scholarly journals The viscosity of strong electrolytes measured by a differential method

1934 ◽  
Vol 145 (855) ◽  
pp. 475-488 ◽  
Keyword(s):  
Dielectric Constant ◽  
Empirical Equation ◽  
Relative Viscosity ◽  
Absolute Temperature ◽  
Differential Method ◽  
Theoretical Equation ◽  
Electronic Charge ◽  
Accurate Data ◽  
Avogadro’S Number ◽  
Strong Electrolytes

Until quite recently no satisfactory equation had been obtained for the representation of the viscosity of dilute solutions of strong electrolytes. An empirical equation was recently proposed by Jones and Dole to fit the only accurate data then available. Their equation may be represented thus : η = 1 + A √ c + B c , η = relative viscosity of the solution c = concentration in moles per litre A and B are constants. Jones and Dole realized that the coefficient A is due to interionic forces and in a series of later publications Falkenhagen, Dole and Vernon have deduced a theoretical equation giving values of A in terms of well-known physical constants. Their complete equation may be written η = 1 + ε √N v 1 z 1 /30η 0 √1000D k T ( z 1 + z 2 ) 4 π × [¼ μ 1 z 2 + μ 2 z 1 / μ 1 μ 2 - z 1 z 2 (μ 1 - μ 2 ) 2 /μ 1 μ 2 (√μ 1 z 1 + μ 2 z 2 + √(μ 1 + μ 2 ) ( z 1 + z 2 ) ) 2 ]√ c , where N = Avogadro's number v 1 , v 2 = numbers of ions z 1 , z 2 = valencies of ions μ 1 , μ 2 = absolute mobilities of ions D = dielectric constant of solvent k = Boltzmann's constant ε = electronic charge η 0 = viscosity of solvent T = absolute temperature.

scholarly journals The viscosity of dilute solutions of strong electrolytes

1931 ◽  
Vol 134 (824) ◽  
pp. 413-427 ◽  
Keyword(s):  
Empirical Equation ◽  
Relative Viscosity ◽  
Theoretical Treatment ◽  
High Dilution ◽  
Equivalent Concentration ◽  
Pure Solvent ◽  
Wide Range ◽  
Strong Electrolytes ◽  
Negative Viscosity ◽  
Stiffening Effect

Until very recently, no empirical equation had been found to represent satisfactorily the variation with concentration of the relative viscosity of electrolytes, nor had any adequate theoretical treatment of the problem been put forward. In 1929, however, Jones and Dole showed that the fluidity (or reciprocal of the relative viscosity) of a salt solution could be represented over a fairly wide range of concentration by an equation of the form ϕ = 1 + A√ c +B c , where ϕ is the fluidity, c the equivalent concentration, and A and B are empirical constants. The value of B is negative in the case of salts which increase the viscosity of water, and positive in cases of so-called “negative viscosity,” where the viscosity of the solution is less than that of the pure solvent. Jones and Dole argued further that the stiffening effect of the interionic forces would tend to make the constant A, which determines the viscosity at high dilution, always negative. A little later, Falkenhagen and Dole treated the problem theoretically from the standpoint of the ion-atmosphere theory of Debye and Huckel. They confirmed the suggestion that at high dilution the electrolyte must always increase the viscosity of the solvent, and showed that the relative viscosity of an electrolyte solution at high dilution must be represented by an equation of the form η μ / η 0 = 1 + K √ μ , where η μ is the viscosity of the solution, η 0 is the viscosity of the solvent, μ is the equivalent concentration, K is a constant.

scholarly journals Channel noise in nerve membranes and lipid bilayers

1975 ◽  
Vol 8 (4) ◽  
pp. 451-506 ◽  
Author(s):  
F Conti ◽  
E. Wanke
Keyword(s):  
Brownian Motion ◽  
Lipid Bilayers ◽  
Fluctuation Phenomena ◽  
Channel Noise ◽  
Fluctuation Analysis ◽  
Electronic Charge ◽  
Basic Principles ◽  
Avogadro’S Number ◽  
Insight Into

The basic principles underlying fluctuation phenomena in thermodynamics have long been understood (for reviews see Kubo, 1957; Kubo, Matsuo & Kazuhiro 1973 Lax, 1960). Classical examples of how fluctuation analysis can provide an insight into the corpuscular nature of matter are the determination of Avogadro's number according to Einstein's theory of Brownian motion (see, e.g. Uhlenbeck & Ornstein, 1930; Kac, 1947) and the evaluation of the electronic charge from the shot noise in vacuum tubes (see Van der Ziel, 1970).

scholarly journals The estimation of electric moment in solution by the temperature coefficient method. Part I.—Experimental method and the electric moments of some benzyl compounds

1933 ◽  
Vol 142 (846) ◽  
pp. 173-197 ◽  
Keyword(s):  
Single Molecule ◽  
Polar Solvent ◽  
Fundamental Equation ◽  
Absolute Temperature ◽  
Electric Moment ◽  
Avogadro’S Number ◽  
Boltzmann Gas ◽  
Different Temperatures ◽  
The Moment ◽  
Coefficient Method

