Related papers: Macroscopic equations for the adiabatic piston
The purpose of this note is to see to what extent ideal gas laws can be obtained from simple Newtonian mechanics, specifically elastic collisions. We present simple one-dimensional situations that seem to validate the laws. The first…
We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modelled by stochastic scattering at the…
We suggest and discuss a simple model of an ideal gas under the piston to gain an insight into the workings of the Jarzynski identity connecting the average exponential of the work over the non-equilibrium trajectories with the equilibrium…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly…
We consider the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a container divided in two regions by a movable adiabatic wall (adiabatic piston). In this talk we discuss the thermodynamic limit where…
We develop a kinetic-theory framework to investigate the steady rheology of a dilute gas interacting via a repulsive potential under uniform shear flow. Starting from the Boltzmann equation with a restitution coefficient that depends on the…
Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a…
We continue the study of the time evolution of a system consisting of a piston in a cubical container of large size $L$ filled with an ideal gas. The piston has mass $M\sim L^2$ and undergoes elastic collisions with $N\sim L^3$ gas…
We study a molecular engine constituted by a gas of $N \sim 10^2$ molecules enclosed between a massive piston and a thermostat. The force acting on the piston and the temperature of the thermostat are cyclically changed with a finite period…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…
A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat…
One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum…
A simplified, but non trivial, mechanical model -- gas of $N$ particles of mass $m$ in a box partitioned by $n$ mobile adiabatic walls of mass $M$ -- interacting with two thermal baths at different temperatures, is discussed in the…
We report a formula for the dry adiabatic lapse rate that depends on the compressibility factor and the adiabatic curves. Then, to take into account the non-ideal behavior of the gases, we consider molecules that can move, rotate, and…
We study fluctuating dynamics of a freely movable piston that separates an infinite cylinder into two regions filled with ideal gas particles at the same pressure but different temperatures. To investigate statistical properties of the…
We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In…
A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle dimeters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement…
We revisit the double adiabatic evolution equations and extend them to the relativistic and ultrarelativistic regimes. We analytically solve the relativistic, time-dependent drift kinetic equation for a homogeneous, magnetized,…
It is shown that the ideal gas adiabatic relation, P*V^gamma=constant, can be derived by considering the motion of a particle bouncing elastically between a stationary wall and a moving wall.