(35 pts) Near a small town in central Colombia in South America, a mountain stream meets a large river at the bottom of a tall mountain. The large river (Ro Magdalena) is warm, while the small mountain stream (Ro Pequeo) is very cold, as it begins at very high altitudes and is comprised mostly of water from melting snow. While a few dams and hydroelectric plants have been constructed along the mountain stream to take advantage of its flow to produce electricity, a professor suggests that additional useful work could be extracted by operating a heat engine between the warm river and cold mountain stream. The professor has designed a very efficient heat engine, and has recommended the construction of a small power plant. Such a power plant would be particularly advantageous as it would not require damming the river. Before permits can be granted and construction can start, you have been tasked with evaluating the feasibility of such a power plant. The large river (Ro Magdalena) has a flow rate of 1245m3/s and an average temperature of 305K. The small river/stream (Ro Pequeo) has a flow rate of 32m3/s and an average temperature of 275K. a) What is the maximum possible power which can be obtained from the heat engine? What is the temperature of each river downstream of the heat engine? Assume that the rivers flow co-currently. Assume the density of the river water is 1100kg/m3 and the heat capacity is 4.30J/gK. (Calculate only the power available from the temperature difference; assume at the location of the heat engine, rivers have same altitude/pressure/velocity). b) If the exact flowrate of the larger river was unknown (just known to be much larger than that of the smaller river), what assumption could be made to simplify our approach in part a)? Calculate the maximum power attainable in this case