A well-established way of power generation involves the utilization of geothermal energy-the energy of hot water that exists naturally underground - as the heat source. If a supply of hot water at 140oC is discovered at a location where the environmental temperature is 20oC, determine the maximum thermal efficiency a geothermal power plant built at that location can have.

the maximum thermal efficiency is 29%

Explanation:

the maximum efficiency for a thermal engine that works between a cold source and a hot source is the one of a Carnot engine. Its efficiency is given by

Maximum efficiency = 1 - T2/T1

where

T2 = absolute temperature of the cold sink (environment) = 20°C + 273 = 293

T2 = absolute temperature of the hot source (hot water supply) = 140°C + 273 = 413

therefore

Maximum efficiency = 1 - T2/T1 = 1 - 293/413 = 0,29 = 29%