Methodology for constructing the equation of state and thermodynamic tables for a new generation refrigerant

A unified fundamental equation of state 2,3,3,3-tetrafluoropropene (R1234yf) has been developed, a fourth-generation ozone safe refrigerant, and a method for constructing the equation has been proposed. In the gas region, this equation transforms into the virial equation of state, and in the vicinity of the critical point it satisfies the requirements of the modern large-scale theory of critical phenomena and transforms into the Widom scale equation. On the basis of a single fundamental equation of state in accordance with GOST R 8.614-2018, standard reference data (GSSSD 380-2020) on the density, enthalpy, isobaric heat capacity, isochoric heat capacity, entropy and sound velocity of R1234yf in the temperature range from 230 K to 420 K and pressures from 0.1 MPa to 20 MPa. A comparison of the calculated values of equilibrium properties with the most reliable experimental data obtained in the famous of the world, and tabular data obtained on the basis of the known fundamental equations of state R1234yf. Uncertainties of tabulated data for saturated vapor pressure, density, enthalpy, isobaric heat capacity, isochoric heat capacity, entropy and speed of sound of 2,3,3,3-tetrafluoropropene are estimated – standard relative uncertainties by type A, B, total standard relative and expanded uncertainties. The results obtained in the work show that the proposed unified fundamental equation of state adequately describes the equilibrium properties of R1234yf in the range of state parameters stated above.

Nonlinear Effects in the Phonon System of Diamond Crystal

Thermodynamic properties of diamond are theoretically investigated on the ground of self-consistent description of a phonon gas in lattice, which generalizes the Debye model with taking into account the phonon-phonon interaction. In many cases properties of crystals of certain symmetry can be well approximated by a model of an isotropic continuous medium, if its elastic moduli are chosen optimally. They should be found for a crystal of each symmetry from the condition of their proximity to the exact elastic moduli, which are measured experimentally and are given in the corresponding tables. At high temperatures, the nonlinear phonon interaction takes into account both three- and four-phonon interactions. In this reason we take into account not only the second-order elastic moduli tensor in the reduced isotropic crystal model, but also the third- and fourth-order elastic moduli tensors, which are all together characterized by nine independent components. Account of the phonon-phonon interaction leads to the redefinition of the phonon’s speed and of the Debye energy. Their dependence on the temperature occurs. In the absence of interaction and neglecting the nonlinear effects, the phonons are the same as that of the Debye model. They are called "bare" or "Debye". Phonons whose speed is renormalized due to the interaction are called the “self-consistent” ones. It is shown that, at high temperatures, the theory predicts the linear in the temperature deviation of the isochoric heat capacity from the Dulong-Petit law. Unlike for the most crystals, where the decrease in the isochoric heat capacity is observed, our calculations for diamond and crystals with diamond structure predict the linear increase of the isochoric heat capacity with the temperature, viewed experimentally. The isobaric heat capacity of diamond, similar to other substances, linearly increases with the temperature.