Molecular Theory Of Gases And Liquids Hirschfelder Pdf.16

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WE formulate here a general molecular theory of solutions, which predicts a first order phase transition (boiling), volume changes on mixing, and the complete phase behaviour of pure and mixed fluids. Our formulation is based on a simple hole theory of the liquid state.

The kinetic theory of gases is concerned with molecules in motion and with the microscopic and macroscopic consequences of such motion in a gas. Kinetic theory can be used to deduce some of the equilibrium properties of gases, but the methods of statistical thermodynamics are more powerful in that respect. The importance of kinetic theory lies in its ability to describe nonequilibrium phenomena such as the transport of heat or of momentum in a slightly nonuniform gas or the scattering of molecules by other molecules. Much of modern kinetic theory is due to the efforts of Maxwell, Boltzmann, Enskog and Chapman in the late 19th century and the early 20th century. In this article, emphasis will be placed on the results of these efforts; little attention will be given to the mathematical details involved [Chapman and Cowling (1970)].

The results of kinetic theory may be built up from the kinematics of binary molecular encounters to yield a description of the transport properties of gases at such densities that binary but not ternary collisions are important. For monatomic gases, this theory is both complete and easily applicable [Maitland et al. (1981)]; the microscopic and macroscopic results are presented below. There is no entirely satisfactory kinetic theory for gases at high densities or for liquids although the theory due to Enskog, which will be described briefly, is of some use. For polyatomic gases, the theory is made vastly more complicated by two facts. First, the forces between molecules depend not only upon intermolecular separation but also on the mutual orientation of the molecules. Second, polyatomic molecules have rotational and vibrational degrees of freedom which play an important role in determining the outcome of a collision between molecules. Although much of the relevant theory has been derived in a formal sense, it is, at present, extremely difficult to apply [Maitland et al. (1981)]. Consequently, simplified results will be discussed, from which the transport properties of polyatomic gases may be determined approximately [Reid et al. (1977)].

The kinetic theory of gases in bulk is described in detail by the famous Boltzmann equation This is an integro-differential equation for the distribution function f(r,u,t), where f dxdydzdudvdw is the probable number of molecules whose centers have, at time t, positions in the ranges x to x + dx, y to y + dy, z to z + dz, and velocity components in the ranges u to u + du, v to v + dv, w to w + dw. For a gas in a state of thermodynamic equilibrium, this reduces to the Maxwell-Boltzmann Velocity Distribution Function, from which quantities such as mean speed, mean collision rate and mean free path may be determined. However, the Boltzmann equation may also be solved for cases in which small macroscopic gradients exist in either (bulk) velocity, temperature or composition. The solutions give the relation between the gradient and the corresponding flux in each case in terms of collision cross-sections. The coefficients of Viscosity, Thermal Conductivity and Diffusion are thereby related to intermolecular potential.

As indicated above, the formal theory is much more complicated for polyatomic gases because of the possibility of inelastic collisions, and is very difficult to apply. Fortunately, it appears that the effects of inelastic collisions on the coefficients of viscosity and diffusion are not usually more than a few percent. Furthermore, it is an empirical fact that scaling parameters ε and σ can be found such that the viscosity and diffusion coefficients of polyatomic gases follow the same principle of corresponding states as do monatomic gases. Thus η and D12 may be predicted for pure polyatomic gases and for mixtures containing polyatomic components, provided that some data is available from which to determine the required values of ε and σ.

The thermal conductivity of polyatomic gases is influenced considerably by inelastic collisions and cannot therefore be obtained with any accuracy from the monatomic theory or from the principle of corresponding states. A number of approximate treatments are available by which λ is represented as the sum of two terms: one (λtrans) relating to the transport of translational energy and the other (λint), to the transport of internal molecular energy. In the simplest treatment, the ratio λtrans/η is set equal to its value in a monatomic gas, (15R/4M) and the internal energy of the molecules is assumed to be transported at the same rate as the molecules themselves by the process of diffusion. The result of this treatment is the formula 2b1af7f3a8