A quantum mechanical theory of energy exchanges between inert gas atoms and a solid surface

1932 ◽  
Vol 28 (1) ◽  
pp. 136-164 ◽  
Author(s):  
J. M. Jackson
Keyword(s):  
Solid Surface ◽  
Accommodation Coefficient ◽  
Solid Surfaces ◽  
Order Unity ◽  
True Value ◽  
A Value ◽  
Quantum Mechanical Theory ◽  
Different Temperatures ◽  
Accommodation Coefficients ◽  
Energy Exchanges

The interaction between gas atoms and solid surfaces has been studied experimentally for many years. The first detailed study of the nature of this interaction was perhaps due to Knudsen, who in his classical researches introduced the idea of the accommodation coefficients for energy or momentum exchanges between gas atoms and a solid surface, when the gas atoms and the solid are at different temperatures or possess different mass motions. Knudsen and other investigators have given numerical values for these accommodation coefficients for various gases and solid surfaces, which seem to indicate that the accommodation coefficients are never small and are often of the order unity. This means that the gas molecules before reflection accommodate themselves almost completely to equilibrium with the temperature or motion of the wall. Before the recent work of Roberts referred to below, which has inspired this paper, no special precautions had been taken in the preparation of the wall surface, and as we now know the walls used by all previous investigators must have been completely covered with at least a mono-molecular film of gas. Thus the old observations of the accommodation coefficient do not determine it under precise conditions, and find in fact a value many times larger than that found by Roberts for the energy exchanges between the gas and a clean tungsten surface. For helium and metal with a dirty surface the value of the accommodation coefficient is some 6 times as large as the true value for the clean surface. The older values of the coefficients were so large that there were apparently grave difficulties in the way of any simple theory, but this is so no longer.

scholarly journals The interaction of atoms and molecules with solid surfaces III—The condensation and evaporation of atoms and molecules

1936 ◽  
Vol 156 (887) ◽  
pp. 6-28 ◽  
Keyword(s):  
Solid Surface ◽  
Room Temperature ◽  
Vibrational Energy ◽  
Accommodation Coefficient ◽  
Simple Relation ◽  
Solid Surfaces ◽  
Atoms And Molecules ◽  
Adsorbed Phase ◽  
Adsorbed Atoms ◽  
The Continuum

In the first two papers of this series (to be referred to as papers I and II) calculations were made of the probability that an atom adsorbed on a solid surface would be excited to states of higher vibrational energy and to states in the continuum, equivalent to evaporation. In this paper we carry the theory of evaporation a stage further and also develop a theory of condensation and show the relation of the theory to the method of statistical mechanics. Langmuir showed by a simple dynamical argument that under certain assumptions a solid surface in contact with a gas would be partially covered with adsorbed atoms and that the fraction of the surface covered could be expressed in terms of the pressure of the gas by the simple relation θ = ap /(1 + ap ). The parameter a is proportional to the product of a quantity τ, which is the average time spent by an atom in the adsorbed phase, and a quantity c , which is the probability that an atom striking the surface shall be adsorbed. Recently bowlers has shown that Langmuir's formula is essentially a thermodynamic one and can be obtained without involving a precise mechanism either of adsorption or evaporation. By adjusting the parameter a , the formula can be made to fit many of the experimental results and so the value of the product c τ can be inferred. This is probably as far as the statistical method can go. It cannot determine either c or τ uniquely, and if estimates are to be made of then information about c must be obtained from other sources. It is often assumed that c is of the order of unity, but this cannot be true in all cases, or even in the most interesting ones, for, as Roberts has shown, the accommodation coefficient (which is a measure of the probability that an atom will gain or lose energy on striking a solid surface) is sometimes very small. It is as low as 0·05 for helium striking tungsten and only 0·07 for neon striking tungsten at room temperature.

scholarly journals Energy exchange between inert gas atoms and a solid surface

1932 ◽  
Vol 137 (833) ◽  
pp. 703-717 ◽  
Keyword(s):  
Solid Surface ◽  
Energy Exchange ◽  
Accommodation Coefficient ◽  
Theoretical Explanation ◽  
Inert Gas ◽  
Clean Surface ◽  
Thermal Accommodation ◽  
Accommodation Coefficients ◽  
Thermal Accommodation Coefficient

1. Introduction . — If gas atoms, having energy corresponding to a temperature T 2 , are incident on a solid surface at a temperature T 1 , then the reflected atoms will have a mean energy corresponding to some new temperature T 2 ', which is a function of T 1 and T 2 . For simplicity it is convenient to define Knudsen’s thermal accommodation coefficient as α = lim T 1 → T 2 → T T' 2 - T 2 / T 1 - T 2 . The accommodation coefficient depends on the nature of the gas atom, the nature of the solid surface, and the temperature T. Accommodation coefficients have been measured by various workers, and the present paper is an attempt to give a theoretical explanation of the results of Roberts, who has measured the accommodation coefficient for helium on tungsten at various temperatures, taking particular precautions to obtain a clean surface.

