Abstract
A differential equation of state is presented for a monatomic gas without virial interactions between its particles. Together with suitable boundary conditions this defines a macroscopic concept of the 'perfect' gas. INTRODUCTION Since the time of Boyle, Mariotte and Gay—Lussac many people have considered how an 'ideal' (or 'perfect') gas should be defined. Rather early, the relation p=vkT (1) was accepted, p being the pressure, v the number density (v 1) and T the absolute temperature of the gas. As is well known, this thermal equation of state does not completely determine the thermodynamic properties of the substance. If one also wishes the caloric equation of state, one must known an additional function of one variable, e.g. the molecular heat distribution c(T) whence the molecular energy u(T) = J c(T)dT (2) may be obtained. From both equations of state one derives the molecular entropy s(T, v) c(T) T' dT — logp (3) and from these the chemical potential 1i(T, p) = kT + u(T) — Ts(T, p/kT) (4) which contains the whole thermodynamic information about the substance, because it is a thermodynamic potential. An important quantity measuring the 'power of diffusion' is the fugacity p =e_T. We call a fluid that obeys equation 1 an ideal gas, distinguishing this notion from that of a 'perfect gas', which we are going to describe.
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