Suppose an irreversible adiabatic expansion process and a reversible adiabatic expansion process are starting from the same initial state, say, P1V1. Now, let both of these processes have equal pressure in their final state. My teacher said that the magnitude of the work done in the reversible process will be more than that done in the irreversible process. The reason behind this, my teacher said, was that the final temperature of irreversible process will always be higher than that of reversible process. But we were not taught why this happens. Is there a formula based proof (not graph based) that uses equations related to the first law to explain why this happens?
*I specifically say first law because we haven't been taught the other laws yet.