Two iron blocks of same size are at distinct temperatures \(T_{1}\) and \(T_{2}\), brought in thermal contact with each other. The transfer process is allowed to take place until thermal equilibrium is attained. Suppose, after the attainment of equilibrium, that the blocks are at the final temperature \(T\). Show that the change in entropy of the process is given by

\[\begin{equation*} \Delta S=C_{P} \ln \left[\frac{\left(T_{2}-T_{1}\right)^{2}}{4 T_{1} T_{2}}+1\right] \tag{WBUT,2008} \end{equation*}\]