Final answer:
The work of an isothermal reversible expansion is larger than that of an irreversible expansion because a reversible process operates in equilibrium, doing the maximum work against external pressure while an irreversible process does not maintain equilibrium states and often has less opposing pressure to do work against.
Step-by-step explanation:
The work done by a gas during an isothermal reversible expansion is greater than the work done during an irreversible expansion because, in a reversible process, every intermediate state between the initial and final volumes is an equilibrium state. During a reversible isothermal expansion of a gas, the external pressure is adjusted to be infinitesimally less than the internal pressure of the gas. This ensures that the gas expands slowly and does the maximum amount of work against the external pressure. The temperature remains constant because the system absorbs heat (qin) from the surroundings. As the gas performs work on the surroundings by expanding, heat is transferred to the gas in order to maintain the temperature constant, thus maximizing the work done.
Conversely in an irreversible expansion, the process is carried out quickly. The external pressure isn't exactly balanced with the internal pressure, often being constant or imbalanced leading to a situation where not all intermediate states are equilibrium states. Because equilibrium isn't maintained less work is done by the gas as it expands against a lower or unchanging opposing pressure.
Therefore, the content loaded question of why the work of an isothermal reversible expansion is larger than an irreversible expansion is because a reversible process can adapt to infinitesimally small changes in pressure, doing maximum work, whereas irreversible processes do not adjust and hence do less work.