ABSTRACT
“The equilibrium properties of a pure substance can be described in at least eight distinct ways in thermodynamics and statistical mechanics. These eight different descriptions are interrelated through a Laplace-Legendre transformation scheme.” The comparison between an isothermal process and an adiabatic process provides excellent insight into what distinguishes an adiabatic ensemble from an isothermal ensemble. Isothermal ensembles are in thermal contact with a reservoir, while adiabatic ensembles are thermally insulated. Legendre transforms provide relations between thermodynamic state functions. There is, however, a fundamental difference between isothermal and adiabatic ensembles. In isothermal ensembles, random moves are accepted based on their Boltzmann probability, which depends on the value of the change in potential energy due to the moves. Indeed, the system, initially in the vapor phase, becomes a liquid. Copper undergoes a first-order phase transition, with entropy and molar volume discontinuities at the transition.
