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In order to construct the alternate, reversible process to connect the
initial and final states, I will have to introduce other interacting
entities in the system's environment. It is true that there will be zero
entropy change in the the total super-system during the alternate reversible
process. However my system can change entropy, as can the new environment.
For the alternate, reversible process to "replace" the Rumford boring, I
introduce a sequence of heat reservoirs going between the initial and final
temperatures.
These reservoirs will lose entropy, while the cannon gains an equal amount
of entropy.