Chemical Thermodynamics and Thermal Analysis最新文献

{"title":"Phase stability of Ce, La and U oxides in the presence of hydrogen and water: Thermodynamic modeling and experimental insights","authors":"Danielle Schweke,&nbsp;Daniel Rabin,&nbsp;Eli Brosh","doi":"10.1016/j.ctta.2025.100198","DOIUrl":"10.1016/j.ctta.2025.100198","url":null,"abstract":"<div><div>Standard metal-oxygen or metal-hydrogen phase diagrams neglect the presence of water vapor. However, water vapor present in the environment often destabilizes the oxide or hydride phase, leading to the stabilization of hydroxide, oxy-hydroxide or hydrate phases. Appropriate phase diagrams are required to properly describe and predict the chemistry of a metal and its oxide or hydride in realistic conditions.</div><div>In the present work, M-O-H phase stability diagrams were computed for uranium, lanthanum and cerium (U, La and Ce), based on previously compiled as well as newly assessed thermodynamic data, in CALPHAD (CALculations of PHAse Diagrams) formalism. We show how the ternary phase diagrams relate to diverse experimental observations on the behavior of these elements in environments containing hydrogen or water vapor.</div><div>The phase diagrams allow the identification of common trends as well as differences between the systems studied. For example, all the elements form hydride phases but minor concentrations of oxygen or water are sufficient to destabilize the hydride. The oxide phases have a wide range of stability, but the oxide may react in the presence of water vapor to form a hydroxide (in the case of La) or hydrates (in the case of U). The range of stability of the hydroxide and hydrate phases increases as the temperature is lowered.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"19 ","pages":"Article 100198"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamic behavior and related phase transitions in SeTeSn and SeTeSnM (M = Ge, In, Pb, and Sb) chalcogenide glass ceramics","authors":"Kaushal Kumar Sarswat ,&nbsp;Ishu Sharma ,&nbsp;Neeraj Mehta","doi":"10.1016/j.ctta.2025.100202","DOIUrl":"10.1016/j.ctta.2025.100202","url":null,"abstract":"<div><div>This study addresses the critical need for a deeper thermodynamic understanding of chalcogenide glass–ceramic systems by investigating Se₇₆Te₂₀Sn₂ and Se₇₈Te₂₀Sn₂M₂ (M = Ge, In, Pb, Sb) alloys. Although previous research has focused on thermal stability and crystallization behavior, limited attention has been given to the systematic analysis of specific heat behavior and its kinetic correlations near the glass transition temperature (<em>T_g</em>). While prior studies have emphasized thermal stability and crystallization, this work focuses on the composition-dependent evolution of specific heat (<em>C_p</em>) across the glass transition temperature (<em>T_g</em>). Differential scanning calorimetry (DSC) was employed under non-isothermal conditions to evaluate the specific heat (<em>C_p</em>) and derive associated thermodynamic parameters: enthalpy (<em>H</em>), entropy (<em>S</em>), and Gibbs free energy (<em>G</em>).</div><div>Two novel kinetic–thermodynamic correlations were identified: (i) a linear relationship between the rate of conversion change Δ<em>(dα/dT)</em> and log<em>β</em>, and (ii) a direct correlation between the specific heat jump (Δ<em>C_p</em>) and log<em>β</em>. These results offer new insights into how heating rate influences thermal transitions. The thermodynamic profiles of <em>C_p, H, S</em>, and <em>G</em> exhibit continuous transition characteristics, indicating that <em>T_g</em> functions as a dynamic threshold rather than a sharp boundary. This work contributes to a deeper understanding of glass transition phenomena and provides a framework for tailoring phase-change behavior in functional chalcogenide materials.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"19 ","pages":"Article 100202"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A thermodynamic conundrum through the ages","authors":"Sunil Nath","doi":"10.1016/j.ctta.2025.100196","DOIUrl":"10.1016/j.ctta.2025.100196","url":null,"abstract":"<div><div>Recently, in a series of three papers, Tolley, Woodfield, and Hansen analyzed six types of <em>spontaneous</em> ideal processes where <span><math><mrow><mi>Q</mi><mo>=</mo><mi>W</mi><mo>=</mo><mn>0</mn></mrow></math></span> and for which <span><math><mrow><mstyle><mi>Δ</mi></mstyle><mi>U</mi></mrow></math></span> and <span><math><mrow><mstyle><mi>Δ</mi></mstyle><mi>S</mi></mrow></math></span> are also zero. But this leads to a conundrum because it does not answer the question why the process occurs spontaneously, and where the entropic increase originated from. The papers resolve an apparent contradiction in classical thermodynamics that was recognized by Max Planck in his famous <em>Treatise on Thermodynamics</em> a century ago. Planck realized the need for inclusion of the distribution of matter in a more complete