work in terms of whether they are associated with entropy flow or not (see Chap. 5):
the answer is heat flow (Yes); work (No).
4.5.5 Equivalence of the Clausius Statement
and the Kelvin-Planck Statement
One interesting application of the concept of thermodynamic reversibility is the use
of the Carnot cycle to prove the equivalence of the two statements of the second
law. Let us assume, in contradiction to the Clausius statement, it is possible to
transfer Q 1 from a heat reservoir at T 1 to a heat reservoir at a higher temperature T 2
in such a way that no other change occurs in the state of any system or medium that
are involved. Then a Carnot cycle can be used to absorb Q 1 + Q 2 from the
high-temperature reservoir and reject Q 1 to the T 1 -reservoir producing Q 2 amount
of work. The combined heat transfer steps result in zero net heat exchange in the T 1 -
reservoir. On the other hand, the T 2 -reservoir gives up Q 2 amount of net heat, which
equals the amount of work produced by the Carnot cycle. The sole consequence of
the whole operation is the complete transformation of (Q 2 )-heat into (Q 2 )-work, in
contradiction to the Kelvin–Planck statement.
It can be similarly demonstrated that if the Kelvin–Planck statement were not
valid, the Clausius statement would not be valid as well. The two statements are
thus equivalent.
Carnot’s principle and the two Statements, as well as the MEH, were expressed
originally in terms of heat (more precisely, heat at high temperature and heat at low
temperature) and work. Note that the first law of thermodynamics, while it had had
its origin in the MEH in terms of heat and work (mechanical energy), underwent an
evolutionary process to becoming expressed in terms of heat, work, and energy. It is
important, therefore, to note how the two Statements underwent an idea evolution
as well to becoming expressed in terms of energy and its dissipation (Sects. 4.6 and
4.7) and, eventually, in terms of entropy and its growth (Chap. 5).
4.6 Limitation in the Amount of Heat to be Converted
into Mechanical Energy
What is the meaning of “consumption of heat” used in the MEH?
The MEH, or equivalence principle, initially meant different things to different
investigators. Rumford, Mayer, and Joule committed the MEH to be a principle of
conversion between mechanical work and heat. To another group of investigators
including Carnot, Clapeyron, Holtzmann, and Thomson (initially before 1850), the
concept meant to be an assumption of “a certain association between heat and work,
such that the two existed independently of one another but could influence each
other” [9]. It meant the coexistence of heat and work: “Sometimes coexistence was
4.5 Falling of Caloric in Reversible Processes
81
the answer is heat flow (Yes); work (No).
4.5.5 Equivalence of the Clausius Statement
and the Kelvin-Planck Statement
One interesting application of the concept of thermodynamic reversibility is the use
of the Carnot cycle to prove the equivalence of the two statements of the second
law. Let us assume, in contradiction to the Clausius statement, it is possible to
transfer Q 1 from a heat reservoir at T 1 to a heat reservoir at a higher temperature T 2
in such a way that no other change occurs in the state of any system or medium that
are involved. Then a Carnot cycle can be used to absorb Q 1 + Q 2 from the
high-temperature reservoir and reject Q 1 to the T 1 -reservoir producing Q 2 amount
of work. The combined heat transfer steps result in zero net heat exchange in the T 1 -
reservoir. On the other hand, the T 2 -reservoir gives up Q 2 amount of net heat, which
equals the amount of work produced by the Carnot cycle. The sole consequence of
the whole operation is the complete transformation of (Q 2 )-heat into (Q 2 )-work, in
contradiction to the Kelvin–Planck statement.
It can be similarly demonstrated that if the Kelvin–Planck statement were not
valid, the Clausius statement would not be valid as well. The two statements are
thus equivalent.
Carnot’s principle and the two Statements, as well as the MEH, were expressed
originally in terms of heat (more precisely, heat at high temperature and heat at low
temperature) and work. Note that the first law of thermodynamics, while it had had
its origin in the MEH in terms of heat and work (mechanical energy), underwent an
evolutionary process to becoming expressed in terms of heat, work, and energy. It is
important, therefore, to note how the two Statements underwent an idea evolution
as well to becoming expressed in terms of energy and its dissipation (Sects. 4.6 and
4.7) and, eventually, in terms of entropy and its growth (Chap. 5).
4.6 Limitation in the Amount of Heat to be Converted
into Mechanical Energy
What is the meaning of “consumption of heat” used in the MEH?
The MEH, or equivalence principle, initially meant different things to different
investigators. Rumford, Mayer, and Joule committed the MEH to be a principle of
conversion between mechanical work and heat. To another group of investigators
including Carnot, Clapeyron, Holtzmann, and Thomson (initially before 1850), the
concept meant to be an assumption of “a certain association between heat and work,
such that the two existed independently of one another but could influence each
other” [9]. It meant the coexistence of heat and work: “Sometimes coexistence was
4.5 Falling of Caloric in Reversible Processes
81