This template examines how the work associated with stepwise irreversible isothermal expansion and compression of an ideal gas changes as the number of expansion or compression steps increases (Figure 1). This template uses the graphing power of Mathcad to lead the user to discover that the work approaches an asymptote as the number of steps becomes very large and that the asymptote is the work for the reversible expansion or compression. It then challenges the user to recognize that the work for the reversible expansion or compression represents a limiting value for the work for the corresponding irreversible processes

Figure 1. Work (kJ/mole) as a function of the number of isothermal steps (NSTEPS) in the stepwise irreversible expansion of an ideal gas.