A body of constant heat capacity cp and at a temperature ti, English

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A body of constant heat capacity cp and at a temperature ti

A body of constant heat capacity C_p and at a temperature T_i is put in contact with a reservoir at a higher temperature T_f. The pressure remains constant while the body comes to equilibrium with the reservoir. Show that the entropy change of the universe is equal to

where x = -(Tf - Ti)/Tf. Prove that the entropy change is positive.

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