A geothermal power plant uses geothermal water extracted at 150°C at a rate 210 kg/s as the heat source and produces 8000 kW of net power. The geothermal water leaves the plant at 90°C. If the environment temperature is 25°C, determine a) the actual thermal efficiency, b) the maximum possible

a) the actual thermal efficiency is 15.17%

b) the maximum thermal efficiency is 29.55%

Explanation:

a) the actual thermal efficiency is for a heat engine is,

E actual = Power obtained / Necessary heat rate as input = P/q

q = F * c * (Tinitial - Tfinal), F = mass flow rate, c=specific heat of water (we assume c = 1 cal/gr°C = 4.186 J/gr°C = 4.186 kJ/kg°C)

q = 210 Kg/s * 4.186 kJ/kg°C (150°C - 90 °C) = 52743.6 kW

therefore

E actual = 8000 kW / 52743.6 kW = 0.1517 = 15.17%

b) the maximum thermal efficiency for the same heat source and heat sink corresponds to the one of a Carnot engine. Where,

E max = 1 - Tc/Th, Th is the absolute temperature of the hot heat source and Tc is the absolute temperature of the cold heat sink.

therefore

Th = 150°C + 273 °C = 423 K

Tc = 25°C + 273°C = 298 K

thus

E max = 1 - 298/423 = 0.2955 = 29.55%