N. G. Polikhronidi

Isochoric Heat Capacity Measurements for Heavy Water Near the Critical Point

Isochoric heat capacity measurements of D2O are presented as a function of temperature at fixed densities of 319.60, 398.90, 431.09, and 506.95 kg·m−3. The measurements cover a range of temperatures from 551 to 671 K and pressures up to 32 MPa. The coverage includes one- and two-phase states and the coexistence curve near the critical point of D2O. A high-temperature, high-pressure, adiabatic, and nearly constant-volume calorimeter was used for the measurements. Uncertainties of the heat capacity measurements are estimated to be 2 to 3%. Temperatures at saturation TS(ρ) were measured isochorically using a quasi-static thermogram method. The uncertainty of the phase transition temperature measurements is about ±0.02 K. The measured CV data for D2O were compared with values predicted from a parametric crossover equation of state and six-term Landau expansion crossover model. The critical behavior of second temperature derivatives of the vapor pressure and chemical potential were studied using measured two-phase isochoric heat capacities. From measured isochoric heat capacities and saturated densities for heavy water, the values of asymptotic critical amplitudes were estimated. It is shown that the critical parameters (critical temperature and critical density) adopted by IAPWS are consistent with the TS–ρS measurements for D2O near the critical point.

Isochoric Heat Capacity Measurements for Light and Heavy Water Near the Critical Point

The isochoric heat capacity was measured for D2O at a fixed density of 356.075 kg·m−3 and for H2O at 309.905 kg·m−3. The measurements cover the range of temperatures from 623 to 661 K. The measurements were made with a high-temperature, high-pressure, adiabatic calorimeter with a nearly constant inner volume. The uncertainty of the temperature is 10 mK, while the uncertainty of the heat capacity is estimated to be 2 to 3%. Measurements were made in both the two-phase and the one-phase regions. The calorimeter instrumentation also enables measurements of PVT and the temperature derivative (∂P/∂T)V along each measured isochore. A detailed discussion is presented on the experimental temperature behavior of CV in the one- and two-phase regions, including the coexistence curve near the critical point. A quasi-static thermogram method was applied to determine values of temperature at saturation TS(ρ) on measured isochores. The uncertainty of the phase-transition temperature measurements is about ±0.02 K. The measured CV data for D2O and H2O are compared with values predicted from a recent developed parametric crossover equation of state and IAPWS-95 formulation.

Isochoric Heat Capacity Measurements for 0.5 H2O + 0.5 D2O Mixture in the Critical Region

The isochoric heat capacity CV of an equimolar H2O+D2O mixture was measured in the temperature range from 391 to 655 K, at near-critical liquid and vapor densities between 274.05 and 385.36 kg⋅m−3. A high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter was used. The measurements were performed in the one- and two-phase regions including the coexistence curve. The uncertainty of the heat-capacity measurement is estimated to be ±2%. The liquid and vapor one- and two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from the experimental data for each measured isochore. The critical temperature and the critical density for the equimolar H2O+D2O mixture were obtained from isochoric heat capacity measurements using the method of quasi-static thermograms. The measurements were compared with a crossover equation of state for H2O+D2O mixtures. The near-critical isochoric heat capacity behavior for the 0.5 H2O+0.5 D2O mixture was studied using the principle of isomorphism of critical phenomena. The experimental isochoric heat capacity data for the 0.5 H2O+0.5 D2O mixture exhibit a weak singularity, like that of both pure components. The reliability of the experimental method was confirmed with measurements on pure light water, for which the isochoric heat capacity was measured on the critical isochore (321.96 kg⋅m−3) in both the one- and two-phase regions. The result for the phase-transition temperature (the critical temperature, TC, this work=647.104±0.003 K) agreed, within experimental uncertainty, with the critical temperature (TC, IAPWS=647.096 K) adopted by IAPWS.

