By Tamas I. Gombosi
Gaskinetic thought is an introductory textual content at the molecular thought of gases and on glossy delivery thought appropriate for top department undergraduates in physics and primary 12 months graduate scholars in aerospace engineering, top atmospheric technological know-how and area learn. the 1st half introduces easy ideas, together with the distribution functionality, classical conception of particular heats, binary collisions, suggest unfastened direction, and response premiums. delivery concept is used to specific coefficients reminiscent of viscosity and warmth conductivity by way of molecular homes. the second one a part of the e-book covers complicated delivery concept. Generalized shipping equations are derived from the Boltzmann equation. The Chapman-Enskog and the Grad tools are mentioned to procure larger order shipping equations for low density gases. The aerodynamics of sturdy our bodies is explored and the e-book concludes with the kinetic description of outrage waves.
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Additional info for Gaskinetic Theory (Cambridge Atmospheric and Space Science Series)
Finally, the two results will be compared and thus an expression will be obtained for the P parameter. 1 Gas pressure on a wall We start with the kinetic determination of the gas pressure on a wall. It is assumed that the gas is in kinematic equilibrium and therefore the velocity distribution of gas molecules is given by the Maxwell-Boltzmann distribution function. For the sake of simplicity the hard sphere (or 'billiard ball') model of molecular collisions will be used. This means that in the following derivation the molecules are considered to be very small, perfectly spherical, rigidly elastic bodies.
We first consider a small, locally planar surface area, dS. 6). The mass of the wall is so much larger than the mass of the individual molecules that the colliding hard sphere molecules are reflected elastically from the surface. 6). One can readily calculate the change of the particle velocity vector due to the collision with the wall. If the Cartesian velocity components of a molecule before the collision with the wall were v=(v ,v ,-v ), then after the collision the velocity x y z can be expressed as v =(vx,v ,vz).
It is interesting to note that this result can readily yield the well known Dalton's law (which states that the pressure of a gas mixture is the sum of partial pressures of the gas components). 54) is the well known Dalton's law. It should be emphasized again that we were able to explain this empirical law by using first principles and the basic assumptions of equilibrium gaskinetic theory. 3 Moments of the Maxwell-Boltzmann distribution Next we examine some of the fundamental macroscopic properties of the Maxwell-Boltzmann function which describes the equilibrium distribution of molecular velocities in a gas containing a single molecular species.