Chapter 2: Macroscopic Energy and Entropy Balances in Phase Equilibrium Studies

Macroscopic energy and entropy balances are utilized to solve persistent problems in differential ebulliometry and in flow calorimetry for excess enthalpy measurement. New procedures are developed for measuring and calculating the evaporation ratio (ϕ) required to calculate the true liquid equilibrium composition from the charge composition, (and other subsidiary quantities) in an ebulliometer. Data are presented for measurements on cyclohexane at several pressures and energy input levels, using an ebulliometer, which eliminates temperature gradients along the thermowell. Procedures are examined for eliminating fluid frictional energy in excess enthalpy measurement by flow calorimetry. The often considerable influence of 2nd virial coefficient values, used to calculate limiting activity coefficients, is examined. Exact derivative expressions suggest that this influence is much greater when computing the activity coefficient for the less volatile component, γ$2∞$, and indicate for which virial coefficients the greatest accuracy is required. Exact expressions for the derivatives (∂T/∂x₁)_p and (∂p/∂x₁)_T, consistent with the Gibbs–Duhem equation, provide a means for testing whether experimental temperature or pressure profiles are consistent with a measured or reported γ$i∞$.