Kinetic Theory of Gases

In this report, a standard Maxwell-Boltzmann distribution (B) is defined by analogy to the concept of the standard Gaussian distribution. The most important statistical properties of B, as well as a simple method for generating random numbers from the standard Maxwell-Boltzmann distribution are presented. Given that the properties of B are already known, it is advantageous to describe any arbitrary Maxwell-Boltzmann distribution as a function of the standard Maxwell-Boltzmann distribution B. By using this approach, it is possible to demonstrate that the temperature of a material is a function only of the fluctuating component of the average molecular kinetic energy, and that it is independent of its macroscopic kinetic energy.

Pascal’s law or Pascal’s principle, enunciated almost 400 years ago, has been of utmost importance in a wide variety of scientific and engineering disciplines. Currently physics textbooks describe Pascal’s law as follows: “A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.” Such phenomenon can be explained based on the propagation of external forces at a molecular level via intermolecular repulsion (following Newton’s third law of motion). In the case of gases, such propagation of forces does not take place directly, although external forces do influence the pressure of a gas by changing the momentum of the molecules hitting the walls. There is, therefore, a relationship not necessarily identical to that stated in Pascal’s law. However, under certain conditions, Pascal’s law remains as a fairly good approximation for gases. For example, the International Standard Atmosphere model has assumed that the atmosphere is an ideal gas following Pascal’s law, with satisfactory results.

Can Brownian motion arise from a deterministic system of particles? This paper addresses this question by analysing the derivation of Brownian motion as the limit of a deterministic hard-spheres gas with Lanford's theorem. In particular, we examine the role of the Boltzmann-Grad limit in the loss of memory of the deterministic system and compare this derivation and the derivation of Brownian motion with the Langevin equation.

The cubic van der Waals equation of state at the critical condition is reduced to a linear function (Vc vs. Tc /Pc coordinates) with one adjustable parameter. It is shown that at the critical point the relation Vc = 3Vo must not hold as van der Waals suggested, but the attractive constant α = Pc Vc2 remains. Selected values of Tc, Pc, Vc compiled by Ihmels where focused on testing the quality of several empirical equations relating critical conditions. It is shown that the obtained critical constants correlation is a general form of the empirical expressions proposed by Young, Meissner, Bird, Grigoras and Ihmels. From the resulting correlation function, a function for the critical compressibility is proposed. The critical volume Vc and the ratio Tc /Pc have been expressed in group contributions.

From the very beginning of the civilization, human adopted new technologies to make simple their life, it leads them to the urbanization & industrialization. The result of that is the increasement of pollution in the air. After twentieth century, transportation sector became the major contributor to this pollution. This sector produces harmful gases like CO, HC, NOx etc. This has the harmful effects on the human being, more precisely asthma, eye iteration, lung disorder & consequences of fertility etc. To control the effect of that gases continuous monitoring of that gases is one of the way. Our system can be used to do this process properly. The application of IOT make this system more advance in order to control the car emission. It consist of MQ2, MQ7, MQ135 sensors. The system will implemente nearer to the tailpipe of the vehicle to monitor the emission, the result would be sent to the server as well as in the android application from which the concerned authority can check the result, will help to take the necessary step.

Temperature is a physical concept of significant importance in our daily lives. Throughout history, mankind has made big efforts in understanding temperature as an objective property of matter. These efforts led to the interpretation of temperature as a measure of the average kinetic energy of the molecules in a body. Although temperature has been traditionally regarded as a macroscopic property of matter, it will be shown that analog concepts can be introduced at microscopic (local) and molecular scales. The implication of introducing temperature concepts at small scales is that fluctuation becomes relevant and therefore, temperature can no longer be considered as a deterministic variable. The analysis of temperature fluctuations is performed on an ideal gas, following a Maxwell-Boltzmann distribution of molecular speeds at 293.15 K and 101.325 kPa.

Penelitian ini bertujuan untuk mengembangkan media pembelajaran untuk memfasilitasi kegiatan praktek fisika. Penelitian ini dilatarbelakangi dari minimnya intensitas aktivitas praktikum fisika di sekolah, dikarenakan sarana prasarana praktikum fisika di sekolah kurang memadai, menyatakan alokasi waktu untuk praktikum fisika kurang mencukup dan lembar kerja yang digunakan kurang memfasilitasi siswa berpikir deduktif . Oleh karena itu, tujuan penelitian ini adalah mengembangkan Hands-On Activity Guided berbasis Open Ended Approach untuk meningkatkan kemampuan hipotesis deduktif fisika SMA. Metode penelitian yang digunakan adalah penelitian dan pengembangan model ASSURE. Instrumen yang digunakan adalah tes benar-salah untuk mengukur kemampuan hipotesis deduktif siswa. Validasi dilakukan oleh ahli materi, ahli media, ahli pembelajar dan guru. Media yang dikembangkan berupa kumpulan muatan aktivitas praktikum fisika siswa yang menggunakan alat dan bahan sehari-hari berbasis open ended approach dan diharapkan mampu mengarahkan siswa pada proses berpikir terbuka dan divergen sehingga siswa akan meningkat kemampuan hipotesis deduktifnya dalam pembelajaran fisika

In a finite volume CFD method for unsteady flow fluxes of mass, momentum and energy are exchanged between cells over a series of small time steps. The conventional approach, which we will refer to as "direction decoupling", is to estimate fluxes across interfaces in a regular array of cells by using a one-dimensional flux expression based on the component of flow velocity normal to the interface. This means that fluxes cannot be exchanged between diagonally adjacent cells since they share no cell interface, even if the local flow conditions dictate that the fluxes should flow diagonally. The direction decoupling imposed by the numerical method requires that the fluxes reach a diagonally adjacent cell in two time-steps. Here we present a 'true direction flux method', which is an updated version of Pullin's Equilibrium Flux Method (EFM) in which fluxes are derived from kinetic theory. Previous implementations of EFM in higher dimensions have used direction decoup...

