The Geothermal Power Plant Efficiency Puzzle · AI Generator #GEN-25815017
Physics · thermodynamics
Problem
A geothermal power plant operates between a hot underground reservoir at temperature Th=180°C and cooling towers that reject heat to the atmosphere at Tc=25°C. The plant uses a modified thermodynamic cycle where the working fluid undergoes four processes: (1) isothermal expansion at Th, (2) adiabatic expansion to temperature Tc, (3) isothermal compression at Tc, and (4) an unusual process where the fluid is heated at constant volume back to the initial state.
During the constant volume heating process (4), the pressure increases by a factor of α=2.5 and the temperature rises from Tc to Th. The working fluid behaves as an ideal gas with γ=1.4.
(a) Find the efficiency of this modified cycle.
(b) Compare this efficiency to the theoretical maximum efficiency (Carnot efficiency) for the same temperature reservoirs.
(c) If the plant produces 50MW of electrical power with an overall conversion efficiency of 85% from thermal to electrical, what is the rate of heat extraction from the geothermal reservoir?