development of thermodynamics. However no such development was forthcoming. The conundrum is resolved by Hansen and colleagues by the novel proposal of a probability distribution of particles, and an entropy change associated with this distribution, <span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>S</mi><mi>D</mi></msub></mrow></math></span>. Equations for <span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>S</mi><mi>D</mi></msub></mrow></math></span> have been worked out for the six types of processes considered. Applications of their fundamental work to efficient energy conversion in real chemical and biological systems—that presents new challenges and conundrums—and intersects with the author’s own research are discussed, and some suggestions for future work are offered.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"19 ","pages":"Article 100196"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CO2 solubility in MEA and AMP aqueous solutions: Experimental liquid compositions and modeling of the liquid and the vapor phase using the CPA equation of state and the modified Kent-Eisenberg model","authors":"Niki Gerasimou,&nbsp;Ioannis Tsivintzelis","doi":"10.1016/j.ctta.2025.100201","DOIUrl":"10.1016/j.ctta.2025.100201","url":null,"abstract":"<div><div>The solubility of CO₂ in 30 % wt. aqueous ethanolamine (MEA) and 2-amino-2-methyl-1-propanol (AMP) solutions was experimentally investigated. The experimental data are in satisfactory agreement with literature data for MEA at 313 and 333 K and for AMP at 313, 323 and 333 K. The investigated CO₂-amine-water systems were modeled using the modified Kent-Eisenberg (KE) model and the Cubic plus Association (CPA) equation of state coupled with the pseudochemical reaction approach. Initially, the models’ calculations were evaluated against the experimental data of this study. It was shown that both models result in satisfactory correlations of the CO₂ solubility in the liquid solvent. Subsequently, their prediction ability was evaluated against the limited literature data for the vapor phase compositions. It was shown that both models predict a low amine mole fraction in the vapor phase (10^–2 - 10^–4) in accordance with the experimental data. However, the performance of the modified KE model, although based on several simplifications, is in most cases better than the performance of CPA, revealing that the pseudochemical reaction approach is a severe simplification that has an important effect on the prediction ability of the model. Such models’ comparison also reveals that the chemical equilibrium outweighs any contribution of physical interactions affecting the phase equilibrium.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"19 ","pages":"Article 100201"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144535870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamic behavior of pyrimidine derivatives on multilayer Fe crystal structure: Molecular dynamics and surface layer interaction","authors":"Ghadah H. Alwan ,&nbsp;Maysaa A. Mohammed ,&nbsp;Muntadher H. Al-Ameri ,&nbsp;Amira A. Abduljaleel ,&nbsp;Safa H. Mohammed ,&nbsp;Hasan R. Obayes ,&nbsp;Doaa S. El Sayed ,&nbsp;Ali Abdullah Issa","doi":"10.1016/j.ctta.2025.100209","DOIUrl":"10.1016/j.ctta.2025.100209","url":null,"abstract":"<div><div>This study aimed to evaluate the structural, electronic, and adsorption behavior of a series of O- and S-pyrimidine derivatives, substituted with NO₂, Cl, Br, and OH groups, as potential inhibitors on a designed multilayered Fe surface. A comprehensive computational approach was employed, including geometry optimization, frontier molecular orbital (FMO) and molecular electrostatic potential (MEP) analyses, thermodynamic calculations, molecular dynamics simulations, and Monte Carlo-based adsorption modeling. Structural optimization and packing morphology analysis were performed for Pyr 1 and Pyr 2 to assess how substituent variations influence polymorph formation and surface packing behavior on the Fe lattice. FMO and MEP results identified key active sites and indicated good system stability, particularly for Pyr 3 and Pyr 7. Thermodynamic data showed minor stability variations based on substituent type, while molecular dynamics simulations highlighted strong surface interactions for Pyr 1, Pyr 3, Pyr 5, and Pyr 7. The adsorption locator study confirmed effective adsorption and conformational adaptability of the inhibitors on the Fe surface, influenced by the nature of the substituent groups. These findings provide a theoretical foundation for the design of pyrimidine-based inhibitors targeting metal surfaces.