The outcome of the collision between two bodies is dictated by the laws of conservation of mass, momentum and energy. The collision between individual molecules is not an exception. Particularly by assuming elastic collisions, the estimation of the outcome is greatly simplified. In macroscopic systems (composed by a large number of molecules), a large number of molecular collisions take place over relatively short periods of time. Thus, even though understanding individual collisions is important, the expected behavior of a large number of collisions will ultimately determine the macroscopic behavior of the systems. Following this idea, it was possible to show, for monoatomic ideal gases, the following: 1) Internal elastic molecular collisions do not change the motion of a system. 2) Internal elastic molecular collisions do not change the temperature of a system. 3) Elastic molecular collisions between two bodies at different temperatures change at a rate proportional to the temperature difference between the bodies. Clearly, the last observation is closely related to the Second Law of Thermodynamics. Also, an expression for the rate of energy transfer as heat, resulting from elastic molecular collisions at an interface, is obtained and it closely resembles the empirical equation based on an overall heat transfer coefficient. The expression derived from the expected behavior of molecular collisions also predicts the effect of molecular densities, macroscopic flow, composition and temperature of the systems involved. Particularly, the effect of composition indicates that the energy transfer during the collision between a light and a heavy molecule is inefficient, probably explaining why polymers usually have thermal insulation properties.

Molecules are in permanent motion and interaction. Even though a system might be at rest from a macroscopic point of view, it is restless at the molecular scale. Such continuous molecular motion results in the flow of molecules through space. The number of molecules crossing a boundary per unit time per unit area is denoted as a molecular flux. Three different types of boundaries are considered: Completely permeable, semi-permeable rigid and impermeable rigid boundaries. When the system is contained by rigid (impermeable or semi-permeable) boundaries such molecular flux against the walls produce a net force per unit area that is denoted as pressure. The purpose of this report is deriving mathematical expressions for estimating the molecular flux and pressure on rigid boundaries in ideal gases, using only the classical equations of motion and the distribution of molecular positions and velocities in the system. The pressure at the interior of an ideal gas system is zero because there are no forces acting on the molecules. Thus, the concept of equivalent pressure, as the pressure that would be obtained in the presence of an impermeable rigid boundary, is introduced. The mathematical results presented are based on the following general assumptions: i) Molecular collisions in the gas are negligible (ideal gas assumption). ii) There are no external forces acting on the system. iii) There is no net macroscopic motion of the gas parallel to the surface. iv) Molecular positions are uniformly distributed in the system volume. v) The orthogonal component of molecular velocity is normally distributed. vi) The system considered is large compared to the size of the molecules. The results obtained are consistent with the continuity equation. Furthermore, when the ideal gas system is at macroscopic rest, the classical ideal gas thermodynamic equation of state is obtained. In addition, three different regimes of molecular flux and pressure are observed: The thermal motion regime, the macroscopic regime and the transition regime between the first two.

In this chapter, we turn to systems in which there are significant interactions between diffusing molecules. These interactions can strongly affect the apparent diffusion coefficients. In some cases, these effects produce unusual averages of the diffusion coefficients of different solutes; in others, they suggest a strong dependence of diffusion on concentration; in still others, they result in diffusion that is thousands of times slower than expected. The discussion of these interactions involves a somewhat different strategy than that used earlier in this book. In Chapters 1–3, we treated the diffusion coefficient as an empirical parameter, an unknown constant that kept popping up in a variety of mathematical models. In more recent chapters, we have focused on the values of these coefficients measured experimentally. In the simplest cases, these values can be estimated from kinetic theory or from solute size; in more complicated cases, these values require experiments. In all these cases, the goal is to use our past experience to estimate the diffusion coefficients from which diffusion fluxes and the like can be calculated. In this chapter, we consider the chemical interactions affecting diffusion much more explicity, rather than hiding them as part of the empirically measured diffusion coefficient. The interactions affecting diffusion are conveniently organized into three groups. As a first group, we consider in Section 6.1 solute–solute interactions, particularly in strong electrolytes. We want to discover how sodium chloride diffusion is an average of the diffusion of sodium ions and of chloride ions.

this paper, for the derivation of Lorentz transformation from the postulates of Special theory of Relativity, the concept of De Broglie quantum waves is introduced which leads to the conclusions that the derivation of Lorentz transformation does not need the postulate of constancy of light speed in free space in case the postulate of phase coincidence of De Broglie quantum waves is introduced. Consequently, a new proposal is formulated that combines Quantum mechanics and the special theory of relativity and overcomes the technical problem in Feynman's proposal