Thermodynamic entropy — UPSC Physics Optional CSE 2016 Paper I

m gram of water at temperature T_1 is isobarically and adiabatically mixed with an equal mass of water at temperature T_2. Show that the change in entropy is given by \Delta S=2mC_p\ln\left(\dfrac{T_{\mathrm{av}}}{T_{\mathrm{geo}}}\right), where T_{\mathrm{av}}=\dfrac{T_1+T_2}{2} and T_{\mathrm{geo}}=\sqrt{T_1T_2}.