[QUE/TH-07007] TH-PROBLEM

 A mass $m$ of a liquid at a temperature $T_1$ is mixed with an
equal mass of the same liquid at a temperature $T_2$. The system is
thermally isolated. Show that the entropy change is given by
$$
2m\,C_p\,\ln\left({(T_1+T_2)/2\over\sqrt{T_1T_2}}\right)
$$
and prove that this is necessarily positive.