Thermodynamics and the Phase Rule
GLY 4200
Fall, 2012
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Thermodynamic Background
• System: The portion of the universe that is
being studied
• Surroundings: The part of the universe not
included in the system
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Free Energy
• Any change in the system involves a transfer
of energy
• All chemical systems tend naturally toward
states of minimum Gibbs free energy
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Gibbs Free Energy
• G = H - TS
• Where:




G = Gibbs Free Energy
H = Enthalpy (heat content)
T = Temperature in Kelvin
S = Entropy (a measure of randomness)
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Alternative Equation
• For other temperatures and pressures we can
use the equation:
dG = VdP – SdT
 where V = volume and S = entropy (both molar)
• This equation can be used to calculate G for any
phase at any T and P by integrating
 GT2P2 - GT1P1 = ∫P1P2VdP - ∫T1T2SdT
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Using Thermodynamics
• G is a measure of relative chemical stability for a
phase
 We can determine G for any phase by measuring H and S
for the reaction creating the phase from the elements (SiO2
from silicon and oxygen, for example)
 We can then determine G at any T and P mathematically
• How do V and S vary with P and T?
 dV/dP is the coefficient of isothermal compressibility
 dS/dT is the heat capacity at constant pressure (Cp)
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Applying Thermodynamics
• If we know G for various phases, we can
determine which is most stable
• With appropriate reactions comparing two or
more phases, we can answer questions like:
 Why is melt more stable than solids at high T?
 Which polymorphic phase will be stable under
given conditions?
 What will be the effect of increased P on melting?
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High Pressure
High pressure favors low
volume, so which phase
should be stable at high
P?
• Hint: Does the liquid or
solid have the larger
volume?
Figure 5-2. Schematic P-T phase diagram of a
melting reaction. Winter (2001) An
Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.
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High Temperature
• High temperature favors
randomness, so which
phase should be stable
at higher T?
• Hint: Does liquid or
solid have a higher
entropy?
Figure 5-2. Schematic P-T phase diagram of a melting
reaction. Winter (2001) An Introduction to Igneous
and Metamorphic Petrology. Prentice Hall.
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Stability
• Does the liquid or solid
have the lowest G at
point A? at point B?
Figure 5-2. Schematic P-T phase
diagram of a melting reaction.
Winter (2001) An Introduction to
Igneous and Metamorphic Petrology.
Prentice Hall.
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Intensive Property
• An intensive property does not depend on the
amount of material present
 Examples: Temperature, density, electric or
magnetic field strength
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Phase
• Phase: Any homogeneous region, characterized by
certain intensive properties, and separated from other
phases by discontinuities in one or more of those
intensive properties
 Solid, often a mineral
 Liquid
 Vapor
• Note: # of regions is not important, just the # of kinds
of regions
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Reaction
• Some change in the nature or types of phases
in a system
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Josiah Willard Gibbs
• Josiah Willard Gibbs (1839 - 1903)
has been reckoned as one of the
greatest American scientists of the
19th century
• He provided a sound
thermodynamic foundation to much
of Physical Chemistry
• Yale educated, he was awarded the
first Doctor of Engineering in the
U.S., and was appointed Professor
of Mathematical Physics at Yale in
1871
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Phase Rule
• The Phase Rule (J. Willard Gibbs)
f=c-p+2
 System of c components and p phases has variance
“f”, the degrees of freedom
 f = # degrees of freedom = The number of
intensive parameters that must be specified in
order to completely determine the system
 Intensive variables are pressure, temperature, and
composition, that can be changed independently
without loss of a phase
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Phase Rule 2
 p =number of phases
• phases are mechanically separable constituents
 c = minimum number of components, which are
chemical constituents that must be specified in
order to define all phases
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3000K
H2O ↔ H2 + ½O2
• Two components are present - since the
other can be made from whichever of the two
have been chosen
• Thus, a stoichiometric relationship between
substances reduces the number of
components necessary
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Alternative Definition of
Number of Components
• The minimum number of pure chemical
substances that are required for arbitrary
amounts of all phases of the system
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Extended Phase Rule
f=c-p+x
• Where x is the number of intensive variables,
pressure, temperature, composition, and
possibly magnetic and electric fields, that can
be changed independently without loss of a
phase
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