Preamble

An equation of state is a relationship between volume, V, pressure, P, and temperature, T, of a specified mass of material. If density, ρ, is used instead of V then specification of mass is unnecessary, and in some treatments V is specific volume, 1/ρ, but in this text V is the volume of an arbitrary mass, m. Another alternative is molar volume, but moles can be inconvenient units for materials with non-integral proportions of different elements. The simplest and most familiar equation of state is the ideal gas equation for n moles of gas, PV = nRT, where R = NAk = 8.314 47 J mol− 1 K− 1 is the gas constant and is related to Boltzmann's constant, k = 1.380 65 × 10− 23 JK− 1 by Avogadro's number, NA = 6.022 14 × 1023 mol− 1. It is an example of a complete equation of state, by which is meant one representing V as a function of both P and T, not that it gives all of the properties. In dealing with condensed matter (solids and liquids) it is generally convenient to consider the P and T effects separately. Compression at constant T is described by the isothermal bulk modulus or incompressibility, KT = − V(∂P/∂V)T. This is a parameter of elasticity theory (Chapter 10), which is restricted to small strains, that is, for volume compression, P/KT = −ΔV/V ≪ 1.