Reversible and irreversible work

In the preceding we assumed that the work done by the system was along a well-defined path p(V). Actually this is a rather strong assumption - that at each infinitesimal adjustment the curve p(V) exists. We are implicitly assuming that we are in a state of thermodynamic equilibrium at each step - in other words the system has time to come to equilibrium (i.e., uniform temperature throughout, etc.) before the next infinitesimal step. In real processes such as the compression of a piston in an internal combustion engine, the gas in the chamber might be highly nonuniform and locally disturbed by such things as shock waves during the next change in volume (perhaps the equation of state does not even hold during this interval of time). For an irreversible change such as in the internal combustion engine, an amount of work will be done, but it may not be calculable using /p dV .In more advanced books on thermodynamics it is shown that when the system does work (for example by expansion) /p dV is the maximum work that can be done. But when the system is compressed, the reversible (calculable) work (/p dV) is the minimal work done by the system during the compression. In the high compression engine the amount of work done is seldom more than 75% of the estimate based on the reversible assumption. The unfortunate mechanical engineer simply cannot win in the face of irreversible processes. Luckily, most natural processes of interest to the atmospheric scientist are better behaved.

The idealization of reversible work allows us to do calculations using /p d V even though in reality it never quite works that way. In most applications that follow in this book the assumption of reversible work is adequate.

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