The theory of the estimation of the electric moment of molecules dissolved in a non-polar solvent is now well known. The fundamental equation is P 2∞ = 4 π /3 N (α 0 + μ 2 /3 k T) (1) in which the symbols have the following significance: P 2∞ the total polarizability of the solute per grain molecule at infinite dilution, N Avogadro’s number, α 0 the moment induced in a single molecule by unit electric field, k the Boltzmann gas constant, T the absolute temperature, and μ the permanent electric moment of the molecule. This equation is of the form P 2∞ = A + B/T, (2) where A = 4 π /3 Nα 0 and B = 4 π /9 . N μ 2 / k , from which it follows that if A and B are constant, i. e ., independent of temperature, then each may be evaluated from a series of measurements of P 2∞ at different temperatures or alternatively B (and hence μ ) may be obtained from one value of P 2∞ at one temperature, provided that A can be obtained by some independent method.

THE VISCOSITY OF VINYL ACETATE

1937 ◽  
Vol 15b (1) ◽  
pp. 7-12 ◽  
Author(s):  
D. O. White ◽  
A. C. Cuthbertson
Keyword(s):  
Vinyl Acetate ◽  
Latent Heat ◽  
Characteristic Frequency ◽  
Empirical Equation ◽  
Theoretical Equation ◽  
Heat Of Evaporation

The viscosity of monomeric vinyl acetate has been measured over a range of temperatures from 0° to 60 °C. Two equations were obtained which represent the results. The empirical equation is [Formula: see text], and a theoretical equation is given as [Formula: see text]. The characteristic frequency has been obtained from the relation [Formula: see text], where μ is the ratio between the latent heat of evaporation and the heat of cohesion, v was found to be 2.17 × 1012.

Analysis of Tire Performance on Sand

1995 ◽  
Vol 23 (1) ◽  
pp. 52-67 ◽  
Author(s):  
H. Ataka ◽  
F. Yamashita
Keyword(s):  
Empirical Equation ◽  
Theoretical Equation ◽  
Shearing Stress ◽  
Propulsive Force ◽  
Breaking Force ◽  
Measuring Techniques ◽  
The World ◽  
Precise Prediction ◽  
The Difference

Abstract Recently, vehicles on sand have been operated at higher speeds with diversified usage, and requests for the development of radial tires, applicable to both pavements and sandy areas have emerged. Although a large number of studies and analyses of tire performance on paved surfaces have been reported, few reports are available for tire performance on sandy surfaces. This study deals with the behavior of radial tires on the sand. A simple theoretical equation was derived in which the sand traction performance could be expressed as the difference between the propulsive force and the driving resistance on sand. The theoretical equation was found to be highly related to the empirical equation derived from previous work. Sand samples from typical deserts were used for analyses of shearing stress and compressive breaking force of sand through unique measuring techniques, resulting in modification of the theoretical equation to give more precise prediction of the tire performance on sand for most areas in the world.

scholarly journals The kinetic energy of electrons emitted from a hot tungsten filament

1923 ◽  
Vol 102 (719) ◽  
pp. 734-751 ◽  
Keyword(s):  
Kinetic Energy ◽  
Electric Fields ◽  
Average Energy ◽  
Current Method ◽  
Absolute Temperature ◽  
Electronic Charge ◽  
Normal Velocity ◽  
Electric And Magnetic Fields ◽  
The Individual ◽  
Good Agreement

The first measurements of the kinetic energy of the electrons emitted from hot bodies were made by Prof. Richardson and Dr. F. C. Brown in 1907-1909. These experiments showed that the velocity distribution among the emitted electrons was in close agreement with Maxwell’s law of distribution for a gas, of molecular weight equal to that of the electrons, in thermal equilibrium at the temperature of the source. In the simple unidimensional case where the cathode and anode form parallel planes of indefinite extent, the current which flows against a retarding potential, V, depends only on the normal velocity component and with Maxwell’s distribution is given by i = i 0 e -2 hℯ V , where h = 1/2 k T, k being Boltzmann’s constant, T the absolute temperature of the source, and e is the electronic charge. The mean kinetic energy of the electrons in the stream is given by the quantity 2 k T. These experiments showed that with platinum, which was the only metal tried, the exponential equation was very accurately obeyed, and the average of eight determinations of k agreed with the theoretical value to within a fraction of 1 per cent. although the individual determinations differed from the average by almost ±20 per cent. These experiments were,- however, subject to a number of defects, the most important of these being due to the presence of electric and magnetic fields caused by the electric currents used in heating the source. Schottky carried out some experiments in 1914, and he used the case of a filament surrounded by a concentric cylindrical anode. The effects of the magnetic and electric fields of the current used to heat the filament were avoided by an interrupted current method due to v. Baeyer. Schottky’s experiments were made with carbon and tungsten, and the data were in good agreement with the requirements of Maxwell’s law, except that the average energy of the emitted electrons was in every case in excess of the value calculated from the temperature of the source. This, however, was estimated from the value of the saturation current using the emission constants given by other authors. This makes his temperature determinations very uncertain, because of the known large effects on the emission of traces of certain contaminants.

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