[Objective] The supercritical carbon dioxide (S-CO₂) semi-closed Brayton cycle has attracted widespread attention due to its high cycle efficiency and potential for near -zero carbon emissions. The working fluid in this cycle primarily consists of the CO₂/H₂O mixture. Except during the compression and separation processes, the CO2/H2O mixture operates in the low- to medium-density region for most of the cycle. Accurate prediction of thermophysical properties in this region is crucial for the power cycle . Due to the lack of experimental data for the mixture, the applicable temperature range of multiparameter equations of state is limited, making it difficult to meet the demand for thermophysical property calculations at high temperatures. Computational models based on theoretical foundations have greater potential for extrapolation in the high-temperature region. Among these, semi-theoretical cubic equations of state can reasonably describe the trends in thermophysical properties. However, they are limited by their structure and cannot achieve extremely high precision. In contrast, the virial equation of state, with its rigorous theoretical foundation, provides an effective approach for high-precision prediction of thermophysical properties over a wide temperature range. 

[Methods] A predictive model that strictly satisfies physical consistency requirements is established for the cross second virial coefficient of the CO₂/H₂O mixture based on ab initio data. Building upon this, a three-term truncated virial equation of state (VEOS3) is developed to calculate the thermodynamic properties of pure CO₂, pure H₂O, and their binary mixtures. The predictive performance of VEOS3 is systematically evaluated across a range of properties, including pvT(x), isobaric heat capacity, internal energy, enthalpy, entropy, and speed of sound. The effective range of VEOS3 is de termined by comparison with multiparameter equations of state within their respective validity domains. At a given temperature, the maximum density and the corresponding pressure within the region where the absolute relative deviation does not exceed 1% ar e defined as the effective density limit and effective pressure limit, respectively . The model performance is further validated using experimental data. 

[Results] The results show that the effective density limit of VEOS3 remains approximately constant in the high-temperature region or increases linearly with temperature. As the temperature rises, the effective prediction range of VEOS3 can be extended to higher pressures. Meanwhile, VEOS3 reproduces available experimental data with high accuracy. Here, the average absolute relative deviation (AARD) is used to quantify prediction deviations. For pure CO₂ and pure H2O, the AARDs of VEOS3 in density, isobaric heat capacity, and speed of sound are 0.14%/0.30%, 0.28%/0.82%, and 0.02%/0.16%, respectively. For CO₂/H₂O mixtures, the AARD in density is 0.43%. 

[Conclusion] VEOS3 can accurately calculate thermophysical properties in the low - to medium-density region, where the reduced density is less than or equal to 2/3. It also maintains stable and reliable extrapola tion capability at high temperatures, providing model support for thermophysical property calculations in the S-CO₂ semi-closed Brayton cycle.