A Carnot cycle absorbs 100 MW of heat from a hot resevoir at 900 K, and releases
ID: 1312928 • Letter: A
Question
A Carnot cycle absorbs 100 MW of heat from a hot resevoir at 900 K, and releases waste heat to a cold resevoir at 300 K. What is the efficiency of the cycle? How much power does it produce? How much waste heat does it release to the cold resevoir? What is the change in entropy of the universe associated with this process? Some researchers at Antarctica would like to build a geothermal power plant to take advantage of the underground volcanoes. The flow rate around the cycle will be 5 mol/s of water. Their plant would use the hot lava as a heat source, and the Antarctic atmosphere, where summer highs reach negative 15 degree C, as a heat sink. What is the maximum efficiency of this cycle? Assume that the steam enters the turbine at 300 atm and 1000 degree C. If the steam exits the turbine at 1 atm, what is its outlet temperature? Now much work is done by the turbine? Saturated liquid water leaves the condenser at 1 atm. How much heat is released to the Antarctic? How much heat is absorbed from the volcanoes? What is the overall efficiency of this cycle?Explanation / Answer
1. efficiency = (1- (300/900))*100 % = 66.67%
it produces 10*0.6667 MW = 6.667 MW power
it releases (10 - 6.667 ) MW = 3.333 MW heat to cold reservoir.
change of entropy of universe in this process = 0 because the process is reversible.
12.
assuming the lava temperature is 1000 degree C
according to carnot's theorem, maximum theoritical efficiency = ( 1- (288/1273))*100% = 77.37%
However, no real engine can have an efficiency more than 50%
P1/T1 = P2/T2
outlet tempetature = 1000/300 = 333.33 degree C
work done = 5*8.314*(1000 - 333.33) W = 27.713 KW
heat released = (4.18)*(333.33+15)*5*0.018 W = 131.041 KW
heat absorbed from volcanos = work done + waste heat = 158.754 KW
overall efficiency = 27.713 KW / 158.754 KW = 17.45%
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