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 quantum-corrected cubic equation of state paves the way for technological applications of quantum fluids that require models with both high accuracy and computational speed.

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氦、氖、氢、氘及其混合物的精确量子校正三次状态方程

摘要 迄今为止，三次状态方程对诸如氢、氦和氘等量子流体在低温下的热力学性质的预测效果不佳。此外，氦和氢的最佳 α 函数的形状已被证明不会像其他流体一样单调衰减。在这项工作中，我们通过将三次状态方程的余体积参数映射到由量子校正的 Mie 势预测的排除体积上来推导出与温度相关的量子校正。Twu α 函数的后续回归恢复了在大部分温度范围内具有单调衰减的近乎经典的行为。量子校正可显着提高准确度，尤其是对于热量特性。虽然目前最先进的液氢饱和等容热容的平均偏差超过 80%，但量子校正的平均偏差为 4%。所有四种流体的饱和压力平均偏差都远低于 1%。使用 Peneloux 体积位移，氦的饱和密度平均误差低于 2%，氢、氘和氖的饱和密度误差约为 1%。给出了两个三次状态方程的参数：Peng-Robinson 和 Soave-Redlich-Kwong。量子校正三次状态方程也能够再现量子流体二元混合物的汽液平衡，它们是第一个能够准确模拟氦氖气液平衡的三次状态方程混合物。与用于开发共体积校正的量子校正 Mie 势相似，需要共体积的相互作用参数以高精度表示氦氢混合物。量子校正三次状态方程为需要高精度和计算速度的模型的量子流体技术应用铺平了道路。