The Second Law: Machinery

1
Chapter 5

• The Second Law Machinery

2
Internal Energy
U is a function of S and V
Purely thermodynamic definition of temperature
Generate relations between the properties of a
system and discover the power of thermodynamics
for establishing unexpected relationships.
3
Maxwell Relations
4
Gibbs Energy
5

• Gibbs energy varies with temperature and
  pressure.
• As S gt 0, G decreases when the T is raised at
  constant p and composition.
• G decreases most sharply when the entropy of the
  system is large
• Therefore, the Gibbs energy of the gaseous phase
  of a substance, which has a high molar entropy,
  is more sensitive to temperature than its liquid
  and solid phases.
• V gt 0, G always increases when the pressure is
  increased at constant T and composition.
• As the molar volumes of gases are large, G is
  more sensitive to pressure for the gas phase than
  others.

6
T dependence of G

• If the enthalpy of the system is know, then the
  temperature dependence of G/T is known.
• The equilibrium constant of a reaction is related
  to G/T.

This equation is most useful when applied to
changes DG Gf - Gi
7
p dependence of G
The Gibbs energy of solids and liquids are
supposed to be independent of pressure.
If we set pip
8
Chemical Potential
For real gases, the true pressure, p, is replaced
by an effective pressure called fugacity,f.
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Fugacity and Pressure
Hypothetical kinetic energy only gas
Entire effect of all the intermolecular forces
All gases are perfect as p 0, so f p
as p 0, then f 1 as p 0
10

• For most gases Z lt 1 up to moderate p and Z gt 1
  for higher p.
• If Z lt 1 throughout the integration, then f lt 1.
• This means f lt p, the molecules tend to stick
  together.
• Chemical potential of the gas is less than that
  of a perfect gas.
• At higher p, Z gt 1, f gt 1 and f gt p, repulsive
  interactions are dominant and tend to drive the
  particles apart.
• Chemical potential of the gas is greater than
  that of a perfect gas at the same T.
• The fugacity of nitrogen at 273 K.