Part One. An Orthogonal Polynomial Equation of State. Part Two. Application of the Benedict Equation of State to the Methane-n-Pentane System. Part Three. Isobaric Heat Capacity at Bubble Point of n-Decane

Citation

Pings, Cornelius John (1955) Part One. An Orthogonal Polynomial Equation of State. Part Two. Application of the Benedict Equation of State to the Methane-n-Pentane System. Part Three. Isobaric Heat Capacity at Bubble Point of n-Decane. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QSJF-1657. https://resolver.caltech.edu/CaltechETD:etd-01202004-144113

Abstract

PART ONE An equation of state has been developed which is a series expansion in orthogonal polynomials. The evaluation of coefficients by least squares methods is significantly simpler than for the case of a power series expansion. The values of the expansion coefficients are independent of the point of truncation of the series. Additional terms may be added to the equation without necessitating recomputation of existing coefficients. The Tchebichef and Gram polynomials were used. The equation of state has been applied to propane for pressures up to 10,000 psia in the temperature interval 100[degrees] to 460[degrees] F. Terms involving eighth and higher powers of reciprocal molal volume were found not to contribute significantly to the description. The equation predicts volumetric behavior, phase behavior, thermodynamic properties, the critical state, and the second virial coefficient with an accuracy that is promising. Limited experience in application indicates that the equation is easier to handle with automatic digital computing equipment than is the Benedict equation of state. PART TWO Values of the coefficients for the Benedict equation of state were determined by least squares methods from experimental data for each of a series of mixtures of the methane-n-pentane system. In addition, values were obtained for the interaction constants for groupings of the Benedict coefficients corresponding to the second and third virial coefficients. Corresponding values of the interaction constants predicted by the methods suggested by Benedict are included for comparison. Measures of the accuracy of description for the interaction constants determined by the several different methods are reported. Interaction constants were evaluated by least squares methods for the methane-n-pentane system in the liquid and gas phases at pressures up to 5,000 pounds per square inch in the temperature interval between 100[degrees] and 460[degrees] F. The accuracy of description of the volumetric behavior was improved severalfold over that obtained with the constants calculated from the behavior of the components by the method suggested by Benedict. Such methods may prove useful in evaluating interaction constants for mixtures as a function of the characteristics of the system involved. PART THREE The isobaric heat capacity at bubble point of n-decane was determined in the temperature interval 80[degrees] to 200[degrees] F. Measurements were made in the two-phase region utilizing a constant volume calorimeter. The energy required to change the temperature of the calorimeter and contents was determined for each of two quantities of n-decane. The effect of the gross heat capacity of the bomb was eliminated by considering the difference of these two sets of measurements. The two-phase isochoric measurements were transformed to values of the isobaric heat capacity at bubble point by applying a thermodynamic correction involving the volumetric properties of the gas and liquid phases and the heat capacity of the gas phase.

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