A body of constant heat capacity cpnbspand at a temperature

Question

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

ΔS = C_p[x - ln(1+x)];

where x = -(T_f - T_i)/T_f. Prove that the entropy change is positive.