Modern Engineering Thermodynamics

210 CHAPTER 7: Second Law of Thermodynamics and Entropy Transport and Production Mechanisms
CLAUSIUS STATEMENT OF THE SECOND LAW OF THERMODYNAMICS
It is impossible to build a continuously operating device that will cause heat energy to be transferred from a low-temperature
reservoir to a high-temperature reservoir without the input of work energy (Figure 7.3).
High-temperature reservoir
Heat out
Cyclic heat
engine
No work!
Impossible!
Heat in
Low-temperature reservoir
FIGURE 7.3
Clausius statement.
An early nonmathematical version of the second law of thermodynamics, expressed in words, is the Clausius
statement 2 of the second law. It is easily understood using the water wheel analogy.
Another early nonmathematical verbalized version of the second law is by William Thomson (Lord Kelvin), later
modified by Max Planck 3 (1858–1947).
Both the Clausius and the Kelvin-Planck “statements” of the second law are really just verbalized consequences
of the second law. Its development by recourse to water wheel technology is clearly wrong, since a water wheel
is not a heat engine, but the conclusions are nonetheless correct. They have historical explanatory value but cannot
be used in engineering design. The power of the second law becomes apparent only when it has a mathematical
formulation. This comes later in the chapter.
The significance of Carnot’s conclusions was not recognized until the 1850s, when Rudolph Clausius (1822–1888)
and William Thomson (Lord Kelvin, 1824−1907) worked out a clear formulation of the conservation of energy
principle, which was then named the first law of thermodynamics. Carnot’s first conclusion was then named the
second law of thermodynamics by Clausius, who also expanded Carnot’s energy transformation concepts into a new
property he called entropy.
The classical Kelvin-Planck and Clausius statements of the second law also provide a classical means for defining
the concept of reversibility. The Kelvin-Planck statement limits the efficiency of a heat engine to something less
than 100%, but as yet, we have no idea how much less. To establish a more realistic efficiency limit, we need to
define the simplest possible heat engine, one that operates with simple idealized processes. Such an engine
would be frictionless and not have any losses. We call such an idealized engine reversible because the energy
flow through it could be reversed without leaving any trace on the environment.
Since the first law of thermodynamics is a conservative law (i.e., energy cannot be produced or destroyed), it has
no effect on the reversibility of a system. But the second law is not a conservative law, since entropy is produced
in every real process. Therefore, the second law is what dictates whether or not a system and its surroundings
can be returned to their original states, and in general, this is not possible if entropy is produced by the process.
Therefore, a reversible process is really synonymous with a zero entropy production process.
Processes that are not reversible are called irreversible. Phenomena that cause processes to be irreversible are
called process irreversibilities. Some typical process irreversibilities within a system are shown in the following
table.
2 The word statement is used here, because it is a verbalized rather than mathematical form of the second law.
3 In the 1890s, Planck added the concept of “continuously operating” to Kelvin’s 1850s verbalized version of the second law, so this
statement now has both names associated with it.