It's well known that real-world engines (non-reversible) have efficiencies
much lower than the Carnot efficiency, despite the fact that mechanical
friction can be quite low if the engine has good lubricated bearings.
Where's the problem? I draw people's attention to an interesting result
first (I assume) derived by F. L. Curzon and B. Ahlborn, AJP 43, pp 22-24
(Jan. 1975). I have the impression that their result is not widely known by
physicists.
The Carnot efficiency 1 - T_L/T_H is for a reversible engine which
necessarily runs infinitely slowly because the temperature difference
between working material and source or sink must be infinitesimal (to avoid
entropy production). Hence the power output of the engine is zero, since
the rate of energy transfer into or out of the working material is a
function of the temperature differential (it's proportional for typical
thermal materials).
Curzon and Ahlborn asked the question, "What is the efficiency of an engine
running at maximum power?" This won't be a reversible engine, since its
power output is zero. Another extreme case is that the engine consists of
source and sink connected by a metal bar, in which case the power output is
also zero (with lots of entropy production, which is the real problem, not
mechanical friction). There should be some operating regime in between
these extremes that yields maximum, nonzero power.
Years ago a colleague at UIUC, Jim Smith, pointed out to me that if fuel is
cheap but capital investment in engines is expensive, you want to run at
maximum power, whereas if fuel is expensive and capital investment in
engines is cheap, you can run near reversibly by having a huge number of
engines to get the nonzero power you need.
Curzon and Ahlborn derived a remarkably simple result for the efficiency at
maximum power: 1 - sqrt(T_L/T_H). 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.
Very roughly, the maximum-power efficiency is about half of the Carnot
efficiency. Make the crude assumption that the two absolute temperatures
aren't very different from each other. Then we have