I am new here and have always loved the history of science as much as the science itself. I have been intrigued by the 2nd law of thermodynamics and entropy for a long time but have also had something about its evolution that bothered me. So I'll summarize its stated development from my thermodynamics book and then ask my question. The relevant chapters cover it this way. First, they describe it as a set of qualitative postulates. Such as Kelvin-Planck which says roughly a device cannot be constructed that raises a weight and exchanges heat with only one reservoir. Or 2nd, the Clausius statement that says a device cannot be made that has no effect other than the transfer of heat from a cold to hot body. And finally, its impossible to construct a perpetual motion machine. Now the book describes the concept of a reversible process and factors like friction or heat transfer through a finite difference that make a process irreversible. Then it discusses a reversible Carnot cycle and proposes that a reversible engine is the most efficient. So far all qualitative. Then finally quantitative. The chapter states that the efficiency of the Carnot cycle is only dependent on temperature. eff = W/QH = (QH - QL) / QH = 1 - QL/QH = f(TH, TL) and finally says that Lord Kelvin proposed this relationship for the development of a temperature scale in a reversible process. QH/QL = TH/TL which also equates for a Carnot cycle that eff = 1 -QL/QH = 1-TL/TH This can be re-written as QH/TH - QL/TL = 0 and finally that is generalized as the Clausius integral where Integral (dQ/T) = 0 for a reversible engine. And since for an irreversible engine, QLirr > QLrev, then for an irreversible engine, Integral (dQ/T) < 0 And that is the 2nd law of thermodynamics stated in a quantitative way. Now here is the problem I have. With the 1st law of thermodynamics, Joule demonstrated it by using a paddle wheel in a container of water and showing that a falling weight connected to the paddle would heat the container by a quantifiable amount. That demonstrated the 1st law. delta U = Q - W Isaac Newton had developed the theory of gravity with F = GMm/d^2 and that was demonstrated because that equation can be used to derive the elliptical orbits of the planets that Kepler had described from observations a few decades earlier. What experiment showed the 2nd Law specifically that the best efficiency of an engine was eff = 1 - TL/TH? The equation eff = W/QH is a definition and the 1st law can be used to show that that is equivilant of eff = (QH-QL)/QH = 1-QL/QH but once that is transformed into efficiency of a reversible engine, eff = 1 - TL/TH, that is a declaration of the 2nd law. Was it believed because it was elegant? Was there an experiment that really showed it, or as I suspect, it wasn't rigorously demonstrated because there was no good way of building a device that matched a Carnot reversible cycle at the time? It could in the 19th century, only generally be shown that as TL/TH decreased for a real engine, the efficiency got better. I know that this is classical 2nd Law developed in the 1st half of the 19th century and that later a statistical concept of the 2nd law was formulated from which Integral (dQ/T) could be derived. But BEFORE that occurred, was the 2nd law demonstrated by experiment? Thanks.