Concepts Of Statistical Thermodynamics Research Articles

Thermochemical Transition in Non-Hydrogen-Bonded Polymers and Theory of Latent Decomposition.

Although thermosets and various biopolymers cannot be softened without being decomposed, the vast majority of thermoplastics are believed to exhibit thermal transitions solely related to physical alterations of their structure-a behavior typical of low molecular weight substances. In this study, Differential Scanning Calorimetry (DSC), Fourier Transform Infrared Spectroscopy (FTIR) and Thermogravimetry (TGA) were used to study the softening of four common non-hydrogen-bonded thermoplastic polymers (polypropylene, polypropylene-grafted-maleic anhydride, poly(vinyl chloride) and polystyrene) along with a hydrogen-bonded polymer as a reference, namely, poly(vinyl alcohol). It is shown that the softening of these polymers is a thermochemical transition. Based on fundamental concepts of statistical thermodynamics, it is proposed that the thermal transition behavior of all kinds of polymers is qualitatively the same: polymers cannot be softened without being decomposed (in resemblance with their incapability to boil) and the only difference between the various types of polymers is quantitative and lies in the extent of decomposition during softening. Decomposition seems to reach a local maximum during softening; however, it is predicted that polymers constantly decompose even at room temperature and, by heating, (sensible) decomposition is not initiated but simply accelerated. The term "latent decomposition" is proposed to describe this concept.

Toward non-Hermitian quantum statistical thermodynamics

Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated remarkable research activity in quantum physics and new insights have emerged. In this paper, we formulate concepts of statistical thermodynamics for systems described by non-Hermitian Hamiltonians with real eigenvalues. We mainly focus on the case where the energy and another observable are the conserved quantities. The notion of entropy and entropy inequalities is central in our approach, which treats equilibrium thermodynamics.

Alternative Derivation of the Maxwell Distribution of Speeds

The Maxwell distribution of speeds, f(v), is the starting point for the calculation of the transport coefficients in kinetic-molecular theory. Most physical chemistry textbooks follow a path to derive f(v) similar to that used by Maxwell, which makes it difficult for students to understand its relationship with the equilibrium state of the system, and its probabilistic character. The mathematical implications of the distribution, such as its relationship with other probability distribution functions, are also not sufficiently developed. Herein, we discuss how deriving the Maxwell distribution of speeds from the Boltzmann distribution function allows students to connect with the basic concepts of statistical thermodynamics, such as those treated in an introductory undergraduate course. We also present the relationship between Maxwell’s distribution and other probability distribution functions, which can be helpful for deriving simple proportionality relationships between f(v) and v, under different conditions.

On the redefinition of the kelvin

The current and the forthcoming definition of the base unit kelvin are critically analysed. Using basic concepts of statistical thermodynamics, an attempt is made to elucidate the physical meaning of the revised definition of the kelvin. The consistency between the revised and the current thermodynamic scales is evaluated and the impact of the redefinition on the measurement infrastructures is speculated on.

Altitude profile of the OH radical complex with water in Earth’s atmosphere: a quantum mechanical approach

The hydroxyl radical (OH) is important in both tropospheric and stratospheric chemical processes that occur in Earth’s atmosphere. The OH radical can also strongly hydrogen-bond to form complexes with other atmospheric constituents, like water molecules. Consequently, there is potential for altered reaction dynamics/kinetics as a result of this complexation. Without direct measurements of the abundances of such complexes in Earth’s atmosphere, we have adopted a theoretical approach to determine such abundances. Electronic structures, enthalpies and free Gibbs energies of formation of OH, H2O and H2O-HO were calculated at CCSD(T) and QCISD(T) levels of theory with either 6–311++G(2d,2p) or aug-cc-pVTZ basis. Statistical thermodynamic concepts were then used to assess the abundance of the complex as function of altitude.

