Expansion Work without the External Pressure, and Thermodynamics in Terms of Quasistatic Irreversible Processes

Klaus Schmidt-Rohr
J. Chem. Educ.


Abstract Image

We demonstrate that the formula for irreversible expansion work in most chemical thermodynamics textbooks does not apply during the expansion process. Instead of the “external pressure” Pext, the pressure Psys,mb on the piston or other moving boundary (hence the subscript mb), which is nearly equal to the system pressure Psys, should be used in the integral over volume. This formula only requires that Psys(V) and T are well defined, that is, a system of uniform P and T (“uPT”) undergoing a “uPT process”, which may be irreversible. An instructive example is an expanding gas accelerating a bullet horizontally and performing work without a conventional external pressure. We emphasize that δw = −Psys,mb dV ≈ −Psys dV is the only useful formula for infinitesimal PV work during a uPT process. The quasistatic approximation Psys,mb = Psys and δw = −Psys dV is usually excellent and enables analyses of irreversible uPT processes, for example, in heat engines; friction in the surroundings and a large piston mass improve the approximation. Slow chemical reactions at constant T and P are quasistatic, and many equations in advanced chemical thermodynamics apply specifically to uPT or quasistatic processes. We show that the equality dS = δqirr/T applies in irreversible quasistatic processes without composition change. In short, with well-defined P and T at constant composition, the simple equations for reversible processes are usually excellent approximations even when the process is irreversible.