The authors combine modern theoretical calculations with evaluated selected experimental data to produce a comprehensive data resource of K- and L-x-ray transition and absorption edge energies for all of the elements from neon to fermium. The theoretical and experimental components of this work are the result of programs of parallel development extending over more than 20 years. At each of several progressively more refined comparisons, it was possible to identify theoretical components whose systematic improvement then led to the next level of refinement in comparisons with an increasingly robust experimental reference data set. We have now reached a certain practical limit in what can be undertaken with reasonable levels of theoretical effort. This limit is not very different from the practical level of accuracy that can be meaningfully associated with the experimental data. For the more prominent diagram lines, experiment and theory are concordant with a zero-centered distribution of residuals whose statistical metrics allow the uncertainties to be estimated. For the light elements $(Zl20)$ and the very heavy elements $(Zg90)$ there are significant difficulties, as is also the case for a few isolated elements and transitions for $20lZl90.$ Overall, the results reported here represent improvements over previously available data compilations not only because of their scope but also because of their attempt to offer internal metrics of the database accuracy. The identified regions of difficulty are areas where further experimental work may be directed to see if there may remain theoretical issues that are still unresolved.

X-ray transition energies: new approach to a comprehensive evaluation

Determination of eh, Using Macroscopic Quantum Phase Coherence in Superconductors: Implications for Quantum Electrodynamics and the Fundamental Physical Constants

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches.

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Compendium of the Foundations of Classical Statistical Physics

The aim of this article is to analyse the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-(a)symmetry and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Carath\'eodory and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-asymmetry plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time

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Bluff Your Way in the Second Law of Thermodynamics

A theory of the double layer in uni‐univalent unadsorbed electrolytes is developed and used to analyze Grahame's experimental measurements of differential capacitance for NaF in water at 0° to 85°C and KF in methanol at 25°C. Excellent agreement with experiment is obtained except in the region of strong anodic polarization; this disagreement is tentatively ascribed to specific adsorption of anions, an effect not quantitatively considered in the present work. Although the quantities calculated herein relate to the entire double layer as, of course, do Grahame's data, the Gouy—Chapman theory of the diffuse part of the double layer (without dielectric saturation) is adequate in the present situation for all concentrations considered and has been used throughout. Consequently, the degree of agreement between theory and experiment found reflects primarily upon the applicability of the present theory of the inner layer. In the absence of specific adsorption this region is taken to be a hexagonally close‐packed charge‐free monolayer of solvent, physically adsorbed on the mercury electrode by dipole image forces. Adsorption anisotropy can lead to some dielectric saturation in the inner layer even at the electrocapillary maximum, the point of zero electrode charge. Neglecting association in the monolayer, the inner‐layer dielectric constant and its dielectric saturation properties are calculated under three situations—where dipole image contributions are neglected, where the monolayer dipoles are imaged in the mercury electrode only, and where they are additionally imaged in an equipotential plane on the other side of the layer. The last case leads to an infinite set of images and to infinite series which are summed. These treatments all lead to much smaller dielectric constants and saturation constants than are found for bulk solvent. Comparison with values of these constants obtained from fitting the theory to the experimental data using a digital computer yields reasonably close agreement. New equations for the dependence of inner‐layer thickness, volume, and dielectric constant on pressure and electric field, are derived and applied. The electrostatic pressure in this region is shown to consist of a capacitor‐plate compressive term and an electrostrictive term, the latter originating only from the distortional and not the orientational polarization of the inner layer. As with the dielectric properties, the compressibility of the inner region found from curve fitting is of the right order of magnitude for both water and methanol solvents. The hump which occurs in water at low temperatures and small anodic polarization is attributed to the interplay of specific adsorption and dielectric saturation. Finally, it is pointed out that the usual method of separation of the inner‐layer capacitance from the total differential capacitance by assuming the former to be in series with the diffuse‐layer capacitance is unjustified in regions of appreciable specific adsorption, where the inner layer is no longer charge free.

Theory of Double-Layer Differential Capacitance in Electrolytes

The need for a separate unit of length for x-ray wavelengths is discussed and compared to the case of electrical units. The introduction and development of the x unit is reviewed. It was effectively defined in terms of calcite crystals and was intended to be very nearly equal to 10−11 cm. The numerical value used to specify it was based on Siegbahn's value of the grating constant of calcite measured relative to rock salt. The latter value had been computed by Moseley from the density of rock salt and from Avogadro's number, which in turn rested on the erroneous Millikan oil-drop value of electronic charge. Ruled grating measurements of x rays eventually revealed the discrepancy. Variations observed among calcite crystals indicated the desirability of basing the definition on a standard wavelength rather than a species of crystal. For these reasons, Bearden, while preparing a new x-ray wavelength table, defined a new A unit in terms of the W Kα1 wavelength (λw kα1  0.209 010 0 A). This scale eliminates the major problems associated with the old x unit. The numerical factor was chosen to make the experimental value of the conversion factor to absolute units (angstroms) unity on the basis of the data then available; the estimated probable error was given as 5 ppm.

Biography of the X Unit—The X-Ray Wavelength Scale

After the concept of entropy has been introduced in the classical approach to thermodynamics, the definition of a reversible process may be refined in a mathematical way. If a given process can be modified by appropriate adjustment of the thermodynamic force involved so that it approaches a limit of zero entropy production, defining a limit process, and if the reverse process can be similarly modified, defining the same limit process in reverse, then we say that the process is reversible in this limit. Two examples are given, one dealing with the heating of a system and the second involving the adiabatic expansion of a viscous ideal gas.

The reversible process: A zero‐entropy‐production limit

Sommerfeld has given an apparent case of a perpetual motion machine of the second kind. This consists of a Carnot engine employing liquid water and operating between the normal and anomalous regions of thermal expansion. His explanation of the paradox is shown to be incomplete when the temperature of maximum density is pressure-dependent. To analyze this case a simple thermodynamic model for a substance with a density extremum is given; this model yields a reasonable approximation to the data for water. Standard thermodynamic properties of the system are computed and useful approximate forms given. Various Carnot cycles and a non-trivial “two-process” cycle are then shown in the p−T, T−s, and p−v planes. Sommerfeld's paradox is resolved by showing that a Carnot cycle qualitatively similar to that in his problem involves expansions for both isothermal processes. Theoretical implications of the analysis and applications to sound waves and shock waves are briefly discussed.

Strange Carnot Cycles; Thermodynamics of a System with a Density Extremum

Quasi-static processes are not reversible when sliding friction forces are present. An example is considered consisting of a cylinder containing a gas and equipped with a piston for which sliding friction forces are significant. It is assumed that the frictional force may be a function of temperature, displacement, and direction of motion. From measurements on the boundary of the system it is then possible to determine energy as a function of temperature and volume. However, force and entropy are not uniquely determined although thermodynamic considerations impose severe restrictions on the possible choice of these quantities. The generalized definition of entropy proposed by Bridgman is discussed in light of these conclusions. The possible analogy between this model and a perfectly plastic material is briefly discussed.

John S. Thomsen

Papers

Biography of the X Unit—The X-Ray Wavelength Scale

The reversible process: A zero‐entropy‐production limit

Strange Carnot Cycles; Thermodynamics of a System with a Density Extremum

Thermodynamics of an Irreversible Quasi-Static Process

Millikan's Lost Problem