From the Arrhenius to the Clausius?Clapeyron Equation

2002 ◽  
Vol 7 (6) ◽  
pp. 347-348 ◽  
Author(s):  
Igor Novak
Keyword(s):  
Clapeyron Equation

Sorption and thermodynamic properties of juvenile Pinus sylvestris L. wood after 103 years of submersion

Holzforschung ◽  
2008 ◽  
Vol 62 (6) ◽  
Author(s):  
Luis García Esteban ◽  
Paloma de Palacios ◽  
Francisco García Fernández ◽  
Antonio Guindeo ◽  
Marta Conde ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Pinus Sylvestris ◽  
Integration Method ◽  
Juvenile Wood ◽  
Crystallinity Index ◽  
Isosteric Heat ◽  
Chemical Modifications ◽  
Clapeyron Equation ◽  
X Ray ◽  
Hemicellulose Degradation

Abstract The hygroscopicity and thermodynamic properties of juvenile Pinus sylvestris L. wood taken from the submerged piles of a bridge built in 1903 over the Jiloca River, in Spain, were compared with the corresponding values of juvenile wood of the same species from recently cut trees. The 35°C and 50°C isotherms were plotted and subsequently fitted using the Guggenheim-Anderson-Boer-Dent method, and the isosteric heat of sorption was obtained through the integration method of the Clausius-Clapeyron equation. The isotherms were compared by means of the hysteresis coefficients. Infrared spectra were recorded to study the chemical modifications, and the crystal structure of the cellulose was studied by X-ray diffractograms. The submersion in water resulted in hemicellulose degradation and a decrease in the crystallinity index and the crystallite length, accompanied by a corresponding increase in the proportion of amorphous zones. Owing to this, the equilibrium moisture contents of the water logged wood are higher than in the recent wood, both in adsorption and in desorption. In terms of the thermodynamic properties, the bond energy is higher in the recent wood than in the water logged wood.

Melting Temperature of FeO under Pressure

2013 ◽  
Vol 717 ◽  
pp. 184-187
Author(s):  
Shuai Zhang ◽  
Lei Chen
Keyword(s):  
Phase Diagram ◽  
Melting Temperature ◽  
Surface Stress ◽  
Clapeyron Equation ◽  
Metallurgical Processes ◽  
Pressure Phase ◽  
Effect Of Surface ◽  
Volume Difference

The melting temperature-pressure phase diagram [Tm(P)-P] for wustite (FeO) is predicted through the Clapeyron equation where the pressure-dependent volume difference is modeled by introducing the effect of surface stress induced pressure. FeO plays an important role in many metallurgical processes and in the Earths mantle mineralogy. FeO is also of great interest in the field of state solid physics and chemistry because of its electrical, magnetic, structural and non-stoichiometric properties.

Vapor-Phase Spectra and the Pressure-Temperature Dependence of Long-Chain Carboxylic Acids Studied by a CO Laser and the Photoacoustic Heat-Pipe Detector

1995 ◽  
Vol 49 (7) ◽  
pp. 994-999 ◽  
Author(s):  
Henk Jalink ◽  
Dane Bicanic ◽  
Mladen Franko ◽  
Zoltán Bozóki
Keyword(s):  
Temperature Dependence ◽  
Heat Pipe ◽  
Vapor Phase ◽  
Saturated Fatty Acids ◽  
Capric Acid ◽  
Spectral Studies ◽  
Clapeyron Equation ◽  
Co Laser ◽  
Phase Spectra ◽  
Long Chain

A resonant photoacoustic heat-pipe (PAHP) cell was constructed and used for spectral studies of four long-chain saturated fatty acids (C10:0 to C16:0) at CO laser wavelengths and temperatures above that of the ambient. Vapor-phase absorption spectra were recorded at temperatures of 383 K for capric acid C10H20O2, 400 K for lauric acid C12H24O2, 438 K for myristic acid C14H28O2, and 445.5 K for palmitic acid C16H32O2, respectively. In addition, the temperature dependence (298 to 393 K) of vapor pressure was determined for C10:0; measurable PA signals were obtained at a temperature only a few degrees above the melting point for this acid. The data observed for C10:0 could be linearly fitted from as low as 323 K, indicating the validity of the Clausius-Clapeyron equation for temperatures lower than the 398 K < T < 541.4 K range anticipated so far.

