Precision of some forms of unified equation of state (on the basis of methane data)

Abstract

The precision of some well-known forms of unified equation of state for gas and liquid was investigated. The first form describes the compressibility factor, Z = pυ/RT, the second the dimensionless Helmholtz energy, Φ = A/RT, as a function of reduced density, ω = ρ/ρ cr , and reduced temperature, τ = T/T cr (where p is pressure, u is specific volume, T is temperature, p is density, subscript cr refers to critical values, R is the gas constant, and A is the Helmholtz energy). Two versions of these equations were considered: simple polynomial and equations additionally containing exponents of density. The investigation was fulfilled with data on density and isochoric specific heat of methane covering the temperature range from the saturation line up to 620 K at pressures up to 1000 MPa. While compiling equations of state Maxwell's rule was satisfied. The calculations showed that for polynomial versions of the equation Z(ω, τ) for different numbers of coefficients (50-30) the values of root mean square (rms) deviations, δρ m , δp sm , and δc υm from the data used were 0.04%-0.07%, 0.03%-0.05%, and 0.5%-0.9%. For analogous versions of the equation for Φ(ω, τ) the deviations were nearly equal. For both forms of equations, including exponential terms significantly reduces the values of the rms deviations. At the second stage of calculations the random errors were added to the initial values of p and specific heat, c v , and new equations of state were compiled. In this case, values of rms deviations for both forms of equation of state increased, but the above-mentioned quality relationship between deviations for polynomial and exponential versions of the equations was preserved.