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During irreversible adiabatic expansion entropy is generated. It means that the gas expands to as greater volume than that during reversible adiabatic expansion for the same change in pressure. How can that be?

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There is viscous dissipation of mechanical energy within the gas, and this "viscous heat generation" causes the final gas temperature to be higher. So the final volume is greater than for the adiabatic reversible expansion. Even though the final volume is greater, the amount of work done is less (because of the lower average pressure at the piston face), and the decrease in internal energy is less (i.e., higher final temperature).

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