Description of heat capacity C v of simple liquids using a thermal equation of state including regular and scaling parts

Abstract

The p,ρ,T data for CO 2 are approximated in the ranges of 0 < ρ/ρ c <2, 217 < T < 430 K, and 0 < p ≤ 25 MPa and for SF 6 in the ranges of 0 < ρ/ρ c < 2.5, 225 < T < 340 K, and 0 < p ≤ 10 MPa using a new unified equation of state. In this equation, pressure p is an explicit function of ρ and T. It includes a new reg ular part to approximate p,ρ,T data in the liquid and gaseous regions of state outside the critical region, a sin gular part that is a scaling equation of state for the critical region, and a crossover function for combining these equations. The regular part consists of the sum of eight terms with eight constants, three of which are deter mined by the conditions at the critical point. The total number of system dependent constants is fourteen, including the critical values of p, ρ, and T. In the scaling part of the equation of state, the critical exponents of the three dimensional Ising model are used. The mean square error of the description by pressure of the p,ρ,T data for CO 2 is ±0.63%, and for the p,ρ,T data obtained for SF 6 , it is ±0.70% over the entire range of gas and liquid states. Using the constants of the combined equation, heat capacity C v is calculated at isoch ores, isotherms, and a binodal, including those in the critical region. The calculation results describes the known experimental data of C v with an error of ±8%.