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"19 ","pages":"Article 100209"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144771904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simple Correlations for Heat Capacity and Thermal Conductivity of Undefined Petroleum Liquid Fractions","authors":"Carl-Martin Carstensen","doi":"10.1016/j.ctta.2025.100205","DOIUrl":"10.1016/j.ctta.2025.100205","url":null,"abstract":"<div><div>The black oil equation of state has for the last century been integral for modelling fluid behaviour in the petroleum industry. Despite the rise of compositional approaches, the black oil equation of state remains widely used in reservoir and process simulations. Traditionally, black oil modelling focuses on the volumetric behaviour of fluids, but it also requires thermophysical properties like heat capacity and thermal conductivity. This study introduces novel empirical correlations for pressure and temperature dependent isobaric specific heat capacity and thermal conductivity of undefined petroleum liquid fractions. Although pressure has a minimal impact on heat capacity, it significantly affects thermal conductivity, making it an essential parameter to include. Four correlations were developed: two for each property, with one set based on in situ density and the other on specific gravity. Statistical analysis reveals that the correlations using in situ density offer higher accuracy. These new correlations outperform existing models, providing a reliable calculation method in early project phases and screening tasks within chemical and process engineering.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"19 ","pages":"Article 100205"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of molecular interactions in glucose-aqueous-human mixtard insulin/metformin solutions by volumetric, acoustic properties","authors":"S.D. Deosarkar ,&nbsp;H.N. Pawar ,&nbsp;R.V. Dudhate ,&nbsp;B.R. Bhosale ,&nbsp;A.D. Arsule ,&nbsp;T.M. Kalyankar","doi":"10.1016/j.ctta.2025.100190","DOIUrl":"10.1016/j.ctta.2025.100190","url":null,"abstract":"<div><div>In order to understand the molecular interactions between glucose and antidiabetic human mixtard insulin and metformin, the present study reports measured density, ultrasonic velocity, refractive index, viscosity and surface tension of glucose + aqueous-{1 %, 3 %, 5 % and 7 % v/w human mixtard insulin and 7 % v/w human mixtard insulin + 0.05 mol·kg^-1metformin} at different temperatures. Apparent molar volume (<span><math><msub><mi>V</mi><mrow><mn>2</mn><mo>,</mo><mi>ϕ</mi></mrow></msub></math></span>) and apparent molar isentropic compressibility (<span><math><msub><mi>κ</mi><mrow><mi>S</mi><mo>,</mo><mn>2</mn><mo>,</mo><mi>ϕ</mi></mrow></msub></math></span>) of glucose were calculated from density and ultrasonic velocity. Concentration dependence of apparent molar properties was studied and respective partial molar volume (<span><math><mrow><mi>V</mi><msub><mrow><msubsup><mrow></mrow><mn>2</mn><mi>o</mi></msubsup></mrow><mrow><mo>,</mo><mi>ϕ</mi></mrow></msub></mrow></math></span>) and compressibility (<span><math><msubsup><mi>κ</mi><mrow><mi>S</mi><mo>,</mo><mn>2</mn><mo>,</mo><mi>ϕ</mi></mrow><mn>0</mn></msubsup></math></span>) were determined using Masson's and Gucker's relation respectively. Standard transfer volumes and compressibilities (<span><math><mrow><msub><mstyle><mi>Δ</mi></mstyle><mi>t</mi></msub><mi>V</mi><msub><mrow><msubsup><mrow></mrow><mn>2</mn><mi>o</mi></msubsup></mrow><mrow><mo>,</mo><mi>ϕ</mi></mrow></msub></mrow></math></span> and<span><math><mrow><msub><mstyle><mi>Δ</mi></mstyle><mi>t</mi></msub><msubsup><mi>κ</mi><mrow><mi>S</mi><mo>,</mo><mn>2</mn><mo>,</mo><mi>ϕ</mi></mrow><mn>0</mn></msubsup></mrow></math></span>) of studied solutions were calculated. Transfer properties like viscosity of studied solutions have been measured and viscosity <em>B</em>-coefficients at different temperatures were determined. In addition to this, surface tension and refractive index measurements were carried out. The measured and derived properties have been evaluated in terms of hydration behavior of glucose and molecular interactions of glucose with insulin and metformin. The results of volumetric and acoustic properties indicated the significant effect of HMI and slight effect of metformin on the hydration of glucose at different temperatures. The viscosity study confirms structure making nature of glucose for aqueous-HMI and aqueous-HMI-Met solutions.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"18 ","pages":"Article 100190"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143820836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamic studies for molecular interactions of tetraalkylammonium bromide salts in aqueous solutions: A volumetric approach","authors":"Vasim R. Shaikh ,&nbsp;Sana R. Shaikh ,&nbsp;Gaurav R. Gupta ,&nbsp;Vijay M. Tangde ,&nbsp;Kapil S. Ganorkar","doi":"10.1016/j.ctta.2025.100187","DOIUrl":"10.1016/j.ctta.2025.100187","url":null,"abstract":"<div><div>Densities for aqueous solutions of tetraalkylammonium bromide (R₄NBr) salts, namely, tetramethylammonium bromide (Me₄NBr), tetraethylammonium bromide (Et₄NBr), tetra-n-propylammonium bromide (n-Pr₄NBr) and tetra-n-butylammonium