(Solved): Problem 3. A bay with a narrow inlet is dammed up so as to separate it from the sea, forming a lak ...

Problem 3. A bay with a narrow inlet is dammed up so as to separate it from the sea, forming a lake. Solar energy evaporates the water causing the level inside the bay to be $$h$$ meters lower than that of the sea. A pipeline admits sea water in just the right amount to compensate for the evaporation, thus keeping $$\mathrm{h}$$ constant (on the average). The inflowing water drives a turbine coupled to an electric generator. Turbine plus generator have an efficiency of $$95\%$$. Assume that there is heat loss neither by conduction nor by radiation. The albedo of the lake is $$20\%(20\%$$ of the incident radiation is reflected, the rest is absorbed). The heat of vaporization of water (at STP) is $$40.6\mathrm{MJ}$$ per kilomole. Average solar radiation is $$250\mathrm{W}/$$ square meter. If the area of the lake is $$100{\mathrm{km}}^2$$, what is the mean electric power generated? What is the efficiency? Express these results in terms of h. Is there a limit to the efficiency? Explain.