https://doi.org/10.1140/epjp/s13360-023-04006-0
Regular Article
Isobaric heat capacity of classical and quantum fluids: extending experimental data sets into the critical scaling regime
, Sechsschimmelgasse 1/21-22, 1090, Vienna, Austria
Received:
2
February
2023
Accepted:
17
April
2023
Published online:
24
May
2023
The singular isobaric heat capacity 
of nitrogen, methane, water and hydrogen at critical pressure 
is studied over an extended temperature range, from the melting point to the high-temperature cutoff of the experimental data sets. The high- and low-temperature branches (above and below the critical temperature 
) of 
can accurately be modeled with broken power-law distributions in which the calculated universal scaling exponent 
of the isobaric heat capacity at critical pressure 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 is obtained. The broken power laws have closed-form Index functions representing the Log–Log slope of the regressed branches of . 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 occurs in a narrow interval, typically within 
or even 
depending on the fluid, and the regressed broken power-law densities provide closed-form analytic extensions of to the melting point and up to dissociation temperatures.
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