Monte Carlo Molecular Simulations To Determine The Isobaric Heat Capacity Of Co2, Methanol, And Their Mixtures Using Thermodynamic Fluctuations In The Isothermal-Isobaric Ensemble And The Grand Canonical Ensemble
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In the vicinity of the critical point, fluids experience variations in second derivative thermodynamic properties, including isobaric heat capacity. In this work, Monte Carlo molecular simulations were used to compute the isobaric heat capacity of pure carbon dioxide (CO2), pure methanol (MeOH), and binary mixtures of CO2 and MeOH. Estimated values were compared to calculations from highly accurate Equations of States. The residual isobaric heat capacity of pure CO2 and MeOH were computed by two different methods. First, thermodynamic fluctuations observed in the isothermal-isobaric ensemble were used to compute the isobaric heat capacity of pure CO2 and MeOH following a method developed by Lagache and coworkers in 2001 (Lagache, Ungerer, Boutin, & Fuchs, 2001). Then, the residual isobaric heat capacity of pure CO2 and MeOH was also computed through a novel method that utilized thermodynamic fluctuations observed in Grand Canonical Monte Carlo simulations. The total isobaric heat capacity was computed by combining the residual isobaric heat capacity and the ideal gas isobaric heat capacity, obtained from experimental correlations. The critical temperatures of pure CO2 and MeOH were computed for the simulated systems through a finite size scaling analysis, and the critical pressures were computed through a semi-empirical fitting. The calculated critical temperatures and pressures were used to reduce the temperatures and pressures of simulations used to compute the isobaric heat capacity of pure CO2 and MeOH. In this way, the calculated isobaric heat capacity was compared to equation of state (EOS) calculations completed at temperatures and pressures reduced by the experimentally measured critical temperatures and pressures. The isobaric heat capacity of CO2 evaluated in both the isothermal-isobaric and grand canonical ensemble matched the calculations of the highly accurate Span and Wagner EOS with near quantitative accuracy. The isobaric heat capacity calculated for pure MeOH in the same manner similarly aligned with the values from IUPAC EOS for MeOH. The isobaric heat capacity of binary mixtures of CO2 and MeOH was computed over a range of compositions using the fluctuation method in the isothermal-isobaric ensemble. Absolute rather than reduced temperatures and pressures were used for the calculations, in the interest of saving computational time. Analogous to the validation of pure components, the mixture isobaric heat capacities were compared with those calculated from the GERG EOS available in the REFPROP Software package, and measured experimentally. Overall, the computed isobaric heat capacities were qualitatively comparable to those calculated from the GERG EOS and measured experimentally.
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