the efficiency amounts to 50-60 % for methanol production by use of electricity. When methanol is used in a methanol fuel cell the electrical efficiency of the fuel cell is about 35 to 50% (status of 2021). Thus the electrical overall efficiency for the production of e-Methanol with electricity including the following energy conversion of e-Methanol to electricity amounts to about 21 to 34% for e-Methanol of directly available CO2 and to about 18 to 30% for e-Methanol produced by CO2 which is obtained by Direct Air Capture. If waste heat is used for a high temperature electrolysis or if waste heat of electrolysis, methanol synthesis and/or of the fuel cell is used then the overall efficiency can be significantly increased beyond electrical efficiency. For example, an overall efficiency of 86% can be reached by using waste heat (e.g. for district heating) which is obtained by production of e-Methanol by electrolysis or by the following methanol synthesis. If the waste heat of a fuel cell is used a fuel cell efficiency of 85 to 90% can be reached. The waste heat can for example be used for heating of a vehicle or a household. Also the generation of coldness by using waste heat is possible with a refrigeration machine. With an extensive use of waste heat an overall efficiency of 70 to 80% can be reached for production of e-Methanol including the following use of the e-Methanol in a fuel cell. The electrical system efficiency including all losses of peripheral devices (e.g. cathode compressor, stack cooling) amounts to about 40 to 50% for a methanol fuel cell of RMFC type and to 40 to 55% for a hydrogen fuel cell of LT-PEMFC type. Araya et al. compared the hydrogen path with the methanol path (for methanol of directly available CO2). Here the electrical efficiency from electricity supply to delivery of electricity by a fuel cell was determined with following intermediate steps: power management, conditioning, transmission, hydrogen production by electrolysis, methanol synthesis resp. hydrogen compression, fuel transportation, fuel cell. For the methanol path the efficiency was investigated as 23 to 38% and for the hydrogen path as 24 to 41%. With the hydrogen path a large part of energy is lost by hydrogen compression and hydrogen transport, whereas for the methanol path energy for methanol synthesis is needed. Helmers et al. compared the Well-to-Wheel (WTW) efficiency of vehicles. The WTW efficiency