Heat capacity in the critical region

The author s theory of the heat capacity of binary mixtures will now be considered. It has many similarities to the random phase or ring diagram approximation, but is much more intuitive in spirit and simpler in mathematical form. The formulae for the heat capacity in the critical region are essentially identical, but the present method avoids the necessity of specif3dng the... 

Compared with ambient values, the specific heat capacity of water approaches infinity at the critical point and remains an order of magnitude higher in the critical region [26], making supercritical water an excellent thermal energy carrier. As an example, direct measurements of the heat capacity of dilute solutions of argon in water from room temperature to 300 °C have shown that the heat capacities are fairly constant up to about 175-200 °C, but begin to increase rapidly at around 225 °C and appear to reach infinity at the critical temperature of water [29]. 

Heimburg, T., Mirzaev, S.Z., and Kaatze, U. Heat capacity behavior in the critical region of the ionic binary mixture ethylammonium nitrate - n-octanol. Phys. Rev. E, 2000, 62, p. 4963-76. 

The uncertainties of the equation of state are 0.2% in density, 2% in heat capacity, and 2% in the speed of sound, except in the critical region. The uncertainty in vapor pressure is 0.2%. The uncertainty varies from 0.5% for the viscosity of the dilute gas phase at moderate temperatures to about 5% for the viscosity at high pressures and temperatures. The uncertainty in thermal conductivity is 2%. 

The uncertainties in density are 0.02% at temperatures below 340 K and pressures below 12 MPa (both liquid and vapor states), 0.1% at temperatures below 270 K and pressures above 12 MPa, 0.2% between 340 and 515 K at pressures less than 0.6 MPa, and 0.4% elsewhere. In the critical region, deviations in pressure are 0.5%. At temperatures above 500 K, the uncertainties in density increase up to 1%. Uncertainties in heat capacities are typically 1%, rising to 5% in the critical region and at pressures above 30 MPa. Uncertainties in the speed of sound are typically 0.5%, rising to 1% at temperatures below 200 K and to 4% in a large area around the critical point. 

The uncertainties of the equation of state are 0.1% in density, 2% in heat capacity, and 1% in the speed of sound, except in the critical region. 

The uncertainties in the equation of state are 0.1% in density in tlie liquid and vapor phases between 220 and 300 K, 0.25% at temperatures above 300 K and at temperatures below 220 K, and 0.5% in the critical region, except very close to the critical point. The uncertainty in vapor pressure is 0.2%, that for heat capacities is 3%, and that for the speed of sound in the vapor phase is 0.05% above 220 K. The uncertainty in the liquid phase is not known but is estimated to be within 5%. 

Typical uncertainties in density are 0.02% in the liquid phase, 0.05% in the vapor phase and at supercritical temperatures, and 0.1% in the critical region, except very near the critical point, where the uncertainty in pressure is 0.1%. For vapor pressures, the uncertainty is 0.02% above 180 K, 0.05% above 1 Pa (115 K), and dropping to 0.001 mPa at the triple point. The uncertainty in heat capacity (isobaric, isochoric, and saturated) is 0.5% at temperatures above 125 K and 2% at temperatures below 125 K for the liquid, and is 0.5% for all vapor states. The uncertainty in the liquid-phase speed of sound is 0.5%, and that for the vapor phase is 0.05%. The uncertainties are higher for all properties very near the critical point except pressure (saturated vapor/liquid and single pliase). The uncertainty in viscosity varies from 0.4% in the dilute gas between room temperature and 600 K, to about 2.5% from 100 to 475 K up to about 30 MPa, and to about 4% outside this range. Uncertainty in thermal conductivity is 3%, except in the critical region and dilute gas which have an uncertainty of 5%. 

Typical uncertainties are 0.05% for density, 0.02% for vapor pressure, 0.5% to 1% for heat capacity, 0.05% for vapor speed of sound, and 1% for liquid speed of sound, except in the critical region. The uncertainty in viscosity is 1.5% along the saturated-liquid line, 3% in the liquid phase, 0.5% in the dilute gas, 3% to 5% in the vapor phase, and 5% in the supercritical region, rising to 8% at pressures above 40 MPa. Below 200 K, the uncertainty is 8%. The uncertainty in thermal conductivity is 5%. 

The estimated uncertainties of properties calculated using the equation of state are 0.1% in density, 0.5% in heat capacities, 0.02% in the speed of sound for the vapor at pressures less than 1 MPa, 0.5% in speed of sound elsewhere, and 0.1% in vapor pressure, except in the critical region. 

The uncertainties in the equation of state are 0.2% in density, except in a small region close to the critical point, 0.2% in vapor pressure between 250 and 360 K, 0.4% in vapor pressure outside this region, 1% in heat capacities (with increasing uncertainties in the critical region and at higher temperatures), 0.1% in the vapor-phase speed of sound, and 3% in the liquid-phase speed of sound. 

The uncertainty in density of the equation of state ranges from 0.1% at low temperatures in the liquid and vapor to 0.5% at the highest temperatures. The uncertainty in heat capacities is 2%, and the uncertainty in vapor pressure is 0.4% at temperatures above 270 K. The uncertainty in vapor pressure increases at lower temperatures due to the lack of experimental data. In the critical region, the uncertainties are higher for all properties except vapor pressure. 

The uncertainties in density are 0.03% for pressures below 12 MPa and temperatures below 350 K and up to 0.07% for pressures less than 50 MPa. For the speed of sound, the uncertainty ranges from 0.03% (in the vapor phase) to 0.3% depending on temperature and pressure. Heat capacities may be generally calculated within an uncertainty of 1%. The uncertainty in viscosity is 2%, except in the critical region which is 5%. The uncertainty in thermal conductivity of the dilute gas between 130 and 625 K is 2.5%. For temperatures below 130 K, the uncertainty is less than 10%. Excluding the dilute gas, the uncertainty is 2% between 110 and 725 K at pressures up to 70 MPa, except near the critical point which has an uncertainty of 5% or greater. For the vapor at lower temperatures and the dense liquid near the triple point, an uncertainty of 10% is possible. 

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