A Molecular Dynamics Study on Energy Accommodation Coefficients in Microchannels

2008 ◽  
Author(s):  
Jun Sun ◽  
Zhixin Li
Keyword(s):  
Temperature Difference ◽  
Wall Temperature ◽  
Gas Flow ◽  
Accommodation Coefficient ◽  
Energy Accommodation ◽  
Micro Gas Flow ◽  
Different Temperatures ◽  
Accommodation Coefficients ◽  
Lower Temperature ◽  
Non Equilibrium

Energy accommodation coefficient (EAC), used in thermal boundary condition in micro gas flow and heat transfer, is reported to be always less than unity and greatly influenced by the wall characters. According to EAC’s definition, the statistical algorithm was described and EAC for argon gas was studied by two dimensional NEMD simulations with heat conduction between two smooth platinum plates at different temperatures. With one wall’s temperature fixed, the non-equilibrium EACs were calculated by changing the other wall’s temperature. Meanwhile, the equilibrium EAC at one temperature can be extrapolated from a series of non-equilibrium EACs as the temperature difference approaches to zero. The effects of wall temperature, wall temperature difference, and Kn on EAC were investigated. Non-equilibrium EAC increases with wall temperature difference decreased, and becomes larger with increased Kn. And equilibrium EAC is larger for lower temperature and larger Kn.

scholarly journals Determination of the Value of Intangible Assets in the Companies of Lithuania

2017 ◽  
Vol 14 (2) ◽  
pp. 55-68 ◽  
Author(s):  
Rita Bužinskienė
Keyword(s):  
Financial Management ◽  
Intangible Assets ◽  
Fair Value ◽  
Financial Information ◽  
Financial Accounting ◽  
True Value ◽  
A Value ◽  
The Impact

AbstractIn accordance with generally accepted accounting standards, most intangibles are not accounted for and not reflected in the traditional financial accounting. For this reason, most companies account intangible assets (IAs) as expenses. In the research, 57 sub-elements of IAs were applied, which are grouped into eight main elements of IAs. The classification of IAs consists in two parts of assets: accounting and non-accounting. This classification can be successfully applied in different branches of enterprises, to expand and supplement the theoretical and practical concepts of the company's financial management. The article proposes to evaluate not only the value of financial information for IAs (accounted) but also the value of non-financial information for IAs (non-accounted), thus revealing the true value of IAs that is available to the companies of Lithuania. It names a value of general IAs. The results of the research confirmed the IA valuation methodology, which allows companies to calculate the fair value of an IA. The obtained extended IAs valuation information may be valuable to both the owners of the company and investors, as this value plays an important practical role in assessing the impact of IAs on the market value of companies.

scholarly journals Measurement of Thermal Accommodation Coefficients Using Laser-Induced Incandescence

2007 ◽  
Author(s):  
K. J. Daun ◽  
P. H. Mercier ◽  
G. J. Smallwood ◽  
F. Liu ◽  
Y. Le Page
Keyword(s):  
Deformation Rate ◽  
Surface Deformation ◽  
Accommodation Coefficient ◽  
Polyatomic Gases ◽  
Thermal Accommodation ◽  
Laser Induced Incandescence ◽  
Translational Mode ◽  
Accommodation Coefficients ◽  
Thermal Accommodation Coefficient ◽  
Gas Molecules

Laser-induced incandescence (LII) is used to measure the thermal accommodation coefficient between soot sampled from a well-characterized flame and various monatomic and polyatomic gases. These measurements show that the thermal accommodation coefficient between soot and monatomic gases increases with molecular mass due to the decreasing speed of incident gas molecules and corresponding decrease in surface deformation rate, and that energy is transferred preferentially from the surface to the translational mode of the polyatomic gas molecules over internal energy modes.

scholarly journals Uncertainty Estimation of the Fe Content Measurement in the Clean Water Using UV- Vis Spectrophotometer

2019 ◽  
Vol 1 (1) ◽  
pp. 1-5
Author(s):  
Adi Syahputra
Keyword(s):  
Quality Standards ◽  
Sample Volume ◽  
Uncertainty Estimation ◽  
Clean Water ◽  
True Value ◽  
A Value ◽  
Fe Content ◽  
Standard Solution ◽  
Range Of Values ◽  
Orange Solution

Good laboratories should be able to apply procedures uncertainty for measuring of both conventional and instrument equipment. As well as the testing for Fe content using UV-Vis Spectrophotometer. As for the purpose for calculating the uncertainty estimated to determine the range of values within which estimated the true value of the testing standard solution Fe using UV-Vis Spectrophotometer. The uncertainty estimation are influenced by several factors such as sample used, reading of spectrophotometer, repeatability, sample volume. The uncertainty of the calculation obtained a value of ± 0,02 mg/L. Further testing of Fe content in the clean water using UV-Vis Spectrophotometer  at the 500 nm wavelength which forms an orange solution as indication of Fe content in the water. The result of Fe content has quality standards according to the spesifications issued by ministry of health Republic of Indonesia  in 2010 for drinking water.

