The Generalization of Choh-Uhlenbeck's Method in the Kinetic Theory of Dense Gases

Abstract

The method proposed by Choh and Uhlenbeck to deal with kinetic phenomena in dense gases is generalized to all orders in the density. The set of integral equations for the functions defining the transport coefficients is derived. It is shown that the thermal conductivity and the shear viscosity are independent of the way in which the local temperature is introduced, namely, through the kinetic energy and through the total energy density. However, the bulk viscosity does depend on the particular definition of temperature. The relationship between the corresponding bulk viscosities is explicitly obtained.

Definition of Temperature in the Kinetic Theory of Dense Gases

“…When we substitute /i(#|w,u,<5) into Eqs. (8), (9), and (10) and fu (x\n,u,d) into Eqs. (8), (9), and (14) we obtain two sets of five macroscopic equations of motion governing, in the first case, n, u, and 5, and in the second, n, u and 6.…”

“…(8), (9), and (10) and fu (x\n,u,d) into Eqs. (8), (9), and (14) we obtain two sets of five macroscopic equations of motion governing, in the first case, n, u, and 5, and in the second, n, u and 6. These equations determine the development of the macroscopic variables in such a way that, if n(q), u(q) y d(q) 1 and n(q), xi(q) and 8(q) are equivalent states at t~ 0, they are equivalent for all times.…”

“…If we have chosen a sufficient number of such quantities to determine a generalized microcanonical ensemble in phase space in which the zeroth-order dynamical system is ergodic, we can expect the macroscopic equations of motion to be differential equations of the first order in time, as are, for example, Eqs. (8), (9), and (10). ever, legitimately ask, which temperature, 6 or 0', does one measure when a finite velocity divergence is present?…”