4.2 The Carnot Cycle and Carnot’s Principle
Before Kelvin formulated the K-P Statement, Sadi Carnot had already realized that
heat from a single body cannot be transformed into work. Carnot’s study of heat
was nominally considered to be based on the caloric theory of heat, even though a
case will be made in Chap. 8 that Carnot’s theory of heat is not a caloric theory of
heat. According to the caloric theory, heat or caloric was thought to be an invisible,
weightless fluid that could be neither created nor destroyed. Therefore, there can be
no consumption of caloric; instead, “the production of motive power is then due in
steam engines not to an actual consumption of the caloric, but to its transportation
from a warm body to a cold body” [1:7]. Again, in his own words
The motive power of a waterfall depends on its height and on the quantity of the liquid; the
motive power of heat depends also on the quantity of caloric used and on what may be
termed the height of its fall, that is to say, the difference of temperature of the bodies
between which the exchange of caloric is made. In the waterfall the motive power is exactly
proportional to the difference in level between the high and low reservoirs. In the fall of the
caloric the motive power undoubtedly increases with difference in temperature between the
warm and cold bodies [1:15]. [See Eq. (49) below.]
The motive power of a waterfall is the potential energy (and possibly some
kinetic energy also) of the waterfall. In accordance with the modern understanding,
the motive power of heat is the “free energy” (see its definition in Chap. 7) of the
thermal energy. However, Carnot in his inquiry into the motive power of heat had
neither this terminology of free energy nor the concept of energy.
Carnot, as we shall see, was nonetheless able to conduct his inquiry by the
method of thought experiment
3 : Imagine air in a cylindrical vessel (Fig. 4.2) provided with a movable piston at an initial position cd. The cylindrical vessel will be
in contact with one of the two bodies, a constant temperature heat source body
A and a constant temperature heat sink body B, at certain points during the course of
operations. He prescribed the series of operations as follows [1:17–18]:
1. Bring the vessel with the air enclosed in the space defined by the piston at cd in contact
with the heat source A.
2. The piston rises gradually from the position cd to a position ef (end position of
isothermal expansion step) while the vessel is at all time in contact with heat source A,
which furnishes heat to vessel to keep the air temperature constant.
3. A is removed and the air vessel continues to expand without heating with the piston
rising from ef to gh (end of isentropic expansion [i.e., reversible adiabatic] step). This
“expansion cooling” step lowers the temperature of the air in the vessel to the temperature of B.
3
Thought experiments (theoretically constructed experiments) are devices of the imagination used
to investigate the nature of things. We need only to list a few of the well-known thought
experiments to be reminded of their enormous influence and importance in the sciences: Galileo’s
tower of Pisa, Newton’s bucket, Maxwell’s demon, Einstein’s elevator, Heisenberg’s gamma-ray
microscope, Schrödinger’s cat and, of course, Carnot’s cycle.
64
4 Carnot’s Theory of Heat, and Kelvin’s Adoption …
Before Kelvin formulated the K-P Statement, Sadi Carnot had already realized that
heat from a single body cannot be transformed into work. Carnot’s study of heat
was nominally considered to be based on the caloric theory of heat, even though a
case will be made in Chap. 8 that Carnot’s theory of heat is not a caloric theory of
heat. According to the caloric theory, heat or caloric was thought to be an invisible,
weightless fluid that could be neither created nor destroyed. Therefore, there can be
no consumption of caloric; instead, “the production of motive power is then due in
steam engines not to an actual consumption of the caloric, but to its transportation
from a warm body to a cold body” [1:7]. Again, in his own words
The motive power of a waterfall depends on its height and on the quantity of the liquid; the
motive power of heat depends also on the quantity of caloric used and on what may be
termed the height of its fall, that is to say, the difference of temperature of the bodies
between which the exchange of caloric is made. In the waterfall the motive power is exactly
proportional to the difference in level between the high and low reservoirs. In the fall of the
caloric the motive power undoubtedly increases with difference in temperature between the
warm and cold bodies [1:15]. [See Eq. (49) below.]
The motive power of a waterfall is the potential energy (and possibly some
kinetic energy also) of the waterfall. In accordance with the modern understanding,
the motive power of heat is the “free energy” (see its definition in Chap. 7) of the
thermal energy. However, Carnot in his inquiry into the motive power of heat had
neither this terminology of free energy nor the concept of energy.
Carnot, as we shall see, was nonetheless able to conduct his inquiry by the
method of thought experiment
3 : Imagine air in a cylindrical vessel (Fig. 4.2) provided with a movable piston at an initial position cd. The cylindrical vessel will be
in contact with one of the two bodies, a constant temperature heat source body
A and a constant temperature heat sink body B, at certain points during the course of
operations. He prescribed the series of operations as follows [1:17–18]:
1. Bring the vessel with the air enclosed in the space defined by the piston at cd in contact
with the heat source A.
2. The piston rises gradually from the position cd to a position ef (end position of
isothermal expansion step) while the vessel is at all time in contact with heat source A,
which furnishes heat to vessel to keep the air temperature constant.
3. A is removed and the air vessel continues to expand without heating with the piston
rising from ef to gh (end of isentropic expansion [i.e., reversible adiabatic] step). This
“expansion cooling” step lowers the temperature of the air in the vessel to the temperature of B.
3
Thought experiments (theoretically constructed experiments) are devices of the imagination used
to investigate the nature of things. We need only to list a few of the well-known thought
experiments to be reminded of their enormous influence and importance in the sciences: Galileo’s
tower of Pisa, Newton’s bucket, Maxwell’s demon, Einstein’s elevator, Heisenberg’s gamma-ray
microscope, Schrödinger’s cat and, of course, Carnot’s cycle.
64
4 Carnot’s Theory of Heat, and Kelvin’s Adoption …