Geothermal brine emerges at with specific heat capacity and cools to the dead-state…

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

Energy from Physics, Ch Natural energy flows: rotors, turbines, waves, channels and hot rock

Problem

Geothermal brine emerges at T=420 KT = 420\,\mathrm{K} with specific heat capacity c=4.2 kJ kg−1 K−1c = 4.2\,\mathrm{kJ\,kg^{-1}\,K^{-1}} and cools to the dead-state temperature T0=300 KT_0 = 300\,\mathrm{K}. ((a)) Find its specific exergy ex=c[(T−T0)−T0ln⁡(T/T0)]e_{\rm x} = c[(T-T_0) - T_0\ln(T/T_0)]. ((b)) Find the heat released per kilogram, c(T−T0)c(T-T_0), and the ratio exe_{\rm x} to that heat.

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