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Reversible is expansion/compression against constant pressure, while irreversible is infinitesimal steps of expansion/compression against a changing pressure. Therefore, irreversible does more work, but does not actually happen in real life.
Reversible processes are when the external pressure is changing in minuscule amounts and so the volume is changing in minuscule amounts and can return to it's original state. Irreversible processes have a constant external pressure so once it expands/compresses to a certain volume, it will stay the volume.
A reversible process is one that can be reversed by an infinitely small change in a variable. Whereas an irreversible process is an expansion against an external pressure that differs by a finite amount from the pressure of a system. To get a better understanding of a reversible change, you can consider the reversible, isothermal expansion of an ideal gas. The pressure of the gas falls as it expands; so to achieve reversible expansion, the external pressure must be reduced in step with the change in volume so that at every stage, the external pressure is the same as the pressure of the gas. As you can see, the change in volume is the infinitely small change required for the expansion to be reversible. The work that a system can do is greatest in a reversible process.
Reversible processes can make sense backwards and forwards, but for irreversible processes, there is a clear backward and forward. For example, throwing a chalk up in the air is reversible, but breaking an egg is irreversible.
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