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I think this is how it works. An irreversible expansion is essentially all real life expansions. The change in volume occurs so quickly that it is essentially instantaneous. In the case of an reversible expansion, the instantaneous change in volume dV, is essentially zero, I think but it might be a good idea to clarify. dV I think is zero because the expansion occurs so slowly as a result of the system constantly reaching equilibrium after every infinitely small change in volume. This allows reversible expansion to do more work than the irreversible expansion. As for being able to recognize the difference, I think you will be told whether it is reversible or irreversible. After all, reversible systems do not exist in real life. They are just theoretical concepts that describe the maximum amount of work possible done by expansion.
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