Abstract
Thermodynamic quantities of the hard-sphere system in the steady state with a small heat flux are calculated within the continuous media approach. Analytical expressions for pressure, internal energy, and entropy are found in the approximation of the fourth order in temperature gradients. It is shown that the gradient contributions to the internal energy depend on the volume, while the entropy satisfies the second law of thermodynamics for nonequilibrium processes. The calculations are performed for dimensions 3D, 2D, and 1D.
Highlights
It is known from statistical mechanics that the interparticle interaction manifests itself in thermodynamic quantities gradually passing from low gas densities to intermediate ones, e.g. [1]
Putting the explicit determination of the temperature profile off, we consider the problem of calculation of the thermodynamic quantities from rather general grounds and as before [49] we describe the steady state by the set of temperature value T0 and values {G1, . . . ,Gr } of its r successive gradients referred to the geometrical middle-point of the vessel
We conclude that the nonequilibrium entropy found is less than the entropy of the corresponding equilibrium state and as a consequence it satisfies the second law of thermodynamics for nonequilibrium processes [2, 3, 57]
Summary
It is known from statistical mechanics that the interparticle interaction manifests itself in thermodynamic quantities gradually passing from low gas densities to intermediate ones, e.g. [1]. 1) the first one [12] was on the pressure difference between the equilibrium and nonequilibrium stationary heat-conduction hard-disk gases separated by a porous wall; the phenomenological conclusion on the pressure difference claimed in [13] had not been confirmed; 2) the second problem concerned the description of hard disks between two parallel walls with different temperatures [11]; for the weakly nonequilibrium case, the pressure correction was estimated to be quadratic in the heat flux These results follow from the nonstationary Enskog equation. We attempt to take interparticle interaction into account for the particular case of the hard-sphere system at intermediate densities making use of one of its simplest equations of state This demonstrates the applicability of the method to the calculation of thermodynamic quantities of gases in the situations where the size of particles becomes important.
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