Pressure–Volume Integral Expressions for Work in Irreversible Processes

Different formulations of thermodynamic work w as a pressure�volume integral are examined for a piston moving against a gas in an irreversible process. Proper expressions are obtained using the instantaneous pressure of the gas on the piston as the integrand and also using certain external pressures as the integrand. There are two common yet different ways to define thermodynamic work, and results are obtained for both definitions. In addition, the contribution to w of the atmosphere in such processes is evaluated. An example is given that illustrates the points made in the paper.