scholarly journals A method of describing the saturation line based on the apparent heat of vaporization and Clausius-Clapeyron equation

2017 ◽  
Vol 16 (2) ◽  
pp. 66-72 ◽  
Author(s):  
S.V. Rykov ◽  
◽  
I.V. Kudryavtseva ◽  
M.I. Poltoratskiy ◽  
V.A. Rykov ◽  
...  
Keyword(s):  
Saturation Line ◽  
Clapeyron Equation ◽  
Heat Of Vaporization

scholarly journals Description of the liquid-vapor phase equilibrium line of pure substances within the bounds of scale theory based on the Clapeyron equation

2021 ◽  
Vol 2057 (1) ◽  
pp. 012113
Author(s):  
S V Rykov ◽  
I V Kudryavtseva ◽  
V A Rykov ◽  
E E Ustyuzhanin
Keyword(s):  
Phase Equilibrium ◽  
Saturated Vapor ◽  
Average Diameter ◽  
Saturation Line ◽  
Equilibrium Line ◽  
Modern Theory ◽  
Clapeyron Equation ◽  
Scale Theory ◽  
Pure Substances ◽  
Phase Equilibrium Line

Abstract On the basis of the Clapeyron equation and the scale theory, expressions are developed for the “apparent” heat of vaporization r * = r * (T), vapor ρ- = ρ- (T) and liquid ρ+ = ρ+ (T) branches of the saturation line of individual substances for the range of state parameters from the triple point (pt,Tt,ρt ) to the critical (pc,Tc,ρc ). The peculiarity of the proposed approach to the description of the saturation line is that all exponents of the components of the equations ρ- = ρ- (T) and ρ+ = ρ+ (T) are universal up to the universality of the critical indices α, β and Δ. In this case, the order parameter ds = (ρ+ − ρ-)/(2ρc) and the average diameter df = (ρ+ + ρ-)/(2ρc) − 1 of the saturation line satisfy the saturation line model [2β,1−α], which follows from the modern theory of critical phenomena. The method is tested on the example of describing the phase equilibrium line of refrigerant R1233zd(E) in the range from Tt = 195.15 K to Tc = 439.57 K. It is found that in the temperature range [Tt,Tc ], the developed system of the mutually consistent equations ps = ps (T), r * = r * (T), ρ- = ρ- (T) and ρ+ = ρ+ (T) allows describing the data on the saturated vapor pressure ps and densities ρ- and ρ+ on the saturation line within the experimental uncertainty of these data.

Assessment of the contribution of the air-vapor mixture volume exceeding over the volumes injected to oil and petroleum product losses from evaporation

2021 ◽  
pp. 452-459
Author(s):  
Алексей Анатольевич Коршак ◽  
Андрей Алексеевич Коршак
Keyword(s):  
Petroleum Product ◽  
Molar Mass ◽  
Vapor Mixture ◽  
Instrument Error ◽  
Clapeyron Equation ◽  
Wide Range ◽  
Mixture Volume ◽  
Gas Space ◽  
Space Volume

