Isobaric heat capacity of carbon dioxide at critical pressure: Singular thermodynamic functions as multiply broken power laws

Abstract

The isobaric CO2 heat capacity at critical pressure is regressed in an extended temperature interval from the melting point at 216.6 K up to 2000 K. In the vicinity of the critical temperature Tc=304.13K, the calculated critical scaling exponent of the heat capacity is used to extrapolate the empirical data range into the power-law scaling regime. Closed-form representations of the high- and low-temperature branches of the isobaric CO2 heat capacity are obtained by nonlinear least-squares fits of multiply broken power-law distributions, in which the calculated universal scaling exponent is implemented. The regressed broken power laws cover the temperature range from the melting point up to Tc and from Tc to CO2 dissociation temperatures. Index functions representing the Log–Log slope of the heat capacity are used to quantify the crossover from the high- and low-temperature regimes to the critical power-law scaling regime. Even though the focus is on the isobaric heat capacity of a specific one-component fluid, the formalism is kept sufficiently general to be applicable to other thermodynamic functions with critical singularities and to multi-component mixtures.