Lecutre 2: Brief Review of Thermodynamics

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Lecutre 2 Brief Review of Thermodynamics
Review of Equilibrium Thermodynamics Equilibrium
Entropy Solution Thermodynamics Equilibrium
Phase Diagrams Activity and Activity
Coefficients
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Entropy
Entropy is a state function because the level of
disorder of a system only depends on the current
condition of the system. Consequently, the
entropy change for any process joining the same
two states is the same, whether the process is
reversible or not. To calculate the
entropy change for any process we just find a
reversible path connecting the two states and
calculate its change in entropy using the
above formula.
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The Second Law
The Second Law The entropy of the universe
increases for all processes except
reversible ones, for which there is no change in
Suniv. Once disorder is created, it cannot be
destroyed.
The changes in entropy of the system and
surroundings are balanced for a reversible
process. That is entropy is only transferred, and
the original state of the universe can be
obtained by reversing the process.
If a process is not reversible, entropy is
created and the disorder of the universe is
increased. The entropy of the universe can never
decrease.
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Entropy
Entropy is a measure of the disorder in a system.
Note that for a given process, the larger the
heat flow the greater the increase in S. Also,
that a given heat flow of a process causes a
larger change in S at lower Ts. Also note that
if a reversible process is adiabatic, it is
isentropic.
Slowly remove mass
M
Work W
M
Work W
Heat Q
Heat Q
Gas
Gas
Adiabatic
Isothermal
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Criteria for Equilibrium
Irreversible processes are also called
spontaneous or natural
for irreversible processes for reversible
processes never
Definitions A chemical system is any system made
up of one or more elements. A phase is any
distinguishable region of a chemical system which
is in a well-defined state of internal equilibrium
. Phases can be open or closed depending on
whether they change or do not change the amount
of material in the phase, respectively. A
component is any independently variable chemical
species of the system For example, P in
Si, (C2H5)OH in H2O.
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Equilibrium
In a system that is in internal equilibrium, any
infinitesimal process about a point of
equilibrium is reversible.
An infinitesimal change in the system introduces
no finite driving forces and thus no dissipative
processes.
Examples of reversible and irreversible
processes Heat flow down a temperature
gradient Mixing of NaCl in water Melting of
ice in a glass of water at 273K Separation of
oil and water
For an infinitesimal, reversible process
performed on a single-phase closed chemical
system in internal equilibrium we can write
From our definition of entropy
In a chemical system only mechanical work is done.
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Equilibrium Conditions
Consider an isolated chemical system (dV0, dU0
and dN0) of two phases
?
Since the system is isolated, the total volume,
internal energy and number of particles is
constant. So any change in these quantities
for one phase must be balanced by an equal and
opposite change in the other phase.
?
For phase alpha
Rearranging
Likewise
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Equilibrium Conditions
Thus, for the total entropy we obtain the
following equation, and since entropy is a
maximum for an isolated system in equilibrium it
is equal to zero.
Distributive Equilibrium
Thermal Equilibrium
Mechanical Equilibrium
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Conditions for Phase Stability
Integrate dU
From the definition of G (2nd order Legendre
transform of U)
Substituting U into our expression for G
Gives the Gibbs Free Energy in terms of chemical
potentials and concentrations.

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The Gibbs-Duhem Equation
Starting with our expressions for the Gibbs free
energy We consider how it changes for an
infinitesimal process We see that G changes
because the amount of components changes
or because the chemical potential of the
components changes
G changes because T changes or P changes or
because the composition changes
Since these two expressions for dG are equivalent
we can equate them to find
The Gibbs-Duhem Equation which relates T, P and µ
at equilibrium in a single phase system
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Gibbs Phase Rule
Each phase of a system in internal equilibrium is
governed by its own Gibbs-Duhem equation
Each phase is described by C2 intensive
variables T, P and the C chemical
potentials. Since the Gibbs-Duhem expression
relates these C2 variables within each
phase, only C1 of them are independent. If ?
phases are in equilibrium with each other, then
we have only one T and one P for all the phases,
so we still have C2 variables. However, we now
have ? relationships between the C2 variables
since we have a Gibbs-Duhem expression for each
phase.
Note F is the number of degrees of freedom and P
is the number of equilibrium phases.
Gibbs Phase Rule
One can independently vary f intensive variables
for a system of C components and still keep ?
phases in equilibrium.
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Systems at Constant P and T
For systems at constant pressure and temperature,
equilibrium is established when the system has
minimized its Gibbs Free Energy
Since a closed system at constant T and P will
minimize its Gibbs free energy at equilibrium, we
determine what equilibrium phase a material will
be in at different conditions by determining
which phase has the lowest G.
G
G
Slope V
Slope -S
vap
liq
vap
liq
P
T
The material follows the lowest G
curve, switching from one to another at
transition points.
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Phase Diagrams
If we consider both changes in T and P,
the material follows the lowest G
surface, switching from one to another at
transition points on a coexistence curve, which
is defined as the intersection of the two
Gibbs free energy surfaces.
coexistence curve
P
T
P
liq
sol
Critical point
vap
Triple point
T
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Construction of a Eutectic Phase Diagram
Above TE and below melting points
at TE
Below TE
?GM
?GM
?GM
L
?
?
?
?
?
?
L
XB
0
XB
0
XB
1
0
1
1
at TM(B)
at TM(A)
?GM
?GM
T
L
?L
?L
?
?
?
?
?
??
?
L
L
0
1
0
XB
XB
0
1
1
XB
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Vapor Liquid Equilibrium
T
V
L
XB
0
1
The equilibrium phase diagram for a vapor-liquid
binary system often takes The form of a lens
diagram. The two-phase region is defined by
bubble point and dew point lines which give the
compositions of the liquid and vaporin
equilibrium at a particular temperature. The
difference between these compositions provides
the driving force for several types of
separations methods.