Suppose m_A (g) of species A {molecular weight M_A, heat capacity C_pA [J/ (g∙°C)]} at temperature T_A0 (°C) and m_B (g) of species B (M_B, C_pB) at temperature T_B0 are mixed adiabatically. The heat of mixing of A and B at 25°C is ΔH_m (r) (J/mol A in solution), where r = (m_B/M_B)/ (mA/MA). The heat capacity of the product solution is Cp_s [J/ (g∙°C)]. All heat capacities may be considered independent of temperature.

(a) Derive an expression for T_max, the highest temperature attainable by the product solution, in terms of the other quantities defined. State the conditions that would have Co be met for this temperature to be approached.

(b) Use your expression to estimate T_max for a process in which 100.0 g of sodium hydroxide at 25°C and 225.0 g of water at 40°C are combined to form a product solution with a heat capacity of 3.35 J/(g∙°C).