Thermodynamic Properties of Liquids

4-3 Properties of Liquids 4 3.1 Thermodynamic Properties of Liquids 43.1.1 Liquid Densities 

Liquid densities can be calculated according two types of methods, both based on the principle of corresponding states. 

In the first type of method, the density at saturation pressure is calculated, then this density is corrected for pressure. The COSTALD and Rackett methods belong to this category. Correction for pressure is done using Thompson s method. These methods are applicable only if the reduced temperature is less than 0.98. 

For reduced temperatures higher than 0.98, a second type of method must be used that is based on an equation of state such as that of Lee and Kesler. 

For our needs, the saturation pressure of a mixture will be defined as the vapor pressure of a pure component that has the same critical constants as the mixture ( JT 

The theoretical calculation of the thermodynamic properties of liquids presents an even more difficult problem than that of solids, for in a liquid the molecules are in a state of disorder intermediate between the random motion of a gas, and the long range order of a solid. We must therefore be content with an even cruder approximation than for solids. ) A model which leads to a useful semi-quantitative correlation is based upon the idea of the free volume. 

For the free-volume model of a liquid we assume that the free energy is of the analogous form 

The physical interpretation of A becomes apparent by applying equation (4.34) to (12.43 )  

The term A is therefore the difference between the internal energy of liquid and perfect gas in the same volume it is in effect the energy of vaporization. 

The pressure may now be obtained from (12.43) and (12.40), giving the equation of state 

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McDonald I R and Singer K 1967 Calculation of thermodynamic properties of liquid argon from Lennard-Jones parameters by a Monte Carlo method Discuss. Faraday Soc. 43 40-9... 

Table 3. Physical and Thermodynamic Properties of Liquid Hydrogen...

For liquid mixtures at low pressures, it is not important to specify with care the pressure of the standard state because at low pressures the thermodynamic properties of liquids, pure or mixed, are not sensitive to the pressure. However, at high pressures, liquid-phase properties are strong functions of pressure, and we cannot be careless about the pressure dependence of either the activity coefficient or the standard-state fugacity. 

Considerable progress has been made in the last decade in the development of more analytical methods for studying the structural and thermodynamic properties of liquids. One particularly successful theoretical approach is. based on an Ornstein-Zernike type integral equation for determining the solvent structure of polar liquids as well as the solvation of solutes.Although the theory provides a powerful tool for elucidating the structure of liquids in... 

Thermodynamic properties of liquid 4He at saturated vapour pressure [30]... 

An alternative to the common device of determining relative intensities is a study of the fine structure of the scattered beam. This entails resolving the spectrum of scattered light into its three peaks, viz. a central peak and two side ones. The need is thus obviated to refer to I0 or, according to the apparatus, the scattering power of a standard calibration material. The method is used mainly for determining diffusion constants and thermodynamic properties of liquids. 

Funk, E. W, and J. M. Prausnitz. 1970. Thermodynamic properties of liquid mixtures Aromatic-saturated hydrocarbon systemtod. Eng. Chem62 8-15. 

The electrostatic part, Wg(ft), can be evaluated with the reaction field model. The short-range term, i/r(Tl), could in principle be derived from the pair interactions between molecules [21-23], This kind of approach, which can be very cumbersome, may be necessary in some cases, e.g. for a thorough analysis of the thermodynamic properties of liquid crystals. However, a lower level of detail can be sufficient to predict orientational order parameters. Very effective approaches have been developed, in the sense that they are capable of providing a good account of the anisotropy of short-range intermolecular interactions, at low computational cost [6,22], These are phenomenological models, essentially in the spirit of the popular Maier-Saupe theory [24], wherein the mean-field potential is parameterized in terms of the anisometry of the molecular surface. They rely on the physical insight that the anisotropy of steric and dispersion interactions reflects the molecular shape. 

A computer algorithm has been developed for making multi-component mixture calculations to predict (a) thermodynamic properties of liquid and vapor phases (b) bubble point, dew point, and flash conditions (c) multiple flashes, condensations, compression, and expansion operations and (d) separations by distillation and absorption. 

Nemethy G, Scheraga HA (1962) A model for the thermodynamic properties of liquid water. J Chem Phys 36 3382-3400... 

The Thermodynamic Properties of Liquid Li-Pb Alloys " Translated from Elektrokhimiya, 9, 6, 848-851,... 

Introduction.—Most theoretical v> ork on the relation between intermolecular forces and the thermodynamic properties of liquids and liquid mixtures has been limited to potential fields which are independent of the orientation of the particles. This condition, however, is only strictly satisfied by monoatomic substances. For a great many molecular substances directional intermolecular forces are likely to be important and will have a significant effect on the thermodynamic properties of liquids both because of the additional cohesive energy and because of the loss of entropy associated with hindrance to free rotation. Although many of the observed properties of liquids have been attributed to directional forces in a qualitative manner, there has been little in the way of general quantitative theory. 

In the two final sections an approximate version of the theory, based on a lattice distribution, is used to discuss the thermodynamic properties of liquids and liquid mixtures. 

The assessed thermodynamic properties of liquid and solid Si-based solution can be directly applied to evaluate the influence of third element on the solubility of the main impurity in silicon melt. For example, the effect of the impurity element on the solubility of C in pure Si melt can be evaluated by the following equation ... 

Heintz A, Lehmann JK, Verevkin SP (2003) Thermodynamic properties of liquid mixtures containing ionic liquids. In Rogers RD, Seddon KR (eds) Ionic liquids as green solvents progress and prospects. American Chemical Society, Washington, pp 134-150... 

Selected thermodynamic properties of liquid COFj have been estimated [1683]. These calculated values for the Helmholtz free energy function (-G/RT), liquid entropy (5), and heat capacity at constant volume (C,) are recorded in Table 13.11. 

Tiwari, B.L. (1987) Thermodynamic properties of liquid Al-Mg alloys measured by the EMF method. Metall. Trans. A, 18, 1645-51. 

Now she is the editor of the annual volume Metastable States and phase Transitions / possibly, the only edition devoted exclusively to the phenomenon of metastability. Finally, G.V. Ermakov (1938), the coauthor of the report Investigation of the attainable superheat of liquids in a wide region of pressure at that Conference, has developed the method of a rising droplet to study the nucleation kinetics under pressure and a number of methods to determine the thermodynamic properties of liquids in superheated states. To my opinion, his attitude to science in a broad sense corresponds to the spirit of Heike Kamerlingh Onnes . ... 

G. Nemethy and H, A. Scheraga, J. Chem. Phys., 36, 3382 (1962), The Structure of Water and Hydrophobic Bonds in Proteins. 1. A Model for the Thermodynamic Properties of Liquid Water. G. Nemethy and H. A. Scheraga, ]. Chem. Phys., 36, 3401 (1962). The Structure of Water and Hydrophobic Bonds in Proteins. II. Model for the Thermodynamic Properties of Aqueous Solutions of Hydrocarbons. 

Derived Thermodynamic Properties of Liquid and Vapor Phases 153... 

G. Nemethy and G. H. Scheraga, "Structure of Water and Hydrophobic Bonding in Proteins. I. A Model for< the Thermodynamic Properties of Liquid Water," /. Phys, Chem., 36 3382 (1962). 

Nemethy, G. and H. Scheraga. 1964. Structure of water and hydrophobic bonding in proteins. IV. The thermodynamic properties of liquid deuterium oxide. J. Chem. Phys. 41 680-689. 

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