Thermodynamics of the conversion of diluted radiation

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Abstract
The photon density in diluted black-body radiation is epsilon (0< epsilon 4/ pi Psi =4/3B epsilon X( epsilon ) sigma T3/ pi (X(1)=1) where X( epsilon ) is a function calculated here for the first time. A special type of steady-state non-equilibrium situation is defined, and called effective equilibrium, for which the effective temperatures T/X( epsilon ) identical to T* of the various components of a system are equal. In this state the system cannot yield work. The maximum efficiency eta 0 of such systems is investigated. The application to solar radiation (diffuse and direct) proves possible and involves the function lambda (x)=1-4/3x+1/3x4. In order to allow for diffuse and direct radiation the calculation is somewhat more complicated than previous ones. It shows that, for a black absorber, eta 0 approximately 0.7 (diffuse) rises to 0.93 as the radiation becomes more direct. However, for a grey absorber the efficiency might range typically from 60% to 83% for absorptivity alpha =0.9. For one pump p and a black absorber at ambient temperature T, eta 0= lambda (T/Tp*).