A power plant taps steam superheated by geothermal energy to 475 K (the temperat

Question

A power plant taps steam superheated by geothermal energy to 475 K (the temperature of the hot reservoir) and uses the steam to do work in turning the turbine of an electric generator. The steam is then converted back into water in a condenser at 308 K (the temperature of the cold reservoir), after which the water is pumped back down into the earth where it is heated again. The output power (work per unit time) of the plant is 82,500 kilowatts.

(a) Determine the maximum efficiency at which this plant can operate.


(b) Determine the minimum amount of rejected heat that must be removed from the condenser every twenty-four hours.

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Explanation / Answer

Data: Temperature of hot reservoir, Th = 475 K Temperature of cold reservoir, Tc = 308 K Output power of the plant, Pout = 82500 kW                                                  = 82500 x 10^3 w Time, t = 24 hours             = 24 * 3600             = 86400 s Solution: (a) Maximum efficiency,e = [ ( Th - Tc) / Th ] * 100                                   = [ ( 475 - 308 ) / 475 ] * 100                                   = 35.16 % Ans: Maximum efficiency, e = 35.16 % (b) Efficiency, e = Pout / Pin Pin = Pout / e       = 82500000 / 0.3516       = 234641638.2 W Rejected heat, Q = [ Pin - Pout ] * time                            = (234641638.2 - 82500000) * 86400                            = 1.31 x 10^13 J Ans: Rejected heat, Q = 1.31 x 10^13 J

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