Techniques for calculating properties of materials at high pressures

It is shown that, according to the equation of classical thermodynamics (partial derivative U/partial derivative p)(T) = V(beta p - alpha T), where beta is compressibility and alpha the volume expansion coefficient, the internal energy of materials decreases with increasing pressure, in conflict with the energy conservation law. The assumptions leading to this conflict are analyzed. It is assumed that the only inherent characteristic of a material is its internal energy U and not enthalpy H or heat q. In connection with this, materials should be characterized by energy capacity C-U, rather than by heal capacity C-p. These characteristics are related by C-U = C-p - alpha pV. The relative difference between C-U and C-p increases with pressure and ranges, depending on material, from 0.5 to 5% at 10(8) Pa and from 7 to 9% at 10(9) Pa. An equation is derived for the pressure derivative of internal energy, according to which this derivative is positive, in accordance with the energy conservation law. In addition, equations are obtained for calculating the internal-energy and free-energy changes caused by an increase in pressure at constant temperature.