Abstract
Cubic equations of state have thus far yielded poor predictions of the thermodynamic properties of quantum fluids such as hydrogen,
helium and deuterium at low temperatures. Furthermore, the shape of the optimal α functions of helium and hydrogen have been
shown to not decay monotonically as for other fluids. In this work, we derive temperature-dependent quantum corrections for the
covolume parameter of cubic equations of state by mapping them onto the excluded volumes predicted by quantum-corrected Mie
potentials. Subsequent regression of the Twu α function recovers a near classical behavior with a monotonic decay for most of the
temperature range. The quantum corrections result in a significantly better accuracy, especially for caloric properties. While the
average deviation of the isochoric heat capacity of liquid hydrogen at saturation exceeds 80% with the present state-of-the-art, the
average deviation is 4% with quantum corrections. Average deviations for the saturation pressure are well below 1% for all four
fluids. Using Peneloux volume shifts gives average errors in saturation densities that are below 2% for helium and about 1% for
hydrogen, deuterium and neon. Parameters are presented for two cubic equations of state: Peng–Robinson and Soave–Redlich–
Kwong. The quantum-corrected cubic equations of state are also able to reproduce the vapor–liquid equilibrium of binary mixtures
of quantum fluids, and they are the first cubic equations of state that are able to accurately model the vapor-liquid equilibrium of
the helium–neon mixture. Similar to the quantum-corrected Mie potentials that were used to develop the covolume corrections,
an interaction parameter for the covolume is needed to represent the helium–hydrogen mixture to a high accuracy. The quantumcorrected cubic equation of state paves the way for technological applications of quantum fluids that require models with both high
accuracy and computational speed.
helium and deuterium at low temperatures. Furthermore, the shape of the optimal α functions of helium and hydrogen have been
shown to not decay monotonically as for other fluids. In this work, we derive temperature-dependent quantum corrections for the
covolume parameter of cubic equations of state by mapping them onto the excluded volumes predicted by quantum-corrected Mie
potentials. Subsequent regression of the Twu α function recovers a near classical behavior with a monotonic decay for most of the
temperature range. The quantum corrections result in a significantly better accuracy, especially for caloric properties. While the
average deviation of the isochoric heat capacity of liquid hydrogen at saturation exceeds 80% with the present state-of-the-art, the
average deviation is 4% with quantum corrections. Average deviations for the saturation pressure are well below 1% for all four
fluids. Using Peneloux volume shifts gives average errors in saturation densities that are below 2% for helium and about 1% for
hydrogen, deuterium and neon. Parameters are presented for two cubic equations of state: Peng–Robinson and Soave–Redlich–
Kwong. The quantum-corrected cubic equations of state are also able to reproduce the vapor–liquid equilibrium of binary mixtures
of quantum fluids, and they are the first cubic equations of state that are able to accurately model the vapor-liquid equilibrium of
the helium–neon mixture. Similar to the quantum-corrected Mie potentials that were used to develop the covolume corrections,
an interaction parameter for the covolume is needed to represent the helium–hydrogen mixture to a high accuracy. The quantumcorrected cubic equation of state paves the way for technological applications of quantum fluids that require models with both high
accuracy and computational speed.
