Carnot’s Cycle

Sadi Carnot had the same ambitions as his father. He hoped to abstract, from
the detailed complexities of real machinery, general principles that dictated the
best possible performance. Lazare’s analysis had centered on ideal mechanical
operation; Sadi aimed for the mechanical ideal, and also for ideal thermal
operation.
He could see, first of all, that when heat was dropped from a high temperature
to a low temperature in a heat engine it could accomplish something. His conceptual
model was based on an analogy between heat engines and water engines.
He concluded that for maximum efficiency a steam engine had to be designed so
it operated with no direct fall of heat from hot to cold, just as the ideal water
engine could not have part of the water stream spilling over and falling directly
rather than driving the waterwheel. This meant that in the perfect heat engine,
hot and cold parts in contact could differ only slightly in temperature. One can
say, to elaborate somewhat, that the thermal driving forces (that is, temperature
differences) in Carnot’s ideal heat engine have to be made very small. This designhad more than an accidental resemblance to Lazare Carnot’s principle of continuity
in the transmission of mechanical power.
To make it more specific, Carnot imagined that his ideal heat engine used a
gaseous working substance put through cyclic changes—something like the
steam in the pistons of the Woolf steam engine. Carnot’s cycles consisted of four
stages:
1. An isothermal (constant-temperature) expansion in which the gas absorbed
heat from a heat “reservoir” kept at a high temperature t2.
2. An adiabatic (insulated) expansion that lowered the temperature of the gas
from t2 to t1.
3. An isothermal compression in which the gas discarded heat to a reservoir
kept at the low temperature t1.
4. An adiabatic compression that brought the gas backto the original high temperature
t2.
Stages 1 and 3 accomplish the heat fall by absorbing heat at a high temperature
and discarding it at a low temperature. More workis done by the gas in the
expansion of stage 1 than on the gas in the compression of stage 3; and amounts
of workdone on and by the gas in stages 2 and 4 nearly cancel each other. Thus,
for each turn of the cycle, heat is dropped from a high temperature to a low
temperature, and there is net workoutput.