Publications by Author: David S. Corti

We revisit the thermodynamic analysis of an isothermal ideal gas mixture enclosed within a cylinder and separated from the surrounding atmosphere by a movable and frictionless piston. When equilibrium conditions based on the chemical potentials of one or more species in the mixture are not satisfied at all times, which occurs for example for a chemical reaction with finite and non-zero reaction rates in the forward and reverse directions and for mass transfer of one species across a permeable membrane occurring at a finite and non-zero rate, an irreversibility is necessarily introduced into the system with a resulting increase in the entropy of the Universe. Consequently, when the piston is set in motion, it cannot oscillate indefinitely. The piston must again come to rest despite there not being any mechanical dissipative mechanisms, i.e. friction or viscous dissipation, nor a thermal dissipative mechanism, i.e. irreversible heat transfer, operating within the system. Only when the system is reversible, such that the entropy of the Universe remains constant at all times, will the piston oscillate indefinitely. 'Chemical damping,' or an irreversibility arising from nonequilibrium conditions on the chemical potential, provides another dissipative mechanism that has not yet been analyzed before.

We consider the thermal, mechanical, and chemical contact of two subsystems composed of ideal gases, both of which are not in the thermodynamic limit. After contact, the combined system is isolated, and the entropy is determined through the use of its standard connection to the phase space density (PSD), where only those microstates at a given energy value are counted. The various intensive properties of these small systems that follow from a derivative of the PSD, such as the temperature, pressure, and chemical potential (evaluated via a backward difference), while equal when the two subsystems are in equilibrium are nevertheless found not to behave in accordance with what is expected from macroscopic thermodynamics. Instead, it is the entropy, defined from its connection to the PSD, that still controls the behavior of these small (nonextensive) systems. We also analyze the contact of these two subsystems utilizing an alternative entropy definition, through its proposed connection to the phase space volume (PSV), where all microstates at or below a given energy value are counted. We show that certain key properties of these small systems obtained with the PSV either do not become equal or do not consistently describe the two subsystems when in contact, suggesting that the PSV should not be used for analyzing the behavior of small isolated systems.