The Geothermal Power Station · AI Generator #GEN-CC8C79E1

Physics · thermodynamics

Problem

A geothermal power station operates by extracting hot water from underground reservoirs and using it to drive a heat engine. The station pumps water from a geothermal well at temperature

T_h = 180°\text{C}

and rejects waste heat to a nearby lake at temperature

T_c = 15°\text{C}

. The power station is designed to extract

Q_h = 50\;\text{MW}

of thermal energy per second from the geothermal source. (a) What is the maximum theoretical electrical power output of this geothermal station? (b) In practice, the actual power station achieves only

\eta_{actual} = 12\%

efficiency. How much waste heat per second does the station dump into the lake? (c) If the lake has a volume of

V = 2.0 \times 10^6\;\text{m}^3

and the station operates continuously, by how much would the lake temperature rise per day if there were no other heat transfer mechanisms? (Use

\rho_{water} = 1000\;\text{kg/m}^3

and

c_{water} = 4180\;\text{J/(kg·K)}

Related theory

thermodynamics

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