Based on the conceptual design reports for the Future Circular Collider cryogenic system, the need for more accurate thermodynamic property models of cryogenic mixtures of noble gases was identified. Both academic institutes and industries have identified the lack of a reliable equation of state for mixtures used at very low temperatures. Detailed cryogenic architecture modeling and design cannot be carried out without accurate fluid properties. Therefore, the helium–neon equation was the first goal of this work, and it was further extended to other fluids beneficial for scientific and industrial applications beyond the particle physics needs. The properties of the noble gas mixtures of helium–neon, neon–argon, and helium–argon are accurately modeled with the equations of state explicit in the Helmholtz energy.

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