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viscosity- 2O7:>ABL
critical enhancement :@8B8G5A:>5 C25;8G5=85
UNIT 6
CORRELATION EQUATIONS FOR THE VAPOR PRESSURE AND FOR THE ORTHOBARIC DENSITIES OF WATER SUBSTANCE
ABSTRACT
Very effective correlation equations for the vapor pressure and the densities of saturated liquid and vapor of ordinary water have been developed using a special optimization method. From the triple point up to the critical point the recent experimental data on these three properties are represented within their experimental uncertainty. Comparisons with the corresponding 1963 Skeleton Table values are also given.
INTRODUCTION
The state variables on the coexistence line vapour-liquid are some of the most characteristic properties of a fluid.
Surprisingly, for the technically most important substance - water, there do not exist in any accurate and simple correlation equations representing the orthobaric densities.
Of course, these properties can be calculated from equations of state fulfilling the condition of the vapour-liquid equilibrium, e.g, from the HGK equation and the Pollak equation. However, if only the thermal state variables on the coexistence line vapour-liquid are to b5 calculated, it is much easier to use special correlation equations for these properties.
Therefore, it is the purpose of this paper to develop correlation equations for the vapour pressure and the densities of the saturated liquid and vapour, respectively. Based on the latest experimental data and the recently evaluated and internationally agreed critical parameters
Tc=647.14K, pc=22.064MPa, pc =322kg/m
the equations shall cover the whole temperature range from the triple point up to the critical point. A special optimization method is used to obtain a very effective structure of these equations with respect to the number of terms and their combination.
VAPOUR PRESSURE
In 1974 Wagner reviewed the well-known vapour-pressure equations for water containing seven (Osborne et al.) to twelve (Ambrose and Lawrenson) adjusted coefficients. Having reviewed the existing experimental vapour pressures, a data set was selected representing the true vapour-pressure curve of water from the triple point up to the critical point at that time. Based on this knowledge, a very accurate vapour-pressure equation with only five adjusted coefficients was given in. Because of the following reasons this internationally used vapour-pressure equation is to be revised:
-The equation is not consistent with the extremely accurate triple point measurement published by Guildner et al. in 1976.
- There are systematic deviations from Stimson's superprecise data (2980 to 3730 K) and from the data at 5000 of Osborne et al.
-New measurements were published and there are new internationally agreed critical parameters.
In Table 1 the selected vapour-pressure data are listed.
In comparison with the old data set (Douslin, Osborne, et al., Stimson), the exchange of Douslin's data for Guildners triple point result is the most important change; the other added data confirm essentially Osborne's measurements. From the latest data, Schefflers results (6210 K-6470 K) were not selected because they show small, but systematic, negative deviations from all the other data of this region.
The first step in establishing the new vapor-pressure equation was to formulate a comprehensive expression functioning as banks of terms
1n(Ps/Pc)=Tc/T
This general from of a vapor-pressure equation used at first for nitrogen and argon has been successfully applied to form vapour-pressure equations for a large number of substances.
Table 1. Summary of the selected vapour-pressure data. The temperatures correspond to the IPTS-68
AuthorsYearTemp. range:No. ofRefs.T/KdataOsborne et al.19373-647382(14)Rivkin et al.1964646-64713(16)Stimson1969298-3737(13)Guildner et al.1976 273.161(12)Hanafusa et al.1983643-6464(17)Kawai et al.19836471(18)Kell et al.1984423-62312(19)
The second step was the determination of the most effective combination of terms out of the 21 terms of Eq. (2) using tha evolutionary optimisation method E0M" developed by Ewers and Wagner. The most effective combination is that one which yields the smallest weighted least square sum (WLS) for a given number of terms after fitting to the data. This WLS value and the responding coefficients a result simultaneously from the WLS fit formulated by
EMBED Equation.3 , where
EMBED Equation.3
M = number of data points
EMBED Equation.3 = variance of EMBED Equation.3
EMBED Equation.3 , EMBED Equation.3 = actual coefficients and exponents, respectively. (2)
According to the Gaussian error propagation formula, the variance EMBED Equation.3 is related to the two single variances EMBED Equation.3 and EMBED Equation.3 of each experimental Ps value by
EMBED Equation.3
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