Definition of Temperature in Nonequilibrium Processes

Abstract

The validity of using a multiple-temperature heat bath model for the description of nonequilibrium processes is examined. Several models have been proposed which utilize temperatures defined by statistical distribution functions or chemical mass action laws. Since, however, the heat bath model is described by classical thermodynamic temperatures which are defined in terms of heat exchange between a reversible engine and energy reservoirs, the validity of such models requires justification. It is shown that the classical thermodynamic temperature can sometimes be used to characterize a particular degree of freedom, such as vibration, even if it is not in equilibrium with the other degrees of freedom. However, it does not appear to be possible in general to associate a thermodynamic temperature with a nonequilibrium chemical composition. To demonstrate this, the entropy rise in vibrational and chemical nonequilibrium processes is computed using the concept of multiple temperatures and compared to the classical result. The results agree for vibrational nonequilibrium. For chemical nonequilibrium the results do not agree except for chemical systems in which the reactants and products have equal constant volume mass specific heats. An example of such a system is the ideal dissociating gas of Lighthill.