Past exam of the physics B course of the University of Cambridge / 2013 / Paper 1 / Section A / A3

With the standard liquid-water approximation $\rho \simeq 10^3\mathrm{kg}{\mathrm{m}}^{-3}$, each portion has mass $100\mathrm{kg}$. The equal heat capacities give final temperature $T_f=310\mathrm{K}$ by energy conservation. For an insulated mixing process with no other changes,The reversible integrals $mc\int dT/T$ evaluate entropy differences between equilibrium states; the actual heat transfer is irreversible. These are two portions of the same substance, so there is no additional ideal-mixture compositional entropy.