Hirschfelder

Hirschfelder J O, Curtiss C F and Bird R B 1954 Molecular Theory of Gases and Liquids (New York Wley)... 

Hirschfeld T and Chase B 1986 FT-Raman spectroscopy development and justification Appl. Spectrosc. 40 133-9... 

Pack R T and Hirschfelder J O 1968 Separation of rotational coordinates from the W-electron diatomic Schrddinger equation J. Chem. Phys. 49 4009... 

Stogryn D E and Hirschfelder J O 1959 Contribution of bound, metastabie and free moieouies to the seoond viriai ooeffioient and some properties of doubie moieouies J. Chem. Phys. 31 1531-5... 

T. Hirschfeld and co-workers, "Remote Spectroscopic Analysis of Parts-Per-MiUion-Level Air Pollutants by Raman Spectroscopy," Appl Phys. Eett. 22(1), (fan. 1973). 

J. O. Hirschfelder, C. F. Curtis, and R. B. Bird, Molecular Theory of Gases and Eiquids,]ohxi Wiley Sons, Inc., New York, 1954. 

An alternate method for gas diffiisivity of binary gas mixtures at low pressures is the method of Hirschfelder et al. The method requires several molecular parameters and, when evaluated, gives an average absolute error of about 10 percent. The method is discussed in detail in the Data Vrediction Manual. 

The diffusion coefficient can be determined from the Hirschfelder-Bird-Spotz equation as follows ... 

Thus, for example, if V(r) were proportional to r ", F(r) would be proportional to -g conventional to take as the zero of potential energy the state in which the particles are infinitely separated. A negative V(r) is attractive, a positive value is repulsive. We are interested in the dependence of V(r) on r. The following treatment is drawn from Hirschfelder et al. (13). 

Hirschfelder, J.O. Curtiss, C.E. Bird, R.B. Molecular Theory of Gases and Liquids Wiley New York. 1954 Chapter 1. 

Hinchliffe, A. and Munn, R. W. (1985) Molecular Electromagnetism, Wiley, Chichester. Hirschfelder, J. O., Curtiss, C. F. and Bird, R. B. Molecular Theory of Liquids and Gases, Wiley, New York. 

For the monatomic gases the values of eK/k and gk determined by Whalley and Schneider were used,66 for the other gases, those reported by Hirschfelder, Curtiss, and Bird.15 To the unknown factor z eQlk) t the value 294 was assigned in order to fit the theoretical predictions to the aggregate of experimental data at present available. 

Intermolecular potential functions have been fitted to various experimental data, such as second virial coefficients, viscosities, and sublimation energy. The use of data from dense systems involves the additional assumption of the additivity of pair interactions. The viscosity seems to be more sensitive to the shape of the potential than the second virial coefficient hence data from that source are particularly valuable. These questions are discussed in full by Hirschfelder, Curtiss, and Bird17 whose recommended potentials based primarily on viscosity data are given in the tables of this section. 

The values in brackets are those calculated from Eqs. 9 and 10 by using the parameters for the pure substances recommended by Hirschfelder, Curtiss, and Bird33 (with the quantum corrections for the hydrogen-hydrogen interaction). 

In the derivation above, we have included the kinetic energy of the nuclei in the Hamiltonian and considered a stationary state. In Eq. II.3, this term has been neglected, and we have instead assumed that the nuclei have given fixed positions. It has been pointed out by Slater34 that, if the nuclei are not situated in the proper equilibrium positions, the virial theorem will appear in a slightly different form. (A variational derivation has been given by Hirschfelder and Kincaid.11)... 

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