Heating up water for your morning shower provides an excellent example of heat exchange (and mixing that you control). Consider the cold water (Cp = 4.18kJ/kg°C) leading to your shower enters a counter--flow heat exchanger at a rate of 0.5kg/s and 10°C. The water is heated to a more comfortable 42°C by hot water (Cp = 4.20 kJ/kg°C) that enters at 95°C at 2.5 kg/s. Determine the rate of heat transfer and the exit temperature of the hot water.