hidden behind such words as ‘proportionality’ or ‘equivalence,’ which indicated a
numerical relation between heat and work and nothing more” [9].
Then, Thomson experienced a decisive change of mind and in his authoritative
and influential 1851 paper On the dynamical theory of heat, [4:174–200] he opened
with these fateful words, “…Considering it as thus established, that heat is not a
substance, but a dynamical form of mechanical effect, we perceive that there must
be an equivalence between mechanical work and heat, as between cause and effect.”
In this telling, the equivalence correlation was accepted as causality between heat
and mechanical work, which became known as universal interconvertibility of heat
and work [10]. Significantly, Thomson had vacillated about the issue of convertibility and was, famously, the last of the three founders of thermodynamics,
Clausius, Rankine, and Thomson, to adopt fully Joule’s principle of convertibility.
But once converted, he became the most effective champion of Joule’s principle.
However, while the spontaneous transformation from work to heat is limitless,
the convertibility from heat to work is subject to strict limitation because, otherwise,
an unrestricted reverse transformation would have contradicted the Kelvin–Planck
statement that heat in itself cannot be converted into work. This was where Carnot’s
theory of heat came into our discussion. For this part of our discussion, we focus on
the Carnot heat engine.
There are two ways to consider the Carnot heat engine, the conventional way
and a new way of understanding the Carnot heat engine as it will be presented in
Chap. 8. In the conventional way, we understand the Carnot heat engine as follows:
the process is a reverse energy conversion of heat energy from a T A heat body to
mechanical energy; the three grades of energy involved are mechanical energy,
W rev , high temperature heat energy at T A , Q A , and low temperature heat energy at
T B ; for a given amount of Q A , the maximal amount of mechanical energy in the
reversible Carnot heat engine is
W rev ¼ Q A 1 À
T B
T A
ð54AÞ
Correspondingly, the conventional takeaway is the following general statements
(GSs):
GS. It is impossible to extract work from a heat source of Q A amount without at the
same time discarding a fraction of the heat—the minimal amount required is
Q A Á T B =T A
ð
Þ
GS-4.b. Heat, therefore, cannot be converted 100% into work.
This is the first part of the clarification (on the equivalence principle/principle of
the conservation of energy) Kelvin and Clausius introduced, between 1850 and
1854, when they attempted to incorporate Carnot’s theory into the mechanical
theory of heat, which will be referred to as the Kelvin–Clausius synthesis of Carnot’s theory and equivalence principle.
82
4 Carnot’s Theory of Heat, and Kelvin’s Adoption …
numerical relation between heat and work and nothing more” [9].
Then, Thomson experienced a decisive change of mind and in his authoritative
and influential 1851 paper On the dynamical theory of heat, [4:174–200] he opened
with these fateful words, “…Considering it as thus established, that heat is not a
substance, but a dynamical form of mechanical effect, we perceive that there must
be an equivalence between mechanical work and heat, as between cause and effect.”
In this telling, the equivalence correlation was accepted as causality between heat
and mechanical work, which became known as universal interconvertibility of heat
and work [10]. Significantly, Thomson had vacillated about the issue of convertibility and was, famously, the last of the three founders of thermodynamics,
Clausius, Rankine, and Thomson, to adopt fully Joule’s principle of convertibility.
But once converted, he became the most effective champion of Joule’s principle.
However, while the spontaneous transformation from work to heat is limitless,
the convertibility from heat to work is subject to strict limitation because, otherwise,
an unrestricted reverse transformation would have contradicted the Kelvin–Planck
statement that heat in itself cannot be converted into work. This was where Carnot’s
theory of heat came into our discussion. For this part of our discussion, we focus on
the Carnot heat engine.
There are two ways to consider the Carnot heat engine, the conventional way
and a new way of understanding the Carnot heat engine as it will be presented in
Chap. 8. In the conventional way, we understand the Carnot heat engine as follows:
the process is a reverse energy conversion of heat energy from a T A heat body to
mechanical energy; the three grades of energy involved are mechanical energy,
W rev , high temperature heat energy at T A , Q A , and low temperature heat energy at
T B ; for a given amount of Q A , the maximal amount of mechanical energy in the
reversible Carnot heat engine is
W rev ¼ Q A 1 À
T B
T A
ð54AÞ
Correspondingly, the conventional takeaway is the following general statements
(GSs):
GS. It is impossible to extract work from a heat source of Q A amount without at the
same time discarding a fraction of the heat—the minimal amount required is
Q A Á T B =T A
ð
Þ
GS-4.b. Heat, therefore, cannot be converted 100% into work.
This is the first part of the clarification (on the equivalence principle/principle of
the conservation of energy) Kelvin and Clausius introduced, between 1850 and
1854, when they attempted to incorporate Carnot’s theory into the mechanical
theory of heat, which will be referred to as the Kelvin–Clausius synthesis of Carnot’s theory and equivalence principle.
82
4 Carnot’s Theory of Heat, and Kelvin’s Adoption …