For example, at relativistic speeds closer to the speed of light, the "law" PV=nRT breaks down and needs to be reformulated...
Well, this is certainly interesting, and it may be that it's just you and me reading here, but...
I'm pretty ignorant about the math that goes into relativistic thermodynamics, but it seems to me that it generalizes the interrelationships between energy, heat, mass, temperature and entropy which occur in relativistic conditions. The resulting conservation equations become much more complex since energy and mass can interchange but I do believe that they still conserve. They just conserve a combination of energy/mass/momentum, all of which begin to act squirrely in those conditions.
If you understand the math, you're better than me; and if you think that math allows violation of relativistic conservation, then you'll have to explain it to me....
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As for burning seawater with microwaves to gain energy, I take comfort in Einstein's (?) relativistic postulate, that:
"all laws of physics are the same in all inertial reference frames"
so that classical conservation of energy still applies to those microwave guys since none of us is moving much faster than 1000 mph relative to each other (and even though we are in a rotating reference system...).
I also like the short form version of both classical and relativistic thermo someone once wrote down:
Rule 1 (conservation of energy): You can't win.
Rule 2 (increase of entropy): You can't break even.
Rule 3 (unattainability of absolute zero): And you can't get out of the game.
...which work for me.
...The field of relativistic thermodynamics is very young and not entirely established....The problem is that scientists are trying to force the classical laws of thermodynamics to hold true at relativistic speeds, but the only way to do it is to redefine energy. In my mind, this is "scientific cheating"...
I'm not sure what you mean by "redefine energy". If by that you mean the equivalency of energy and matter at relativistic speeds (by Einstein's good old E=mc2), that's a pretty well established fact (why the atom bomb and sun both work) and far from scientific "cheating". If you mean something else, well then that's over my head...
...I am also a strong proponent of this for closed systems. But are systems ever truely closed? We have our universe, sure. But is it truely closed if energy is shared among multiple universes? Where does the definition of "closed" end? It works well on paper, but for practical purposes, it's not so easy.
Multiverses, branes, and interactions among them which create the quantum foam are (to me) waayyy speculative. They might be true, but ideas like that always float out there, just beyond the reach of my light...
However, as an engineer, closure is a necessity to establish the context for a problem, without which meaningful solutions (and conversations) are hard to have. Getting something for nothing by tapping energy from a truly infinite source (e.g. from transfinite aleph null 2 multiverses) requires that there be a true physical manifestation of such an infinity in our physical universe (the Big one). While mathematicians and poets speak of infinities often, actually encountering such a thing in the flesh would be, I think literally, overwhelming. We would see ourselves as small, indeed...
Anyway, enough philosophizing. This has been fun but it's getting late - so ...:sleepy:...and have a good evening...