Saturated and compressed liquid heat capacity at constant volume for 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide)

One-phase liquid and two-phase liquid + vapour equilibrium, isochoric heat capacities () and densities () were measured for ionic liquid (IL) 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([C6mim][NTf2]). Measurements were concentrated near the liquid-gas phase transition curve in order to closely observe the changes. The measurements have been made over the temperature range from (330 to 480) K and pressures up to 20 MPa using a high-temperature, high-pressure, nearly constant volume adiabatic calorimeter. The values of temperature at the liquid-gas phase transition curve for each measured isochore (phase transition parameters, ) were obtained by analysis of the quasistatic thermograms (readings of PRT, T− plot) and barograms (readings of the pressure transducer, P− plot). The combined expanded uncertainty of the density, , and isochoric heat capacity, , measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be 0.06% and 2.0%, respectively.

Chapter 15. Yang–Yang Critical Anomaly

Following a critical review of related research, a method is described to evaluate the Yang–Yang critical anomaly strength function, Rμ(T), from experimental measurements of two-phase liquid and vapor isochoric heat capacities and liquid (V′) and vapor (V″) specific volumes. Direct measurements of internal energy ΔU(V,T) increments and its temperature derivative cV(T,V)=(∂U/∂T)V are made possible with a highly specialized adiabatic calorimeter. The proposed method has been applied to molecular liquids (hydrocarbons, alcohols, water, carbon dioxide, nitrogen tetroxide, etc. to accurately determine the values of the Yang–Yang anomaly strength parameter, Rμ(T=TC)=Rμ0. The calorimeter provides two-phase (liquid and vapor) isochoric heat capacities and liquid and vapor specific volumes (V″, V′) data at saturation near the critical point. These measurements have been used to evaluate the Yang–Yang anomaly strength function, Rμ(T). The values of Rμ(T)=Rμ(TC) (Yang–Yang anomaly strength parameter) derived from the calorimetric measurements for a series of fluids vary from −8 to 0.46, which is consistent with the theoretical prediction of Cerdeirina et al. (C. A. Cerdeirina and G. Orkoulas, M. E. Fisher, Phys. Rev. Lett., 2016, 116, 040601–040605) Near the critical point, the (T,V) variation of Rμ0 characterizes thermodynamic behavior in this region. For the first time, experimental determinations of Rμ0 have validated theoretical predictions by Cerdeirina et al. (C. A. Cerdeirina and G. Orkoulas, M. E. Fisher, Phys. Rev. Lett., 2016, 116, 040601–040605) that were based on the Compressible Cell Gas (CCG) model which obeys the Complete Scaling model with pressure mixing. With a valid Complete Scaling model for the physical nature and details of the temperature and the specific volume dependences of the cV2, we may now separate the measured total two-phase heat capacity into individual contributions of chemical potential cVμ and vapor pressure cVP and further, to illustrate their relative importance as a function of temperature.

Chapter 16:Internal Pressure and Internal Energy of Saturated and Compressed Phases

Following a critical review of the field, a comprehensive analysis is provided of the internal pressure of fluids and fluid mixtures and its determination in a wide range of temperatures and pressures. Further, the physical meaning is discussed of the internal pressure along with its microscopic interpretation by means of calorimetric experiments. A new relation is explored between the internal pressure and the isochoric heat capacity jump along the coexistence curve near the critical point. Various methods (direct and indirect) of internal pressure determination are discussed. Relationships are studied between the internal pressure and key thermodynamic properties, namely expansion coefficient, isothermal compressibility, speed of sound, enthalpy increments, and viscosity. Loci of isothermal, isobaric, and isochoric internal pressure maxima and minima were examined in addition to the locus of zero internal pressure. Details are discussed of a new method of direct internal pressure determination by a calorimetric experiment that involves simultaneous measurement of the thermal pressure coefficient (∂P/∂T)V, i.e. internal pressure Pint=(∂U/∂V)T and heat capacity cV=(∂U/∂T)V. The dependence of internal pressure on external pressure, temperature and density for pure fluids, and on concentration for binary mixtures is considered on the basis of reference (NIST REFPROP) and crossover EOS. The asymptotic scaling behavior of the internal pressure near the critical point was studied using a scaling type EOS.