Three heat engines each reject waste heat to a condenser at

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Earth, Climate & Energy Physics · The laws of thermodynamics

Energy from Physics, Ch Heat engines on fuel: exergy, real cycles, biomass and the nuclear heat source

Problem

Three heat engines each reject waste heat to a condenser at T0=300 KT_0 = 300\,\mathrm{K}, but take in heat from three different sources. ((a)) A binary geothermal plant is supplied with brine that enters its heat exchanger at 450 K450\,\mathrm{K} and leaves, cooled, for reinjection at 350 K350\,\mathrm{K}. Use the entropy-weighted mean temperature of a cooling liquid, Tˉ=(T1−T2)/ln⁡(T1/T2)\bar T = (T_1 - T_2)/\ln(T_1/T_2), to find the mean temperature at which this heat is delivered. ((b)) A solar-thermal collector delivers heat to its working fluid at a nearly constant absorber temperature of 420 K420\,\mathrm{K}. ((c)) A coal boiler heats its working fluid sensibly, at constant cpc_p, from 300 K300\,\mathrm{K} to 840 K840\,\mathrm{K}. For each source, state the entropic mean temperature of heat addition TmT_m and the reversible efficiency η=1−T0/Tm\eta = 1 - T_0/T_m, and rank the three by efficiency.

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