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A reversible process is a process that can be reversed by infinitesimally small changes in the system and without increasing entropy and the system is in equilibrium with surroundings. Compared to an irreversible process which increases entropy and isn't reversible with infinitesimally small changes.
According to the second law of thermodynamics, any process that would reduce the entropy of an isolated system is impossible. If a reaction takes place in the forward direction and the entropy increases, then for the reverse process the entropy would decrease, which is impossible, so the forward reaction is irreversible. If a reaction takes place and the entropy is unchanged, then it would also be unchanged by the reverse reaction. This reaction could go in either direction without contradicting the second law, so it is considered reversible.
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