressure and temperature is presented. This method is based on fundamental thermodynamic principles and is applicable for any redox material with known thermodynamic properties. Despite the simplicity of the method, it is believed that this analysis will support future research in targeting thermodynamic properties of redox-active metal oxides.

water splitting↗
DOE OSTI2021

Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born–Oppenheimer molecular dynamics performed at a single temperature. In conclusion, this advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Thermodynamics of calcium binding to heparin: Implications of solvation and water structuring for polysaccharide biofunctions

Heparan sulfates are found in all animal tissues and have essential roles in living systems. This family of biomacromolecules modulates binding to calcium ions (Ca 2+ ) in low free energy reactions that influence biochemical processes from cell signaling and anticoagulant efficacy to biomineralization. Despite their ubiquity, the thermodynamic basis for how heparans and similarly functionalized biomolecules regulate Ca 2+ interactions is not yet established. Using heparosan (Control) and heparins with different positions of sulfate groups, we quantify how SO 3 − and COO − content and SO 3 − position modulate Ca 2+ binding by isothermal titration calorimetry. The free energy of all heparin-Ca2+ interactions (ΔG rxn ) is dominated by entropic contributions due to favorable water release from polar, hydrophilic groups. Heparin with both sulfate esters (O-SO 3 − ) and sulfamides (N-SO 3 − ) has the strongest binding to Ca 2+ compared to heparosan and to heparin with only O-SO 3 − groups (~3X). By linking Ca 2+ binding thermodynamics to measurements of the interfacial energy for calcite (CaCO 3 ) crystallization onto polysaccharides, we show molecule-specific differences in nucleation rate can be explained by differences in water structuring during Ca 2+ interactions. A large entropic term (-TΔS rxn ) upon Ca 2+ –polysaccharide binding correlates with high interfacial energy to CaCO 3 nucleation. Combining our measurements with literature values indicates many Ca 2+ –polysaccharide interactions have a shared thermodynamic signature. The resulting enthalpy–entropy compensation relationship suggests these interactions are generally dominated by water restructuring involving few conformational changes, distinct from Ca 2+ –protein binding. Our findings quantify the thermodynamic origins of heparin-specific interactions with Ca 2+ and demonstrate the contributions of solvation and functional group position during biomacromolecule-mediated ion regulation.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Evidence of ordering in Cu-Ni alloys from experimental electronic entropy measurements

Phase diagrams exhibiting extended solid-solution and lenslike melting are often reproduced using ideal solutions, where ideal mixing considers a fully random configurational entropy of mixing. In the field of irreversible thermodynamics, experimental measurements of the composition variation of high-temperature electronic transport and molten-state properties suggest, however, a strong role for short-range atomic ordering in these systems. Herein, measurements of the thermopower and resistivity are reported for Cu-Ni solid solutions as a function of temperature and composition. The electronic transport properties were interpreted with an irreversible thermodynamic framework, revealing a large electronic contribution to the entropy of mixing. By considering a cluster model for the configurational entropy that uses the electronic contribution to inform the existence of ordered associates, we rationalize such a contribution of the electronic entropy with the ideal entropy of mixing commonly used to model such systems. In conclusion, these results suggest that the short-range order of the atoms plays a significant role in both solid and liquid states, even when there are no dominant intermetallic compounds in these alloys.

36 MATERIALS SCIENCE↗
NASA NTRS1974

Computer program for calculation of real gas turbulent boundary layers with variable edge entropy

A user's manual for a computer program which calculates real gas turbulent boundary layers with variable edge entropy on a blunt cone or flat plate at zero angle of attack is presented. An integral method is used. The method includes the effect of real gas in thermodynamic equilibrium and variable edge entropy. A modified Crocco enthalpy velocity relationship is used for the enthalpy profiles and an empirical correlation of the N-power law profile is used for the velocity profile. The skin-friction-coefficient expressions of Spalding and Chi and Van Driest are used in the solution of the momentum equation and in the heat-transfer predictions that use several modified forms of Reynolds analogy.

Boney, L. R.↗
DOE OSTI2026

Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Furthermore, those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.

42 ENGINEERING↗
NASA NTRS1949

Compression Shocks in Two-Dimensional Gas Flows

The following are arguments on the compression shocks in gas flow start with a simplified representation of the results of the study made by Th. Meyer as published in the Forschungsheft 62 of the VDI, supplemented by several amplifications for the application.In the treatment of compression shocks, the equation of energy, the equation of continuity, the momentum equation, the equation of state of the particular gas, as well as the condition Of the second law of thermodynamics that no decrease of entropy is possible in an isolated system, must be taken into consideration. The result is that, in those cases where the sudden change of state according to the second law of thermodynamics is possible, there always occurs a compression of the gas which is uniquely determined by the other conditions.

Busemann, A.↗
DOE OSTI2024

A simple method for obtaining heat capacity coefficients of minerals

Abstract Heat capacity data are unavailable or incomplete for many minerals at geologically relevant temperatures. Despite the availability of entropy and enthalpy values in numerous thermodynamic tables (even sometimes at elevated temperatures), there remains need for extrapolation beyond, or interpolation between, temperatures. This approach inevitably results in estimates for entropy and enthalpy values because the heat capacity coefficients required for optimal thermodynamic treatment are less frequently available. Here we propose a simple method for obtaining heat capacity coefficients of minerals. This method requires only the empirically measured temperature-specific heat capacity for calculation via a matrix algorithm. The system of equations solver is written in the Python computing language and has been made accessible in an online repository. Thermodynamically, the solution to a system of equations represents the heat capacity coefficients that satisfy the mineral-specific polynomial. Direct coefficient calculation will result in more robust thermodynamic data, which are not subject to fitting uncertainties. Using hematite as an example, this method provides results that are comparable to conventional means and is applicable to any solid material. Coefficients vary within the traditional large 950 K temperature interval, indicating that best results should instead utilize a smaller 400 K temperature interval. Examples of large-scale implications include the refinement of geothermal gradient estimation in rapidly subsiding sedimentary basins or metamorphic and hydrothermal evolution.

Geochemistry & Geophysics↗