Tomaschitz, R. (2023). Isobaric heat capacity of carbon dioxide at critical pressure: Singular thermodynamic functions as multiply broken power laws, Physica A 611, 128421, DOI: 10.1016/j.physa.2022.128421
Abstract ScienceDirect
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 = 304.13 K, 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.
description: Roman Tomaschitz (2023) Isobaric heat capacity of carbon dioxide at critical pressure: Singular thermodynamic functions as multiply broken power laws, Physica A 611, 128421.
Keywords: Critical singularities and power-law scaling; Multiply broken power-law distributions and their Index functions; Isochoric and isobaric specific heat of single-component fluids; Isothermal and adiabatic compressibility and speed of sound; Isobaric and isentropic volume expansivity (expansion coefficient)
Highlights
The singular isobaric CO2 heat capacity at critical pressure is modeled with multiply broken power-law distributions from the melting point up to dissociation temperatures.
The calculated critical exponent of the heat capacity is used to extend the experimental data range into the critical power-law scaling regime.
The high- and low-temperature branches of the heat capacity are obtained by nonlinear regression of broken power-law densities in which the critical scaling exponent is implemented.
Index functions representing the Log-Log slope of the regressed heat capacity illustrate the crossover from the experimental data range to the critical regime.
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