Geology Reference
In-Depth Information
interpretation of the mixing of ions, atoms or molecules in a solid solution, thereby
demonstrating the relationship between entropy and probability.
9.3.1 Entropy of mixing, pollution, separation and purification
Mixing is one of the most common and yet one of the most irreversible processes that
exist. Any contaminating process is one of mixing. The cost to return everything to
the initial state and recover individual substances does not hold a linear relationship
with purity grade but instead requires an added exergy input which is several times
greater in order of magnitude than the amount of exergy that was destroyed upon
mixing (Naredo and Valero, 1999).
Whilst the most common thermal, chemical, electrochemical and metallurgical
processes can have a wide range of e
ciency (oscillating between 1-90%, as was
seen in Chap. 8), those relating to separation are typically various orders of mag-
nitude lower than their minimum thermodynamic value. Indeed for the separation
of a mixture, which is in reality a decontamination process, only the microscopic
organisms such as bacteria and fungi can ever hope to achieve a notable level of
success. It is this contamination/purification or mixing/separation that holds great
importance for one of the underlying messages of the topic and which subsequently
should be analysed.
The general expression of entropy change of an ideal gas is:
Z
C
p
dT
T
Z
dP
P
S =
R
(9.2)
C
p
depends on temperature, with generic polynomial expressions like Cp
0
=
a+bT +cT
2
+:::. Only in the case of a perfect gas is C
p
constant and equal to 7=2R
if it is diatomic. Therefore, for diatomic gases and for the same percentage change,
entropy is approximately 7/2 times more sensitive to thermal effects than to pressure
ones. Generally, entropy is highly sensitive to thermal effects, whereas increased
pressure has minor negative influence. Mixing processes are usually isothermal and
isobaric, in such case the partial pressure of each gas decreases in proportion to
their molar fraction.
Therefore, the entropy generated in a mixing process of two ideal gases, A and
B, with n
A
and n
B
referring to the number of respective moles is expressed in
Eq. (9.3).
Z
x
1
P
Z
x
B
P
dP
P
n
B
R
dP
P
S
g
= S
g;A
+ S
g;B
= n
A
R
(9.3)
P
P
= R [n
A
lnx
A
+ n
B
lnx
B
]
with molar fractions x
A
= n
A
=(n
A
+ n
B
) and x
B
= n
B
=(n
A
+ n
B
), and x
A
=
(1 x
B
).
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