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The kinetic theory of gases deals not only with gases in thermodynamic equilibrium, but also very importantly with gases not in thermodynamic equilibrium. This means using Kinetic Theory to consider what are known as "transport properties", such as viscosity, thermal conductivity, mass diffusivity and thermal diffusion.
Elementary kinetic theory and simple empirical models [1] [2] [3] - viscosity for dilute gas with nearly spherical molecules; Power series [2] [3] - simplest approach after dilute gas; Equation of state analogy [3] between PVT and T P; Corresponding state [2] [3] model - scaling a variable with its value at the critical point
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
Chapman–Enskog theory also predicts a simple relation between thermal conductivity, , and viscosity, , in the form =, where is the specific heat at constant volume and is a purely numerical factor. For spherically symmetric molecules, its value is predicted to be very close to 2.5 {\displaystyle 2.5} in a slightly model-dependent way.
At the molecular level, gas dynamics is a study of the kinetic theory of gases, often leading to the study of gas diffusion, statistical mechanics, chemical thermodynamics and non-equilibrium thermodynamics. [2] Gas dynamics is synonymous with aerodynamics when the gas field is air and the subject of study is flight.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
The exact k-ε equations contain many unknown and unmeasurable terms. For a much more practical approach, the standard k-ε turbulence model (Launder and Spalding, 1974 [3]) is used which is based on our best understanding of the relevant processes, thus minimizing unknowns and presenting a set of equations which can be applied to a large number of turbulent applications.
James Clerk Maxwell introduced this approximation in 1867 [3] although its origins can be traced back to his first work on the kinetic theory in 1860. [ 4 ] [ 5 ] The assumption of molecular chaos is the key ingredient that allows proceeding from the BBGKY hierarchy to Boltzmann's equation , by reducing the 2-particle distribution function ...