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 CO_{2} 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 *T*_{c}
= 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 CO_{2} 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 *T*_{c}
and from *T*_{c} to CO_{2} 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 CO_{2} 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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