- Author(s)
- Klaus Schmidt-Rohr
- Publisher
- J. Chem. Educ.
- Year
- 2014
- Volume
- 91
- Pages
- 402-409
- DOI
- 10.1021/ed3008704

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” *P*ext, the pressure *P*sys,mb on the piston or other moving boundary (hence the subscript mb), which is nearly equal to the system pressure *P*sys, should be used in the integral over volume. This formula only requires that *P*sys(*V*) and *T* are well defined, that is, a system of uniform *P* and *T* (“u*PT*”) 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 δ*w* = −*P*sys,mb d*V* ≈ −*P*sys d*V* is the only useful formula for infinitesimal *PV* work during a u*PT* process. The quasistatic approximation *P*sys,mb = *P*sys and δ*w* = −*P*sys d*V* is usually excellent and enables analyses of irreversible u*PT* 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 u*PT* or quasistatic processes. We show that the equality d*S* = δ*q*irr/*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.