Transport phenomena and thermodynamics: Multicomponent mixtures

In Swaney and Bird [Chem. Eng. Educ. 51, 83 (2017)], the authors discussed some heretofore unappreciated relations between the equations of transport phenomena and those of thermodynamics for the case of pure fluids. Here we extend the discussion to multicomponent mixtures and open systems with the associated convective terms, and show how several key equations in thermodynamics may be derived by using the equations of energy, mechanical energy, and entropy from transport phenomena. These derivations point out some features of the thermodynamic equations that are not often recognized, and elucidate the meaning of phrases such as "quasi-steady-state processes." We show how one can obtain our version of the first law dU = dQ -(sic)dV + integral(V(t))[-(tau:del v) + Sigma(N)(alpha=1) (j(alpha) . g(alpha))]dVdt - integral(A(t)) (n . rho(H) over cap(v) over tilde dAdt, our version of the second law (sic)dS = dQ + integral(V(t)) [-(tau:del v) + Sigma(N)(alpha=1) (j(alpha) . g(alpha))]dVdt -Sigma(N)(alpha=1) (sic)(alpha)dn(alpha) - integral(A(t)) (n. (H) over cap(v) over tilde dAdt, and Gibbs' fundamental relation dU = (sic)dS-(sic)dV+Sigma(alpha)(sic)(alpha)dn(alpha). The double overbars indicate suitably averaged values and extend the familiar results to systems that are not uniform and not in equilibrium macroscopically. At various places in the development, we make use of the equations of conservation of mass, momentum, and energy, as well as the equation of change for entropy, from transport phenomena. Published under license by AIP Publishing.