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[subscript ext], the pressure P[subscript sys,mb] on the piston or other moving boundary (hence the subscript mb), which is nearly equal to the system pressure P[subscript sys], should be used in the integral over volume. This formula only requires that P[subscript sys](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 dw = -P[subscript sys,mb] dV ˜ -P[subscript sys] dV is the only useful formula for infinitesimal PV work during a uPT process. The quasistatic approximation P[subscript sys,mb] = P [subscript sys] and dw = -P[subscript sys] 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 = dq[subscript 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.