It may be possible to develop a heat engine that operates by taking advantage of

Question

It may be possible to develop a heat engine that operates by taking advantage of the temperature difference between the top and bottom of a lake (or ocean). The sun’s energy provides a constant source of power for heating the top of the lake (the average solar flux is about 240 W/m2). Suppose that the water at the top of the lake is 25oC and that at the bottom is 15oC. Calculate the Carnot efficiency of this engine? Suppose that the lake is 1 x 104m2 (about twice the size of a football field), what is the maximum work (in watts) that can be obtained from this engine? The average power usage of an average household is about 1.2 kW. Assuming that this engine is technically and economically feasible, how many households could be powered by it? Power is an energy rate: 1 W = 1 J/sec. The efficiency is equal to the work performed divided by the heat absorbed, but it also can be taken to be the power output divided by the power input.

Explanation / Answer

Temperature at surface T1 = 250 + 273 = 523 K

Temperature at bottom of lake T2 = 150 + 273 = 423 K

Canot efficieny = 1- (T1 / T2 ) = 1 - 423/523 = 0.191

Heat obtained = 240 * 10000 W = 2.4 * 106 W

Maximum Work obtained = Carnot efficiency * heat obtained

   = 0.191 * 2.4 * 106 W = 0.456 *106 W

No. of households that can be powered = 0.456 *106 W / 1.2 * 1000 W

= 380 household

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