Modeling Adsorption Properties on the Basis of Microscopic, Molecular, and Structural Descriptors for Nonpolar Adsorbents

We propose a method for analytically predicting single-component adsorption isotherms from molecular, microscopic and structural descriptors of the adsorbate-adsorbent system and concepts of statistical thermodynamics. Expressions for Henry's constant and the heat of adsorption at zero coverage are derived. These functions depend on the pore size, pore shape, chemical composition, and density of the adsorbent material. They quantify the strength of the solid-fluid interaction, which governs the low-pressure part of the adsorption isotherm. For intermediate and high pressures, the fluid-fluid interactions must also be taken into account. Both solid-fluid and fluid-fluid interactions are combined within the framework of the Ruthven statistical model (RSM). The RSM thus constructs theoretical adsorption isotherms that are entirely based on microscopic molecular and structural descriptors. The theoretical results that we obtained are compared with experimental data for the adsorption of pure CO2 and CH4 on all-silica zeolites. The developed methodology allows for the estimation of the optimum properties of a nonpolar adsorbent for the adsorption of CO2 in cyclic adsorption processes.

A Simple Statistical Thermodynamics Experiment

Comparing the predicted and actual rolls of combinations of both two and three dice can help to introduce many of the basic concepts of statistical thermodynamics, including multiplicity, probability, microstates, and macrostates, and demonstrate that entropy is indeed a measure of randomness, that disordered states (those of higher entropy) are more likely than more ordered ones. It can also show that predictions based on statistics are more accurate with larger samples of data. What follows is a simple experiment introducing some of the basic elements of statistical thermodynamics that can be a light and even fun way to end a unit on thermodynamics, often the end of a challenging first semester of introductory physics.

On the birth of spark channels

The breakdown stage of a spark discharge in air is analyzed. This short duration stage (< 1 μs) has been divided into two phases. In the first, the electrical energy is introduced in a constant volume process. In the second, a sudden expansion occurs which is associated with the generation of a shock wave. The thermodynamic properties of the plasma were calculated by using concepts of statistical thermodynamics, in which molecular dissociation, ionization (up to the 3rd ionization) and the various modes of energy storage in a molecule were considered. The transport coefficients (thermal and electrical conductivities) were evaluated from molecular theory, as modified for partially ionized gas. The plasma conditions at the end of the second phase are expressed in terms of the breakdown energy and the maximum temperature of the plasma. The initial conditions for the arc stage have therefore been established. It is shown that owing to the drastic changes in the gas composition at high temperatures, the relationship between the input energy and the plasma temperature and its dimensions is quite complicated. The total thermal energy of the kernel at the end of the breakdown stage, as predicted by a simple model, was found to be four times higher than predicted by the present rigorous model.

A group contribution method for second virial coefficients

AbstractA semitheoretical group contribution method for predicting pure‐compound second virial coefficients is proposed. An expression for the second virial coefficient, expressed as the product of a nonpolar and a polar contribution, is derived using statistical thermodynamic concepts and an approximate form for the radial distribution function. For polar compounds the nonpolar contribution is assumed to be given by the Tsonopoulos correlation with the nonpolar acentric factor defined by Thompson and Braun. The polar contribution is represented by an energetic term expressed in terms of group contributions. Second virial coefficient predictions for strong polar and associating systems are comparable with those obtained with the correlations of Tsonopoulos and Hayden and O'Connell. Cross‐second virial coefficients for mixtures obtained using well‐defined molecular mixing rules compare well with literature values.

Thermodynamics of gas-surface interactions

Abstract

Visualizing Statistical Thermodynamics: The Boltzmann Distribution Model

Entropy change, work and heat effects, temperature, distribution functions, Brownian movement, and other elementary concepts of statistical thermodynamics can be visually demonstrated with a mechanical device that simulates some of the microscopic thermodynamic behavior of a nonatomic ideal gas.

Demonstrating concepts of statistical thermodynamics: More on the Maxwell Demon bottle

The Maxwell Demon bottle can illustrate the nature of entropy, the difference between a work effect and a heat effect, the difference between reversible and irreversible work effects, the mechanical equivalent of heat, and similar intangibles.