Marrying Wright's Law to Thermodynamics for a Relative Final Cost-predicting Model of Carbon-fuel Substitution

The problem of assessing the relative final cost of energy technology substitution is approached by means of a general interpretation of Wright's law and the introduction of the concept of thermodynamic utility which derives from energy carrier specific energy. Via the Bienaymé-Chebyshev inequality the ideal relative final cost of C-fuel substitution (diesel/gasoline) is estimated at three different probabilities (50 %, 87.5 % and 96 %) for compressed hydrogen, liquid hydrogen, metal hydrides and Li-ion technology. C-fuel substitution at cost parity is an event clearly below the 50 % probability horizon of insight, 96 % values range between 1.8 (Li-ion) and 4.3 (LH2/350 bar) times the cost of C-fuel technology. The results are evinced in a cost/price comparison between the Toyota Mirai, Tesla 3 and Skoda Superb and found to reflect reality properly (see ESI). The approach also offers a systematic explanation for previously as-is reported findings of parameter studies from literature. The issue of mitigating the cost discrepancy is briefly discussed, too.