A solar tower plant runs its receiver at the optimum receiver temperature found from…

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

Energy from Physics, Ch Storing energy: cells, rotors, air, heat and hydrogen

Problem

A solar tower plant runs its receiver at the optimum receiver temperature found from the earlier treatment of concentrated solar collectors, here

T_{\rm rec} = 800\,\mathrm{K}

, and uses this heat to charge a molten-salt store from

573\,\mathrm{K}

up to

800\,\mathrm{K}

. The salt's specific heat may be taken as constant over this range. The store is later discharged through a heat engine fed by the salt as it cools back to

573\,\mathrm{K}

, rejecting heat to cooling water at

310\,\mathrm{K}

; take the engine's efficiency as the Curzon-Ahlborn model efficiency

\eta_{\rm CA} = 1 - \sqrt{T_c/T_h}

met in the treatment of real heat-engine cycles, with

T_h

set to the salt's entropic mean temperature

T_m

and

T_c = 310\,\mathrm{K}

. Take the dead-state (ambient) temperature for exergy as

T_0 = 290\,\mathrm{K}

. ((a)) Compute the entropic mean temperature

T_m

of the heat added to the salt as it warms from

573\,\mathrm{K}

800\,\mathrm{K}

, and hence the exergy fraction

1 - T_0/T_m

of the stored heat. ((b)) Compute the Curzon-Ahlborn efficiency of the discharge engine. ((c)) Compare the two numbers and explain, in a sentence, why the engine converts less of the stored heat to work than the exergy fraction alone would suggest is possible.

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