A power plant taps steam superheated by geothermal energy to 480 K (the temperat

Question

A power plant taps steam superheated by geothermal energy to 480 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 299 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 91,000 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.

Explanation / Answer

(a) We know that n = 1 - T2 / T1 = 1 - 299k/480K = 0.37708 = 37.708% (b) We know that n = W / QH Given that W/unit time = 91,00 kW ==> Qh = W/n = 91,000 kW/ 0.37708 = 241328.100 kW So that Qc = Qh - W = 241328.100 kW - 91000 kW = 150328.100 kW Therefore Qc = 150328.1 x 10^3 J/s * 24 * 3600 s = 12988347.85 MJ

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