Results obtained from the Epstein equation of state15 i.e. equation (8), which is theoretically valid up to the critical density, are compared with the experimental values of the compressibility factor. The calculated values of compressibility factor or ethylene, ethane, propane, and n-butane were obtained using two methods of evaluation for the second and third virial coefficients. In addition, using these two methods and excluding fourth, fifth, and sixth virials in the Epstein equation of state, compressibility factors were calculated for all the four compounds to test the effect of higher virial terms. In the proposed method-(A) and method-(C), the force constants were calculated from critical properties while, in methods-(B) and (D), force constants which are based on experimental p-v-t data, were directly taken from the literature. For methods-(A) and (B), Epstein equation of state i.e. equation (8), was used. While, for methods-(C) and (D), fourth, fifth, and sixth virials were neglected in the Epstein equation of state, which reduced to equation (11).
The proposed method-(A) which only requires the information on critical properties, gave results within the acceptable range of accuracy for all the four compounds. The other methods gave poor results. Epstein has suggested that his equation is valid only for non-polar and spherical molecules. It is, however, shown in this work that his equation is also valid for linear molecules, if the force constants from critical properties are used in the evaluation of second and third virial coefficients. The proposed method-(A) requires only three parameters i.e. critical constants, and is comparable in accuracy to the Beattie-Bridgeman equation.
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