State law of corresponding

Keller J B and Zumino B 1959 Determination of intermolecular potentials from thermodynamic data and the law of corresponding states J. Chem. Phys. 30 1351... 

A theoretical basis for the law of corresponding states can be demonstrated for substances with the same intemiolecular potential energy fimction but with different parameters for each substance. Conversely, the experimental verification of the law implies that the underlying intemiolecular potentials are essentially similar in fomi and can be transfomied from substance to substance by scaling the potential energy parameters. The potentials are then said to be confomial. There are two main assumptions in the derivation ... 

The equation of state detemiined by Z N, V, T ) is not known in the sense that it cannot be written down as a simple expression. However, the critical parameters depend on e and a, and a test of the law of corresponding states is to use the reduced variables T, and as the scaled variables in the equation of state. Figure A2.3.5 bl illustrates this for the liquid-gas coexistence curves of several substances. As first shown by Guggenlieim [19], the curvature near the critical pomt is consistent with a critical exponent (3 closer to 1/3 rather than the 1/2 predicted by van der Waals equation. This provides additional evidence that the law of corresponding states obeyed is not the fomi associated with van der Waals equation. Figure A2.3.5 (b) shows tliat PIpkT is approximately the same fiinction of the reduced variables and... 

Figure A2.3.6 illustrates the corresponding states principle for the reduced vapour pressure P and the second virial coefficient as fiinctions of the reduced temperature showmg that the law of corresponding states is obeyed approximately by the substances indicated in the figures. The useflilness of the law also lies in its predictive value.

This is Widom s scaling assumption. It predicts a scaled equation of state, like the law of corresponding states, that has been verified for fluids and magnets [102]. 

Many other equations of state besides van der Waals lead to laws of corresponding states, although naturally these will not be of the form (1). 

G. Meslin (1893) has investigated the conditions under which an equation of state can lead to a law of corresponding states. The most general form of equation possible is ... 

By means of these equations we can eliminate three constants from (2). But, if the equation (2) is now reduced, as is required by the law of corresponding states, it must not contain any constants characteristic of the substance, hence (2) can contain only three independent characteristic constants. In this case (2) can always be written in the form ... 

The necessary condition that an equation of state shall lead to a law of corresponding states is, therefore, that it shall contain only three characteristic constants, and shall exhibit a critical point. 

Madame Ivirstine Meyer (1900) has shown that the discrepancies are not to be explained by errors in the critical data the law of corresponding states can be tested without making use of these constants, and differences between the observed and calculated magnitudes are still apparent. D. Berthelot (Journ. de Phys., 1903) has deduced some new equations. 

Equation (6.30) leads to a final method of obtaining an approximate value for In4> by making use of the law of corresponding states. This law states that all gases obey the same equation of state when expressed in terms of the reduced variables T, — T/Tc, pT - p/pc. and V, — V/Vc, where T., pc. and Vc are the critical temperature, pressure, and volume, respectively. 

At temperatures greater than the critical temperature, the law of corresponding states is a reasonably good approximation for most gases. Goug-Jen Su5 showed the correspondence by graphing the compressibility... 

The law of corresponding states indicates that all gases should show the same behavior in applying equation (6.31). This enables one to construct a chart showing Tt isotherms of z against px, such as that shown in Figure 6.4, from which can be estimated. 

Mostinski, I.L. Brit. Chem. Eng. 8 (1963) 580. Calculation of boiling heat transfer coefficients, based on the law of corresponding states. 

Mostinski IL (1963) Calculation of Boiling Heat Transfer Coefficients, Based on the Law of Corresponding States, Br Chem Eng, 8 580. 

The equation does not contain the constants a and 6, characteristic of the substance, and therefore applies to all substances. Hence it is known as the law of corresponding states. 

Each of the two-parameter semi-empirical equations above leads to the law of corresponding states, first formulated by Van der Waals in 1881 [9], which says that all... 

Figure 5.6. Fit of experimental data for ten gases to the law of corresponding states. By permission from G. J. Su, Ind. Eng. Chem. 38, 803 (1946).

The assumption known as the law of corresponding states asserts that the compressibility factor Z should be a function only of the reduced temperature Ti and the reduced pressure Pi, which is approximately correct for many real gases. It is seen that, for a van der Waal gas, the minimum value of Vr = 1/3, which can be achieved only at infinite pressure. From the equation of state written for the reduced temperature and pressure, we can derive the equivalent formula of compressibility as... 

Young RH (1994) A law of corresponding states for hopping transport in disordered materials. Phil Mag B 69 577... 

A modified law of corresponding states suitable for real gases was proposed in 1946 by Gouq-Jen Su of Univ of Peiping, China (Ref 1). A term called the "ideal critical volume was defined and the ratio of volume over the ideal critical volume was called the "ideal reduced volume . It was shown that for 17 gases within the temperature and pressure ranges studied, the over-all deviation was only 1%. The value of the critical ratio was not a restrictioh or a criterion for the applicability of the modified law... 

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