Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 18

mentioned here and is well described in various texts (e.g.,Atkins and de Paula, 2006).
To quantify this inexorable transition toward a chaotic state for the universe, the sec-
ond law introduces a term called entropy , denoted by S . It is also a state function. The
change in entropy is defined as the result of dividing the energy transferred as heat by
the absolute temperature at which the transfer took place.After a spontaneous change
for a system, the total entropy of the system plus its surroundings is greater. Clausius
enunciated the second law thus: the entropy of the universe tends to a maximum .A
more precise statement of the second law is: as a result of any spontaneous change
within an isolated system the entropy increases .
The entropy transferred to a system by its surroundings is defined by

d S surr = δ q

T .

(2.9)

The total entropy change of the isolated system, that is, the universe, is the sum of the
entropy changes within the system, d S sys , and the entropy change transferred from
the system to the surroundings,

− d S surr . Thus,

d S univ = d S sys − d S surr . (2.10)

Since for any permissible process within an isolated system, d S univ ≥ 0, we have

d S sys ≥ δ q/T . This is called the Clausius inequality . Entropy is a measure of the

quality of the stored energy; it can be appropriately identified with disorder.

2.2.4 T HIRD L AW OF T HERMODYNAMICS
The third law defines the value of entropy at absolute zero. It states that theentropyof
allsubstancesispositiveandbecomeszeroatT

=

0 ,anddoessoforaperfectlycrys-

tallinesubstance. Thus, S 0.Although there have been several attempts,

no one has ever succeeded in achieving the absolute zero of temperature. Thus, the
third law explicitly recognizes the difficulty in attaining absolute zero.
To summarize, according to the first law, energy is always conserved, and, if work
has to be done by a system, it has to absorb an equal amount of energy in the form
of heat from its surroundings. Therefore, a perpetual motion machine capable of
creating energy without expending work is a pipe dream. The permissible changes
are only those for which the total energy of the isolated system, that is, the universe,
is maintained constant. The first law of thermodynamics is thus a statement regarding
the permissible energy changes for a system. The second law gives the spontaneous
changes among these permissible changes. The third law recognizes the difficulty in
attaining the absolute zero of temperature.

→ 0as T →

E XAMPLE 2.1 P RESSURE AND T EMPERATURE P ROFILES IN THE A TMOSPHERE

Problem Statement : If atmospheric air can be considered an ideal gas, it obeys the
ideal gas law in the form PV = R , where V is the molar volume of air, V = M/ ρ . ρ is