Tomaschitz,
R. (2023). Isobaric heat capacity of classical and quantum fluids: Extending
experimental data sets into the critical scaling regime, *European Physical
Journal Plus ***138**, 457, DOI: 10.1140/epjp/s13360-023-04006-0

**Abstract **SpringerLink , EDP Sciences

The
singular isobaric heat capacity *C*_{P }(*T*, *P*)
of nitrogen, methane, water and hydrogen at critical pressure *P*_{c}
is studied over an extended temperature range, from the melting point up to the
high-temperature cutoff of the experimental data sets. The high- and
low-temperature branches (above and below the critical temperature *T*_{c})
of the critical isobaric heat capacity *C*_{P }(*T*, *P*_{c})
can accurately be modeled by broken power-law distributions in which the
scaling exponent 1 - 1 / *δ* of the 3D Ising
universality class is implemented. (The enumerated fluids admit 3D Ising
critical exponents.) The parameters of these distributions are inferred by
nonlinear least-squares regression from high-precision data sets. In each case,
a non-perturbative analytic expression for *C*_{P }(*T*, *P*_{c})
is obtained. The broken power laws admit closed-form Index functions
representing the Log-Log slope of the regressed branches of *C*_{P
}(*T*, *P*_{c}) . These Index functions quantify the
crossover from the experimentally more accessible high- and low-temperature
regimes to the critical scaling regime. Ideal power-law scaling (without
perturbative corrections and discounting impurities and gravitational rounding
effects) of *C*_{P }(*T*, *P*_{c}) occurs
in a narrow interval, typically within |*T* / *T*_{c} - 1| <
10^{-4} or even 10^{-5} depending on the fluid, and the
regressed broken power-law densities provide analytic extensions of *C*_{P }(*T*,
*P*_{c}) to the melting point and up to dissociation
temperatures.

description:
Roman Tomaschitz (2023) Isobaric heat capacity of classical and quantum fluids:
Extending experimental data sets into the critical scaling regime, *Eur.
Phys. J. Plus ***138**, 457.

**Keywords:**
Isobaric specific heat of nitrogen, methane, water, and hydrogen; Critical
singularities and critical exponents; 3D Ising universality class (phase
transitions); Crossover to the critical power-law scaling regime; Multiply
broken power-law distributions and their Index functions; Nonlinear
least-squares regression with parameter constraints

download
full-text article (PDF) __Full
Text HTML__

back to index