В настоящее время при экспериментальном определении потерь нефтепродуктов от «больших дыханий» резервуаров используют формулу Черникина - Валявского. При этом «однако» не учитывается, что объем вытесняемой в атмосферу паровоздушной смеси, как правило, превышает объем закачиваемой нефти (нефтепродукта). Соответствующий параметр - коэффициент превышения, - по экспериментальным данным, может принимать значения более 8. До недавнего времени не до конца были ясны даже причины этого явления, соответственно, эмпирические зависимости для расчета коэффициента превышения не учитывали всех влияющих факторов. Авторами статьи на основе уравнения Менделеева - Клапейрона в дифференциальной форме получено аналитическое выражение для вычисления среднего коэффициента превышения. Установлено, что данная величина зависит от молярной массы и температуры паровоздушной смеси в начале и конце закачки, а также от соотношения объемов газового пространства резервуара и закачиваемого продукта. Для анализа полученной зависимости был спланирован и проведен вычислительный эксперимент, предусматривающий изменение определяющих параметров в широком диапазоне. Расчеты выполнялись для нефти и бензина. По результатам 25 вычислительных «опытов» определено, что при операциях с бензином средний коэффициент превышения (за одну операцию заполнения резервуара) в исследованном диапазоне температур принимает значения от 1,029 до 1,678, а при операциях с нефтью - от 1,016 до 1,338, то есть, как правило, превышает погрешность инструментальных замеров потерь нефти (нефтепродуктов) от испарения. Математическое ожидание рассматриваемой величины при операциях с бензином составляет 1,26, с нефтью - 1,16. Таким образом, учет среднего коэффициента превышения при обработке результатов инструментальных измерений потерь углеводородов от испарений вследствие «больших дыханий» резервуаров является обязательным. Currently, the Chernikin - Valyavsky formula is used in the experimental determination of petroleum product losses from “large breaths” of reservoirs. However, it does not take into account that the volume of air-vapor mixture displaced into the atmosphere usually exceeds the volume of pumped oil/petroleum product. The corresponding parameter, the excess ratio, according to the experimental data can have values of more than 8. Until recently, even the causes of this phenomenon were not completely clear, and thus, the empirical dependencies for calculating the excess ratio did not take into account all the influencing factors. Based on the Mendeleev-Clapeyron equation in differential form, the analytic expression to calculate the average excess ratio was obtained. It was found that this value depends on the molar mass and temperature of the air-vapor mixture at the beginning and the end of the injection, as well as on the ratio of the tank gas space volume and the injected product volume. To analyze the resulting dependency, a computational experiment involving changes in the defining parameters over a wide range was planned and conducted. The calculations were performed for oil and gasoline. According to the results of 25 computational experiments, it was determined that during operations with gasoline the average excess ratio (per one tank filling operation) in the investigated temperature range has values from 1.029 to 1.678, and during operations with oil - from 1.016 to 1.338; that generally exceeds the instrument error of oil/petroleum product losses from vaporization measurement. The mathematical expectation of the value in question during operations with gasoline is 1.26, it is 1.16 with oil. It is therefore mandatory to take into account the average excess ratio when processing the results of instrumental measurements of hydrocarbon losses from evaporation due to “large breaths” of reservoirs.

Phase Transitions

2019 ◽  
pp. 205-222
Author(s):  
Robert H. Swendsen
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Phase Transitions ◽  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Van Der Waals ◽  
Ideal Gas ◽  
Phase Rule ◽  
Clapeyron Equation ◽  
Maxwell Construction

Phase transitions are introduced using the van der Waals gas as an example. The equations of state are derived from the Helmholtz free energy of the ideal gas. The behavior of this model is analyzed, and an instability leads to a liquid-gas phase transition. The Maxwell construction for the pressure at which a phase transition occurs is derived. The effect of phase transition on the Gibbs free energy and Helmholtz free energy is shown. Latent heat is defined, and the Clausius–Clapeyron equation is derived. Gibbs' phase rule is derived and illustrated.

A novel zinc(ii) metal–organic framework with a diamond-like structure: synthesis, study of thermal robustness and gas adsorption properties

2016 ◽  
Vol 45 (3) ◽  
pp. 1233-1242 ◽  
Author(s):  
Miroslav Almáši ◽  
Vladimír Zeleňák ◽  
Arnošt Zukal ◽  
Juraj Kuchár ◽  
Jiří Čejka
Keyword(s):  
Gas Adsorption ◽  
Metal Organic Framework ◽  
Adsorption Properties ◽  
Clapeyron Equation ◽  
Structure Synthesis ◽  
Metal Organic ◽  
Organic Framework

A novel 3D metal–organic framework with a diamond-like structure has been synthesised and structurally characterized. Adsorption of Ar, CO2, H2 and N2 has been studied. Heats of CO2 and H2 adsorption were calculated according to the Clausius–Clapeyron equation.

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