Maximum and minimum quantities of work

For the integral to have a maximum value, P p must have the largest possible value at each stage of the process. But if the gas is to expand, F p must be less than the pressure p of the gas. Therefore, to obtain the maximum work, at each stage we adjust the opposing pressure to P p = p — dp, 3, value just infinitesimally less than the pressure of the gas. Then 

This is true only if the temperature is constant along the path of the change in state. If the temperature is allowed to vary along the path, there is no upper limit on the work produced. 

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