If the final temperature of the metal is tfnbspand that of, Physics

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If the final temperature of the metal is tfnbspand that of

A hot metal of mass m, specific heat c_p, and temperature T, is immersed in a cooler liquid of mass m specific heat c'_p and temperature T'_i The entire system is thermally insulated.

If the final temperature of the metal is T_f and that of the liquid is T_j, then show by the method of Lagrangian multipliers that the condition for the entropy change of the universe to be a maximum is that T_f = T_j.

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