Re: [Phys-L] efficiency versus Carnot efficiency

[John Denker <jsd@av8n.com>]

On 03/18/2013 08:41 PM, Bruce Sherwood wrote:
> I have the distinct impression that power plants, whether coal-fired
> or nuclear, don't use internal-combustion engines, and Curzon and Ahlborn
> said nothing about internal-combustion engines.

OK.  There was a discussion of engines in general, and then a segue
to "power plants".  Evidently I missed those two words, or didn't 
appreciate their significance.  My bad.  Sorry.

However ... my main point survives.  The idea of operating at "max
power" violates basic engineering principles. 

> They compared their result with the
> efficiencies of actual power plants and found agreement with their simple
> formula, which is consistent with fuel having been historically cheap and
> engines expensive.

Again, I don't buy that at all.

For the most obvious reasons, people try to operate engines (especially
stationary engines) near the max-efficiency point.

  For an aircraft engine, you might trade some efficiency to obtain a
  good power-to-weight ratio, but that is not what we're talking about
  in this thread.

There are LOTS of ways to throw together a second-order model for engine
efficiency such that the efficiency comes out to be very near 1-sqrt(T1/T2)
... when the engine is operating at max _efficiency_ ... which is nowhere
near max power.

An example of this is documented at
  http://www.av8n.com/physics/power-plant-efficiency.htm
including a couple of diagrams.

I did not cook the parameters to make it come out this way. 

The claim that fuel is cheap and engines are expensive is not consistent
with common sense and is also not consistent with the other claims.  You 
spend money on the engines to make them efficient, precisely because fuel 
is expensive.

Also, you would have to ruggedize the engine to make it capable of operating
at high power, so that would make the engine even more expensive.  Every 
engine I've ever seen, when operated at redline RPM, still has a positive
slope to the power curve, meaning power is still increasing as a function
of RPM.  The redline is set by mechanical strength, and is far below the
max thermodynamic power point ... for the simple reason that the designers
knew in advance that nobody would ever want to operate anywhere near max
power.

Starting from the max power point, throttling back to a lower RPM is a big 
win.  It saves money to first order, while making only a /disproportionately/ 
small change in power output.  For details, see 
    http://www.av8n.com/physics/power-plant-efficiency.htm

Bottom line:  Yes, it is interesting to think about how thermal resistances
can lead to a thermodynamic limit, namely max power.  However, as soon as 
you think about it, you realize that you don't want to operate there.