A power plant taps steam superheated by geothermal energy to 583 K (the temperat

Question

A power plant taps steam superheated by geothermal energy to 583 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 334 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 81.5 megawatts. Determine (a) the maximum efficiency (as a decimal number between zero and one) at which this plant can operate and (b) the minimum amount of rejected heat that must be removed from the condenser every twenty-four hours.

Explanation / Answer

a) max efficiency = 1 - Tc/Th = 1- 334/583=0.427

b) e = W/Qh

Qh = W + Qc

0.427 = 81.5/(81.5+x)

x=109.37 MW

E = 109.37E6*24*60*60=9.45E12 J

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