Two blocks of copper metal are of same size (heat capacity = C) but at different temperatures and . — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

Equilibrium temperature $T_f = \frac{T_1 + T_2}{2}$. The total entropy change is $\Delta S = C \ln\left(\frac{T_f}{T_1}\right) + C \ln\left(\frac{T_f}{T_2}\right) = C \ln\left(\frac{T_f^2}{T_1 T_2}\right) = C \ln\left[\frac{(T_1+T_2)^2}{4T_1 T_2}\right]$. The term $\frac{(T_1+T_2)^2}{4T_1 T_2}$ structurally expands and rearranges precisely to $\frac{(T_2-T_1)^2}{4T_1 T_2} + 1$.