Failure Analysis of Heat Exchangers

2021 ◽  
pp. 3-19
Author(s):  
Dusan P. Sekulic
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Failure Analysis ◽  
Thermal Energy ◽  
Solid Surface ◽  
Heat Exchangers ◽  
Heat Transfer Surface ◽  
Tubular Heat Exchanger ◽  
Erosion Corrosion ◽  
Different Temperatures

Abstract Heat exchangers are devices used to transfer thermal energy between two or more fluids, between a solid surface and a fluid, or between a solid particulate and a fluid at different temperatures. This article first addresses the causes of failures in heat exchangers. It then provides a description of heat-transfer surface area, discussing the design of the tubular heat exchanger. Next, the article discusses the processes involved in the examination of failed parts. Finally, it describes the most important types of corrosion, including uniform, galvanic, pitting, stress, and erosion corrosion.

Direct spectrophotometry of magnesium in serum after reaction with hexokinase and glucose-6-phosphate dehydrogenase.

1985 ◽  
Vol 31 (5) ◽  
pp. 703-705 ◽  
Author(s):  
M Tabata ◽  
T Kido ◽  
M Totani ◽  
T Murachi
Keyword(s):  
Spectrophotometric Method ◽  
Present Method ◽  
Reaction Rate ◽  
Colorimetric Method ◽  
Simple Method ◽  
True Value ◽  
A Value ◽  
Glucose 6 Phosphate Dehydrogenase ◽  
Direct Spectrophotometry

Abstract We describe a simple method for determining magnesium in serum by using hexokinase (EC 2.7.1.1) and glucose-6-phosphate dehydrogenase (EC 1.1.1.49). The method is based on determination of the reaction rate of hexokinase activated by Mg2+, which participates in the hexokinase reaction as the substrate in the form of a Mg X ATP2- complex. The reaction rate is determined from the change in absorbance at 340 nm as NADPH is produced by the action of glucose-6-phosphate dehydrogenase. This simple and rapid spectrophotometric method does not require expensive instrumentation, but results correlate satisfactorily with those obtained by atomic absorption spectroscopy. Thus, the present method gives a "true" value for magnesium in serum, a value appreciably lower than that obtained by an earlier colorimetric method, the Xylidyl Blue II method (Biochem Med 7: 208-217, 1973), which lacks specificity.

pH-Induced dissociation of bovine casein micelles. II. Mineral solubilization and its relation to casein release

1989 ◽  
Vol 56 (5) ◽  
pp. 727-735 ◽  
Author(s):  
Douglas G. Dalgleish ◽  
Andrew J. R. Law
Keyword(s):  
Calcium Phosphate ◽  
Inorganic Phosphate ◽  
Bovine Milk ◽  
Universal Relation ◽  
Casein Micelles ◽  
Neutral Ph ◽  
Quantitative Studies ◽  
A Value ◽  
Different Types ◽  
Different Temperatures

SummaryMeasurements of the release of Ca, Mg and inorganic phosphate(Pi) from the casein micelles of bovine milk have been made, as functions of the pH, in the range 4·9–6·7, and at temperatures of 4, 20 and 30 °C. The results are in general agreement with earlier published studies in giving a value of 1·75–1·84 for the micellar Ca:Pi ratio. Mg appeared to behave similarly to Ca, although the amounts of micellar material were much smaller. The results on the acid-solvation of calcium phosphate are considered in relation to published quantitative studies of the pH-induced dissociation of the different types of caseins from the micelle, and of the micellar dissociation caused when micellar calcium phosphate is dissolved at neutral pH. It is evident from this that at present it is not possible to derive a universal relation between the dissociation of minerals and of caseins from the micelles at different temperatures and under different conditions.

scholarly journals The interaction of atoms and molecules with solid surfaces VIII—The exchange of energy between a gas and a solid

1937 ◽  
Vol 158 (894) ◽  
pp. 269-279 ◽  
Keyword(s):  
Morse Potential ◽  
Accommodation Coefficient ◽  
Solid Surfaces ◽  
Adsorbed State ◽  
Thermal Accommodation ◽  
Special Cases ◽  
Thermal Accommodation Coefficient ◽  
The Right ◽  
Energy Interchange

In previous papers of this series the problem of energy interchange between a gas atom and a solid has been discussed for the case when the gas atom makes a transition between two adsorbed states or between an adsorbed state and a free state. In this paper we shall discuss the case of a transition between two free states and apply the results to the determination of the thermal accommodation coefficient. In recent years a number of theoretical papers on this subject have appeared, following the new and accurate experimental work of Roberts, who worked with helium and neon on tungsten. The authors, however, neglect, or only roughly take into account, the attractive field which is known to exist between the solid and the gas; the fact that atoms become adsorbed on the surface is clear evidence of the existence of such a field. In this paper we shall suppose that the interaction potentials between solid and gas atom can be represented by a Morse potential function, for it has the right characteristics; in that it is attractive at large distances and repulsive at small ones, and has a minimum in between. The formulae of this paper are accordingly more general than previous ones and contain them as special cases. They are applicable to experimental results such as those of neon on tungsten for which earlier theories would not be adequate.

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