Ideal Gas Laws

Abstract This is the first chapter to explicitly address fluid media. For springs and solids, Hooke’s law, or its generalization using stress, strain, and elastic moduli provided an equation of state. In fluids, we have an equation of state that relates changes in pressure (stresses) to changes in density (strain). The simplest fluidic equations of state are the Ideal Gas Laws. Our presentation of these laws will combine microscopic models that treat gas atoms as hard spheres with phenomenological (thermodynamic) models that combine the variables that describe the gas with conservation laws that restrict those variables. The combination of microscopic and phenomenological models will give us the important characteristics of gas behavior under isothermal or adiabatic conditions and will provide relationships between gas heat capacities and their constituent particles when augmented with elementary concepts from quantum mechanics. The chapter ends by adding a velocity field to the pressure, temperature, and density, thus providing the equations of hydrodynamics that will guide all of the subsequent development of acoustics in fluids.