Chap 7: The 2nd and 3rd Laws

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Chap 7 The 2nd and 3rd Laws

• Entropy and Gibbs Free Energy
• Why do things fall apart?
• Why doe some things happen spontaneously?
• Why does anything worthwhile take work?
• Im not sure that our discussions will completely
  answer this, but well give it a go.

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7.1 Spontaneous Change

• Last chapter, we learned about work, heat and
  enthalpy (at least I hope we did, it will be on
  the final)
• We learned that all energy in the universe is
  conserved and constant
• But thats not really very useful
• We want to predict the behaviour of the universe
  around us.

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Spontaneous Changes

• We know from our own
• experiences that some
• things will happen
• spontaneously

We can make the reverse happen (heat a metal cube
up, partition a gas), but that takes work (energy)
Metal cools
Gas expands
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Spontaneity in Processes

• A process is spontaneous if it has the tendency
  to occur without being driven by an external
  influence
• Dont confuse spontaneous with speedy or
  rapid!

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7.2 Entropy and Disorder

• If we think about the universe around us and look
  at all of the spontaneous changes we have
  observed over our lifetimes, one thing is
  certain
• Energy and Matter tend to disperse in a
  disorderly fashion
• Gas molecules dont pile up on one side of a
  flask
• Buildings fall apart
• Thing left untended will get worse

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The 2nd Law of Thermodynamics

• The entropy of an isolated system
• increases in the course of any
• spontaneous change
• We can summarize this law mathematically as

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The 2nd Law

• What does this mean?
• If a lot of heat energy is transferred, there is
  a large increase in entropy
• This change in entropy is more noticeable at
  lower temperatures than higher temperatures
  (relatively)
• Temperature must be in Kelvin and heat must be in
  Joules

?
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Entropy

• Entropy is a measure of disorder, according to
  the second law of thermodynamics
• The entropy of an isolated system increases in
  any spontaneous reaction
• Entropy is a state function

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Changes in Entropy

• The equation we obtained from the second law
• is valid for isothermal situations (change of
  state, gas expansion) but we frequently want to
  be able to determine the entropy as temperature
  changes

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Entropy Change as a Function of Temperature at
Constant Volume

• If T2 gt T1, then the logarithm is and entropy
  increases
• Makes sense since we are raising the temperature
  and thermal motion will increase
• The greater (higher) the heat capacity, the
  higher the entropy change

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Entropy Change as a Function of Changing Volume

• We can use a similar logic to derive the change
  in entropy when the volume changes
• When V2 gt V1, the entropy increases
• Note Units are still J/K

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Entropy Change as a Function of Pressure

• Remember Boyles Law?
• We can substitute this relationship into the
  equation for entropy change as a function of
  volume to get

Entropy decreases for a sample that has been
compressed isothermally (P1gtP2)
?
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Entropy Changes Occurring as a Function of
Physical State Changes

• What happens to the entropy of a system as we
  change state?
• Remember Melting point temp Tf
• Boiling Point temp Tb
• Temperature doesnt change as we heat a sample to
  cause a phase change
• Lets look at liquid water --gt water vapor

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Boiling Water and Entropy

• Lets get 3 facts straight
• At a transition temperature (Tf or Tb), the
  temperature remains constant until the phase
  change is complete
• At the transition temperature, the transfer of
  heat is reversible
• Because we are at constant pressure, the heat
  supplied is equal to the enthalpy

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Water Boiling and Entropy
(at the boiling temperature)

• We use the º superscript to denote the
  standard entropy (the entropy at 1 bar of
  pressure)

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Ice Melting and Entropy

• We use the same logic to determine the entropy of
  fusion, ?Sfus

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Troutons Rule

• Because the entropy increases so much in going
  from liquid to a gas, many liquids have similar
  ?Svap values

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Troutons Rule

• Why is this?
• Positional disorder of a gas versus a solid or
  liquid (which are pretty close to the same thing)
• Exceptions Molecules with very weak or very
  strong intermolecular forces
• Helium, Water and Methanol

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7.5 A Molecular Interpretation of Entropy

• Weve looked at the changes to the entropy of a
  system, but now lets look at the absolute
  entropy of the system itself
• If we had a perfect crystal, the positional
  disorder would be ____
• If the temperature was 0K, the would be ___
  thermal disorder, so the entropy would be ___

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The 3rd Law

• The entropies of all perfect crystals approach
  zero as the absolute temperature approaches zero.

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The Boltzmann Formula
Where k Boltzmanns constant 1.381 x10-23
J/K W of ways atoms or molecules in the system
can be arranged and still give the same total
energy

• W is a reflection of the ensemble, the collection
  of molecules in the system
• This entropy value is called the statistical
  entropy

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The Boltzmann Formula

• Lets think about W (Wahrscheinlichkeit) for a
  moment
• Word translates as probability or likelihood
• If we could only arrange the atoms/molecules in
  the system one way, there would be ___ entropy
  since ln(1) __
• As we start to increase the population of the
  system, we can arrange the members of the system
  in different ways and still have the same total
  energy, so W increases.

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The Boltzmann Formula
Example 7.7
Each molecule can be oriented 2 ways W 2 x 2 x
2 x 2 16
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Residual Entropy

• We know Boltzmanns concept of the ensemble is
  correct from observations of molecules at low
  temperature (and using logic with some cynicism)
• As we get near absolute zero, the entropy within
  the crystal becomes increasingly a function of
  the positional entropy within the ensemble cause
  by the packing of the components
• Lets think about this for a minute

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Residual Entropy

• The entropy of 1 mole of FClO3 at T 0 K is 10.1
  J/K. Suggest and interpretation.
• How many molecules do we have?
• How many ways can each molecule be arranged?
• What is the residual entropy?
• Pretty close!