Serway & Jewett — Heat Engines, Entropy, and the Second Law of Thermodynamics: Problem 42

You are working as an expert witness for an environmental agency. A utility in a neighboring town has proposed a new power plant that produces electrical power \(P\) from turbines. The utility claims that the plant will take in steam at temperature \(T_h\) and reject water at temperature \(T_c\) into a flowing cold-water river. The flow rate of the river is \(\Delta m / \Delta t\). The agency supervisor is concerned about the effect of dumping warm water on the fish in the river. (a) The utility claims that the power plant operates with Carnot efficiency. With that assumption, you need to determine for a trial presentation by how much the temperature of the water downstream from the power plant will rise due to the rejected energy from the power plant. (b) If you abandon the utility’s claim that the power plant operates at Carnot efficiency and assume a more realistic efficiency \(e\), you need to determine the increase in water temperature in the stream. (c) Finally, you need to testify whether the increase in water temperature in part (b) will be higher or lower than that found in part (a).