Equation for the Refractive Index of Water

The observations that β−1 (∂ lnf/∂P)T=B is a constant (of order unity, independent of temperature), and —γ−1 (∂ lnf/∂T)P=B+Cγ−1, lead to an equation f(n)≡(n2−1)/(n2+2)=AρB exp(−CT), which describes the refractive index n of water between 0° and 60°C (at any given wavelength in the visible spectrum) to within a few digits in the seventh decimal. Here ρ is the density, β=(∂ lnρ/∂P)T and γ=—(∂ lnρ/∂T)P. The constant C=—(d lnf/∂T)V reflects the change in the structure of water at different temperatures. The temperature of maximum index [(∂n/∂T)P=0] corresponds to γ=—C/B, and the minimum in the Lorenz—Lorentz specific refraction (n2−1)/(n2+2)ρ corresponds to γ=C/(1—B). The values of the parameters A, B, and C are independent of pressure up to 1100 bar in the temperature range examined. It is suggested that refractive index, or dielectric, measurements at higher pressures and temperatures may yield further information on the structure of water in terms of specific models related to the variation of B and C with...

[1]  W. C. Röntgen,et al.  Ueber den Einfluss des Druckes auf die Brechungsexponenten von Wasser, Schwefelkohlenstoff, Benzol, Aethyläther und einigen Alkoholen , 1891 .

[2]  L. W. Tilton,et al.  Refractive Index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 degrees C , 1938 .

[3]  A. Weissberger.  Physical methods of organic chemistry , 1950 .

[4]  S. Szapiro,et al.  Physical properties of heavy oxygen water. Part 1.—Density and thermal expansion , 1963 .

[5]  H. Eisenberg,et al.  Refractive Indices and Piezo‐optic Coefficients of Deuterium Oxide, Methanol, and Other Pure Liquids , 1965 .

[6]  L. W. Tilton.  Standard conditions for precise prism refractometry , 1935 .

[7]  A. Farkas.  Physical chemistry of the hydrocarbons , 1950 .

[8]  R. H. Oppermann,et al.  Properties of ordinary water-substance: by N. Ernest Dorsey. 673 pages, illustrations, tables, 16 × 24 cms. New York, Reinhold Publishing Corporation, 1940.Price $15.00. , 1940 .

[9]  Harold A. Scheraga,et al.  Structure of Water and Hydrophobic Bonding in Proteins. I. A Model for the Thermodynamic Properties of Liquid Water , 1962 .

[10]  Percy Williams Bridgman,et al.  The physics of high pressure , 1931 .

[11]  M. Eigen,et al.  Self-dissociation and protonic charge transport in water and , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  L. W. Tilton,et al.  Accurate representation of the refractivity and densit of distilled water as a function of temperature , 1937 .

[13]  C. Weir,et al.  Effect of Pressure and Temperature Upon the Optical Dispersion of Benzene, Carbon Tetrachloride and Water. , 1964, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[14]  L. Lorenz.  Ueber die Refractionsconstante , 1880 .