Equations of state

Abstract

What we learn in this chapter An equation of state (EOS) of a gas is the pressure as a function of density and temperature, P (ρ, T ). It is fundamental to the understanding of stellar interiors. For an ideal gas, the gas particles have a distribution of momenta described by the Maxwell–Boltzmann (M-B) distribution . The distribution of gas particles is most generally described as a six-dimensional (6-D) phase-space density , f ( x , y , z , p x , p y , p z , t ), known as the distribution function . It is directly related to specific intensity . The phase-space density can vary with time, but, according to Liouville's theorem , it is conserved in a frame of reference that travels in phase space with the particles – under certain conditions. The propagation of cosmic rays in the Galaxy generally satisfies these conditions. From the M-B distribution, one finds the pressure, and hence the EOS, P =(ρ / m av ) kT of an “ideal” particulate gas, which, rewritten, is the ideal gas law, PV = μ R T . This EOS applies to most stellar interiors. A photon gas in equilibrium with its surroundings, blackbody radiation , has an EOS that depends solely on temperature, P = aT 4 /3, as developed in Chapter 6. This pressure plays a dominant role in the centers of the most massive stars and did so in the early universe. Highly dense stars such as white dwarfs and neutron stars have very different equations of state. The former, and in part the latter, are supported by degeneracy pressure , a quantum mechanical phenomenon. […]