Thermodynamic systems for solids and liquids

The basic mathematical consequences which follow from the laws of thermodynamics are explored in a systematic new treatment for establishing fluid thermodynamic systems for a number of materials under conditions where they behave as fluids. For metals and many other solids, but less so for liquids, the specific heat at constant volume c_ν is sensibly constant at all temperatures above room temperature. The partial differential equation of thermodynamics which expresses the constancy of c_ν is easily solved, the solution involving two arbitrary functions of the specific volume. Various approaches are presented to illustrate how one may choose these functions to accord with experimental observations over large thermodynamic ranges, and so produce practical thermodynamic systems. Two complementary thermodynamic systems are presented, which embody significant experimental results; the first is based on linear shock velocity/particle velocity (U, u) relations; the second on the limiting value of the specific heat ratio $\text{c}{}_{\mathrm{p}}\text{c}{}_{\mathrm{v}}$ at high temperatures. They are complementary in the sense that the first has analytically complicated non-Hugoniot properties which differ insignificantly from the comparatively simple non-Hugoniot properties of the second; whilst the second has analytically complicated Hugoniot properties which differ insignificantly from the simple Hugoniot properties of the first. Together, then, the two systems may be combined to give comprehensive practical simplicity. The main interest in these thermodynamic systems lies in the study of the behaviour of liquids, metals and other solids in shock transitions and under extreme conditions such as occur in high velocity impact or in explosion phenomena; but they are also of importance in stress-wave analysis, where complete thermodynamic systems are required in order to derive stress-strain relationships which do not neglect the effects of temperature changes.