🚀 go-pugleaf

   On Oct. 21, Doug Benning asked about a thermodynamics question in
Hewitt.  I sent a reply, but according to the log it didn't get
through.  So I'll try again.  I hope this helps a little bit.
   The question and the explanation aren't stated very clearly.  As you
have already found, what's important is the RATIO of the high and low
temperatures, not their difference.  Raising the high temperature while
keeping the low temperature the same would increase efficiency, and
lowering the low temperature while keeping the high temperature the same
would also increase efficiency.  However, raising both temperatures may
or may not increase efficiency.  In Hewitt's problem, one engine had
both the high and low temperatures raised by 100 K relative to the other
one, so the temperature difference stayed at 200 K.  In that case
(which isn't a very good example), the efficiency went DOWN when the
high temperature went up.  However, had the high temperature been
raised from 500 K to 600 K while keeping the low temperature constant at
300 K, the efficiency would have increased from 0.4 to 0.5, and I think
that's the point he really wanted to get across in the problem.  He
just didn't do it very well.
   In a practical aside, it's interesting to note that the thermal
efficiency of nuclear power plants is sometimes lower than that of coal-
or oil-fired plants because the nuclear plants use lower temperature
steam to drive the turbines than conventional plants.  The exhaust
temperature is about the same in each design, so the high temperature
reservoir (the steam) is what sets the theoretical efficiency.

Steve Luzader
Frostburg State University
Frostburg, MD