Page 15 - Entrophy Analysis in Thermal Engineering Systems

Fundamental concepts 5

1.5 Second law of thermodynamics

The second law is based on the observations that thermodynamic pro-
cesses proceed spontaneously in certain directions. It is an empirical law as
no experimental observation has violated its validity yet. A well-known
statement of the second law credited to Clausius says that heat cannot be
transferred from a cooler body to a warmer body without an external effect.
Based on the observations in nature, the spontaneous heat transfer process
takes place in one direction only: from a hot region to a cold region. An
engineering application of the Clausius statement of the second law is refrig-
erator. To maintain the inside of a refrigerator cool, heat should be trans-
ferred from the interior part of the refrigerator to the surrounding with
the use of a compressor (i.e., the external effect).
Another well-known statement of the second law is credited to Lord
Kelvin (William Thomson) and Max Plank, which says that it is impossible
to construct an engine, which receives heat and converts it all to work. In
other words, the efficiency of a heat engine may never reach 100%. Any
attempt made in the past by engineers or inventors to violate the Kelvin-
Planck statement of the second law was unsuccessful. Indeed, earlier than
Clausius, Kelvin, and Plank, Sadi Carnot had understood the second law
[4]. As an engineer, Carnot’s main goal was to design an engine that would
produce a maximum work from a given quantity of heat. His efforts led to
the invention of an engine that would operate on a cycle consisting of two
isothermal and two adiabatic processes.
The Carnot cycle played an important role in formulation of the second
law by Thomson and Clausius, which led to the introduction of entropy by
the latter as a new thermodynamic property. Clausius showed that in a
reversible process, the change in the entropy of a system, S, is related to
an infinitesimal heat transfer δQ by the following relation.

δQ
dS ¼ (1.9)
T
rev
where T denotes the absolute temperature of the system and has units of
Kelvin.
Eq. (1.9) is the analytical formulation of the second law in differential
form. It explicitly shows that the change in entropy depends solely on the
amount of heat transfer and temperature. To calculate the entropy difference
between two states of a system, Eq. (1.9) is integrated along a reversible path.