A cross-flow heat exchanger with both fluids unmixed has an overall heat transfer coefficient of 200 W/m²·K, and a heat transfer surface area of 400 m². The hot fluid has a heat capacity of 40,000 W/K, while the cold fluid has a heat capacity of 80,000 W/K. If the inlet temperatures of both hot and cold fluids are 80°C and 20°C, respectively, determine

(a) The exit temperature of the hot fluid

(b) The rate of heat transfer in the heat exchanger.