Assume that a village has discovered an underground geothermal well containing water at 95°C, 100m below the surface. They are evaluating the option using the water from this well to provide power to the village. Determine the maximum available work [kJ/kg] that could be obtained from a power plant that will pump water from the well, extract energy from the water and discharge the water to a lake at the surrounding temperature T0 = 25°C. Assume that the water temperature can be reduced to 35°C at the outlet of the power plant.
We now do an Exergy Analysis to determine the maximum available (reversible) work by eliminating q from the above Energy and Entropy equations:
This equation could have been derived directly from the definition of exergy:
Finally, we obtain our numerical answer by considering the question "What" above, in which we substitute the enthalpy (h) and entropy (s) values for liquid water, an incompressible liquid: