Rankine-Kirchoff equation

The Rankine-Kirchoff equation can be simplified further, as described by Mackay et al. [104], The authors assumed that the change in both heat capacities is 0, so the entropy of vaporization is given by Trouton s rule,... 

The Rankine-Kirchoff equation determines on the dependency of vapor pressure on temperature. Indeed it just contains terms proportional to 1IT, -In T, and Thus it does make more sense to explicitly derive a linear regression equation for Vp prediction that will also contain these dependencies. This was demonstrated by Jensen et al. [109] who predicted vapor pressure using the following equation ... 

For the majority of fluxes evaluated, the standard deviation, s, and the average percent variation, A%, is lower for the Kirchoff-Rankine fitted equation vs. the Arrhenius Equation, indicating a better fit of the experimental data. The difference is most pronounced for those fluxes where the nonlinearity of the experimental nTi vs. 1/T data is greatest. 

In this paper, recent work on the viscosity of mold flux compositions is reviewed, and a relation to describe the temperature dependence of viscosity is discussed. This relation is based on the Clausius-Clapeyron Equation and was originally developed by Kirchoff and Rankine to describe the temperature dependence of vapor pressure. 

The viscosity of twenty flux compositions determined earlier ( ) were used to evaluate the Kirchoff-Rankine Equation. The compositions of these fluxes are given in Table I with a summary of the viscosities given in Table II. The flux viscosity data was fitted to the Kirchoff-Rankine equation as... 

When the nonlinearity of the log viscosity vs. reciprocal temperature data was first observed, tests were made to insure that the curvature was real and not an artifact of the experimental apparatus. Hysteresis curves and constant temperature for extended time tests showed that the nonlinearity was not caused gf zovolatilization alkali or fluoride constituents or from thermal deviations in the furnace setup. It was found that the observed curvature of the data was not an artifact and represented the true physical behavior of the materials. The application of the Kirchoff-Rankine equation... 

Additional work on liquid metals, simple chloride salts and some small molecule organic liquids ( ) indicates that the advantage of the Kirchoff-Rankine equation over the Andrade-Arrhenius equation improves as the size of the melt species increases. The improvement in the description of viscosity vs. temperature for metals and simple salts (e.g., NaCl and BiCl2) is not great, but for materials with larger melt species (e.g., silicate melts and organic liquids), there is a distinct improvement. 

Other researchers were bringing on alternatives to these drawn and intuitive methods. A sequence of successes attracted talented mathematicians towards research in statics. Studies of differential equations seemed to show that certain of their characteristics, such as critical points, represented physical phenomena, providing otherwise unattainable insights into the nature of structural instability. Among a host of workers, D.J. Jourawski (1821-1891), Gustave Kirchoff (1824-1887), George Gabriel Stokes (1819-1903), Franz Neumann (1798-1895) and William John Macquorn Rankine... 

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