Re: [Phys-L] efficiency versus Carnot efficiency

[John Denker <jsd@av8n.com>]

On 03/18/2013 02:46 PM, Bruce Sherwood wrote:
> Curzon and Ahlborn derived a remarkably simple result for the efficiency at
> maximum power: 1 - sqrt(T_L/T_H).

OK so far ... subject to the usual huge number of assumptions.

There's a similar result in electronics:  Suppose you have a
power supply with a given open-circuit voltage and a given 
source impedance.
  -- What's the most power you can get out of it?
  -- What is the energy efficiency at this point?

The calculation is a couple of lines long.  It's a garden-variety 
calculus-I extremization problem.

> 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.

I don't believe that for a minute.  Nobody I know operates car engines 
or airplane engines anywhere near max rated power for more than a tiny 
percentage of the time.

Besides, how do you even /define/ T_H for an internal-combustion engine?

Furthermore, note that the energy-efficiency for a person on foot is far
less than for a person on a bicycle ... and it's not because the bicycle 
is slower.

=====================

In any case, comparing efficiency to Carnot efficiency is silly.  The main 
thing that matters is efficiency /relative to the best that could be done/
using the same amount of fuel.  For more on this, see
  http://www.av8n.com/physics/thermo/spontaneous.html#carnot-excess-attention