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
The singular isobaric heat capacity CP (T, P) of nitrogen, methane, water and hydrogen at critical pressure Pc 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 Tc) of the critical isobaric heat capacity CP (T, Pc) 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 CP (T, Pc) is obtained. The broken power laws admit closed-form Index functions representing the Log-Log slope of the regressed branches of CP (T, Pc) . 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 CP (T, Pc) occurs in a narrow interval, typically within |T / Tc - 1| < 10-4 or even 10-5 depending on the fluid, and the regressed broken power-law densities provide analytic extensions of CP (T, Pc) 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