Accordingly, to establish the entropy change for this irreversible process, we must follow the standard procedure of first employing the first law of thermodynamics to establish the final state of the system, and then determining the entropy difference between the initial and final states. This mixing gives rise to irreversibility present in the process. What we are dealing with here is an irreversible process, where some of the gas from chamber 2 at temperature $T_2$ flows through the intervening tube and mixes with the gas already present in chamber 1 at temperature $T_1$. $^*$ according to Callen it should be at most 0.1 of sound speed.
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