Carnot’s Principle

To summarize, Carnot constructed his ideal heat engine, as Lazare had made his
ideal machinery, so that all its parts and stages functioned continuously in very
small steps under very small thermal and mechanical driving forces. This and
the necessity for operating in cycles between two fixed temperatures were, Carnot
realized, the main features required for all ideal heat engine operation. The special
features of the four-stage gas cycle were convenient but unnecessary; other
ways could be found to drop the heat between the two heat reservoirs and produce
workoutput.
Carnot’s point of view insists that the forces driving an ideal heat engine be
so small they can be reversed with no additional external effect and the engine
made to operate in the opposite direction. Run forward, in its normal mode of
operation as a heat engine, the ideal machine drops heat, let’s say between the
temperatures t2 and t1, and provides work output. Run backward, with all its
driving forces reversed, the ideal machine requires work input and it raises heat
from t1 to t2. This is a heat pump, analogous to a mechanical device capable of
pumping water from a low level to a high level. Carnot reached the fundamental
conclusion that any ideal heat engine, operated as it had to be by very small
driving forces, was literally “reversible.” All of its stages could be turned around
and, with no significant effect in the surroundings, the heat engine made into a
heat pump, or vice versa.

This reversibility aspect of ideal heat engine operation led Carnot to his main
result, a proof that any ideal heat engine operating between heat reservoirs maintained
at t2 and t1, had to supply the same workoutput W for a given heat input
Q2. If two ideal heat engines had different workoutputs W and W' with W' larger
than W, say, the engine with higher workoutput W' could be used to drive the engine with lower workoutput W in reverse to pump the heat Q2 backto its
original thermal level in the upper heat reservoir, and with net workoutput W'
W (fig. 3.2).
If this composite device had been possible, it would have served as a
perpetual-motion machine because it supplied workoutput with no need to replenish
the heat supply in the upper heat reservoir; every unit of heat dropped
through the heat engine was restored to the upper reservoir by the heat pump.
In other words, this composite heat engine could have worked endlessly without
having to burn fuel. Lazare Carnot had relied heavily on the axiom that perpetual
motion of any kind was physically impossible, and this was another one of the
father’s lessons learned by the son. Sadi Carnot also categorically rejected the
possibility of perpetual motion and therefore concluded that the two ideal heat
engines in the composite machine had to have the same workoutput, that is, W
W'.
Put more formally, Carnot’s conclusion was that all ideal heat engines operating
in cycles between the two temperatures t1 and t2 with the heat input Q2 have
the same workoutput W. Design details make no difference. The working material
can be steam, air, or even a liquid or solid; the working part of the cycle
can be a gas expansion, as in Carnot’s cycle, or it can be something else. The
workoutput W of the ideal heat engine is precisely determined by just three
things, the heat input Q2 and the temperatures t1 and t2 of the two reservoirs
between which the heat engine operates. This statement expresses “Carnot’s principle.”
It was an indispensable source of inspiration for all of Carnot’s successors.