Why are spontaneous processes irreversible?
Spontaneous processes are irreversible because they can be reversed only by taking a different path to get back to their original state.
A reversible process can take the same path to return to its original state. An irreversible process must take a different path to get back to its original state.
For example, when the partition is removed in the cylinder-and-piston arrangement below (a), the gas expands spontaneously to fill the evacuated space (b). Since the gas is expanding into a vacuum, it does no work on the surroundings (w = 0).
If we use the piston to compress the gas back to its original state (c), the surroundings must do work on the system (w > 0). The path to restore the system to its original state requires a different value of w than did the path by which the system was first changed, so the expansion of a gas into a vacuum is an irreversible process.