I appears to me that you are ascribing only those factors internal to an engine to the causes of efficiency of the engine and system. Even so, this will include the thermodynamic cycle of the engine and the system temperatures.Tom Booth wrote:The so-called "formula" to begin with is nothing but a measure of two temperatures, a hot and a cold "reservoir". To suggest these factors completely external to an engine have anything whatsoever to do with the engines "efficiency" is the "extraordinary claim". Completely illogical, unsupportable and contrary to observable facts and experimental outcomes.
The thermodynamic cycle is constrained by the type of cycle and the temperatures available for the cycle.
A real engine is constrained by nature. The Carnot limit just models an ideal cycle.
The Carnot Limit was originally developed by studying the Carnot Cycle. Other efficiencies formulas were developed for other ideal cycles constrained by the same temperature limits. Some were found to be less efficient, steam, I.C., etc...
This was further expanded to the measured indicator diagrams from real engines. The real engine cycles were found to be even less efficient.
It was also found that internal engine factors, such as friction made them even less efficient.
It has been calculated over and over that there has not been a better cycle efficiency than the ideal Carnot. Some are the same, Stirling, Ericsson.
Therefore the Carnot limit not only applies to the original cycle but to every other conceived cycle so far. In fact if a better cycle is found, it will allow for perpetual motion, over unity, theoretically. So the theory stand as a natural limit.
So the Carnot limit basically says if you break that limit you also break the first law of thermodynamics. Free over unity perpetual motion energy. It naturally can't happen.
You can't run Tesla's cold hole without having the ability to use a heat pump to create a hot peak, thus perpetual motion, over unity.
This is only provable by mathematics because nature makes it impossible to build a supernatural engine.
I tried to explain it simply but you got caught up in the non-existent contradiction semantics battle. It is an ideal cycle limit. It is a supernatural limit that no engine could possibly achieve. Hence it isn't modeling any engine.