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For a system that undergoes a process that takes place at atmospheric pressure, the work done by the gas can be expressed as $-P_{\rm atm}\mathrm{d}V$.

Does this mean that the process is always quasi-static assuming no other forms of work except volume-pressure work?

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It depends on what you mean by isobaric. If you mean that the system starts out at atmospheric pressure and you add heat gradually to cause the system to expand, then it can be regarded as quasi static.

But if you mean that the system is initially at a higher or lower pressure than atmospheric pressure and, at time zero, you suddenly remove a constraint so that the gas can expand or contract spontaneously against constant atmospheric pressure, then the process will not be quasi static (and will be irreversible). Some people would consider this latter process isobaric (even though, just before the process started, the system was at a different pressure than the surroundings). (This latter process can be applied with or without adding or removing from the system).

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