bromide (n-Bu₄NBr) have been measured at 293.15, 298.15 and 303.15 K. Further, the experimental density data were used for the calculations of apparent molar volumes of solute at finite concentration (<span><math><msub><mi>V</mi><mi>ϕ</mi></msub></math></span>) and apparent molar volumes of solute at infinite dilution (<span><math><msubsup><mi>V</mi><mi>ϕ</mi><mn>0</mn></msubsup></math></span>) at studied temperatures. The <span><math><msubsup><mi>V</mi><mi>ϕ</mi><mn>0</mn></msubsup></math></span> values increase as the chain length increases and follow the order Me₄N⁺ &lt; Et₄N⁺ &lt; n-Pr₄N⁺ &lt; n-Bu₄N⁺. The deviation parameter (<em>B_V</em>) found to be negative for studied salts in water, indicates that the tetraalkylammonium ions acts as water-structure making ions. The coefficient of thermal expansion (α) of solutions, apparent molar expansibility of solute at finite concentration (<span><math><msub><mi>E</mi><mi>ϕ</mi></msub></math></span>) and apparent molar expansibility of solute at infinite dilution (<span><math><msubsup><mi>E</mi><mi>ϕ</mi><mn>0</mn></msubsup></math></span>) were also calculated at 298.15 K. The <span><math><msubsup><mi>E</mi><mi>ϕ</mi><mn>0</mn></msubsup></math></span> values are found to be positive for the studied R₄NBr salts in water at 298.15 K and increases as the chain length increases. The result and analysis lead to the elaboration of hydrophobic interaction effects and concept like cation-cation (pair wise) and cation-anion-cation (triplet) interaction.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"18 ","pages":"Article 100187"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamic calculation studies on oil composition and water presence effect on the minimum miscibility pressure of the CO2/two-components oil system","authors":"Hangyu Zang,&nbsp;Zeguang Dong,&nbsp;Zhongwen Zhang,&nbsp;Yingge Li,&nbsp;Dongxing Du","doi":"10.1016/j.ctta.2025.100183","DOIUrl":"10.1016/j.ctta.2025.100183","url":null,"abstract":"<div><div>Minimum Miscibility Pressure (MMP) is a key parameter for guiding the CO₂ Enhanced Oil Recovery (EOR) as well as carbon geological storage applications. In this work, a thermodynamic calculation study is performed concerning the oil composition and the water presence effect on the MMP properties of the CO₂/multicomponent oil system under various temperatures. Two-components oils with different n-C₁₄H₃₀ and n-C₁₉H₄₀ ratios at 7:3, 6:4, 5:5, 4:6 and 3:7, are employed to reveal the oil composition effect on MMPs of CO₂/oil system. Via introducing saturated water into CO₂, the effect of water presence on MMPs of the CO₂/oil system is studied as well. Thermodynamic calculation results show the MMP of the CO₂/two-components oil systems increases from 8.5 MPa to 9.8 MPa, 10.1 MPa to 11.2 MPa, 11.6 MPa to 12.6 MPa, 12.9 MPa to 13.8 MPa, and 14.2 MPa to 15.0 MPa, together with the increasing portion of the heavier C₁₉ oil component from 30 % to 70 % at various temperatures of 40 °C, 50 °C, 60 °C, 70 °C and 80 °C, respectively. Calculation results also reveal the presence of the water component would reduce the MMPs of the CO₂/oil system by 0.2–0.8 MPa compared with the water absence case in the studied oil component and temperature conditions. In particular, the water presence effect on MMP reduction is more significant for the oils with higher portion of heavy components.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"18 ","pages":"Article 100183"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143578592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Macleod equation and constant in pure, binary and ternary systems","authors":"Miguel Gonzalo Arenas-Quevedo,&nbsp;José Luis López-Cervantes,&nbsp;Jesús Gracia-Fadrique","doi":"10.1016/j.ctta.2025.100165","DOIUrl":"10.1016/j.ctta.2025.100165","url":null,"abstract":"<div><div>The Macleod equation establishes a linear relationship between surface tension and the fourth power of the density difference between liquid and vapor, expressed as<span><math><mrow><mspace></mspace><mi>σ</mi><mo>=</mo><msub><mi>C</mi><mrow><mi>M</mi><mi>a</mi><mi>c</mi><mi>l</mi><mi>e</mi><mi>o</mi><mi>d</mi></mrow></msub><msup><mrow><mo>(</mo><msub><mi>ρ</mi><mi>l</mi></msub><mo>−</mo><msub><mi>ρ</mi><mi>v</mi></msub><mo>)</mo></mrow><mn>4</mn></msup></mrow></math></span>. This study demonstrates by a practical and empirical approximation with critical exponents and the theory of corresponding states, the foundations behind Macleod's proposal and extends this equation to binary and ternary systems exhibiting liquid-liquid equilibrium. Additionally, it offers a thermodynamic perspective on the Macleod constant through a novel variable termed the entropic molar volume, along with other functions.</div></div>","PeriodicalId":9781,"journal":{"name":"Chemical Thermodynamics and Thermal Analysis","volume":"18 ","pages":"Article 100165"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}