Efficiency: Work, Limits, and Zeno's Paradoxes

[Phil Henshaw]

I think the 2nd law of thermodynamics, which places limits on the efficiency of thermal engines, can also be interpreted as saying increasing efforts to improve efficiency result in geometrically decreasing results. I can't find that stated, though. I suppose it's just the first derivative of something, but I'm real rusty on that and don't see quite how to do it. Is that worked out somewhere?

What I'm also looking for is any discussion on the broader principle, consistent with the above, that in exploiting any opportunity it's inevitable that you do the easy parts first and if you want to get more out of the 'same' thing, all that's available are the harder parts. Like in polishing a mirror. Going from 100 grit to 1000 grit to 10000 grit is the way to get a nice shine but each step is lots more work, to move less and less material, and the task approaches a natural point of phsical refusal, unattainable perfection.

I've been thinging about it as one of the rare general cases where Zeno's paradoxes actually do apply, and wondering how to tell all the good folks who are talking about removing growth limits with it the bad news...

Anyone know of a discussion on any part of this?

 

[Cyrus]

I don't understand what your asking.

 

[Claude Bile]

I think the 2nd law of thermodynamics, which places limits on the efficiency of thermal engines, can also be interpreted as saying increasing efforts to improve efficiency result in geometrically decreasing results.

I do not understand this part. How do you quantify effort?

Claude.

 

[Phil Henshaw]

Yes, I recall defining measures as being one of the problems with it discussed before, and it may be why I can't find any literature on it. The closest I can come is that the measure of effort is relative to prior measures of work on the same task. For example, in economics you seek to maximize return, and extract the easy profit first. Then it takes more effort (cost) to extract profit from what you had previously thought of as waste (exploiting efficiencies). As you do that over and over your effort increases and your return decreases. It makes perfect sense that sipping oil from big pools is naturally easier than moving your equipment from one little pool to another, and that's exactly what always happens toward the limits of maximizing any resource. Then going back to sip the last drops from all your large and small abandoned oil fields requires a still higher level of effort. Since that defines a scale, it gives you a measure.

That pattern has a distinct thermodynamic inefficiency character, and is sure obvious and determinitive of behavior in virtually any kind of task, but I can't find a general discussion of it. See what I'm gettin at?