Two same objects with the same initial temperature Ti have a constant specific heat capacity of Cp, now one installs a refrigerator in between these two and tries to lower one of the objects temperatures to T2. Assume the system experience a constant pressure process and no phase change involves. Proof the the minimum work Wmin required by the refrigerator is: (hint apply principle of the increase of entropy)
Wmin= Cp ((T1*T1/T2)+T2-2T1)