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discussionsectionkey - Discussion Section Problems 1...

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Discussion Section Problems; 1) Suppose a lake has a surface area of 10000m 2 . water at the surface of the lake is warmed to a temperature of 298K by heat from the sun. water at the bottom of the lake is 20 degrees lower in temperature. It is proposed that a heat engine be placed in the lake that will exploit this temperature gradient to produce work. It is claimed that this engine can produce energy at an average rate of 1 MWatt (i.e. 10 6 Watts). Assuming the average solar flux into the lake (i.e. the rate of energy transfer from the sun into the lake) is 500 Watts m -2 , does this engine violate: 1) the First Law of Thermodynamics; 2) the Second Law of Thermodynamics; 3) both the First and Second Law; 4) neither the First or the Second Law. Explain your answer. Watt=Js -1 . Solution: The total solar flux into the lake is Flux = 10000 m 2 ( ) 500 Wm ! 2 ( ) = 5 " 10 6 W = 5 MWatts Thermal efficiency = T H ! T L T H = 20 298 = 0.067 Maximum Theoretical Output = 0.067 ( ) 5 " 10 6 W ( ) = 0.34 MW The claim is the engine can output on average 1MWatt. This does not violate the First Law because the average output of energy does not exceed the solar flux. But the
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