Advances in the Thermodynamics of Ideal Gases by Means of Computer Simulations
D. Sands and J. Dunning-Davies
Department of Physics,
University of Hull,
Hull HU6 7RX, England.
Abstract. Irreversible thermodynamic processes in ideal gases are investigated by computer simulations of the compound piston. A hard-sphere model of the gas on either side of a compound piston shows that damping occurs naturally without invoking extraneous mechanisms such as friction. Inter-particle collisions are identified as being responsible, as these redistribute the particle energies by altering all the components of momentum. In collisions with the piston, on the other hand, only the component of particle momentum in the direction of the piston motion is affected. Thus inter-particle collisions effectively dissipate the energy of the piston. These ideas are then incorporated into a simpler, one dimensional model based on kinetic theory in which all the particles have the same initial energy and inter-particle collisions are simulated by randomly adjusting the energy distribution. Varying the rate of energy redistribution alters the rate of decay of the piston motion. In addition, this simple models allows thermal interactions with the walls of the vessel to be simulated easily, and we observe a second mechanism of damping due to delayed heating and cooling. These ideas lead directly to a macroscopic formulation of thermodynamics in terms of rate equations. The models give an insight into the micro-dynamical origins of irreversibility in ideal gases and allow the thermodynamics of these irreversible processes to be investigated. We find surprisingly simple relationships between the volume changes and characteristic pressures in the system. Finally, we apply these ideas to the Carnot cycle and show that a dynamic cycle is executed if the piston is allowed to move under alternately ideal isothermal and adiabatic conditions. In this dynamic Carnot cycle not only is work done but power is developed through the motion of the piston. The implications for classical thermodynamics are discussed briefly.