Entropy and the 2nd Law

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Entropy and the 2nd Law

• Order and Disorder

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Impossible Events

• It is impossible for heat to spontaneously move a
  block across a table
• This does not violate the conservation of energy
  (1st law)

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Impossible Machines

• It is impossible to convert heat completely into
  useful energy
• Again, this does not violate the 1st law
• Heat engines always require a temperature
  difference

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The 2nd Law of Thermodynamics

• In order to explain why some events are
  impossible, we need an additional law besides
  conservation of energy (1st law)
• Definition Entropy is a measure of the amount of
  disorder in a system
• The 2nd Law of Thermodynamics In an isolated
  system, entropy always increases

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Example

• The rock garden at the Ryoan-ji temple must be
  raked every day
• Isolated system (no one rakes) Entropy increases
• Non-isolated system (raked) Entropy remains
  constant

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Reason for the 2nd Law

• The number of ways a system can be in an ordered
  state (low entropy) is much smaller than the
  number of ways a system can be in a disordered
  state (high entropy)
• Example There are a vast number of ways to
  arrange books randomly on a shelf, but only one
  way to arrange them alphabetically

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Other Statements of the 2nd Law

• Heat cannot be converted entirely into work
• Heat cannot spontaneously flow from cold to hot
• No machine can be 100 efficient (that is,
  produce no heat)
• Time only flows in one direction
• All useful energy will eventually end up as
  low-temperature heat

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Mixing Example

• A drop of ink in water will end up evenly mixed
  after a period of time
• Ink is very unlikely to reassemble into a drop
• However, sand mixed with water will eventually
  settle to the bottom because the system is not
  isolated (gravity does work)

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Perpetual Motion Machines

• Two types of perpetual motion machines
• Type 1 Works with no external energy source
  (forbidden by 1st law)
• Type 2 Works with only heat as input (forbidden
  by 2nd law)

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Information Content

• High entropy string of characters (random)
• ABLWEIOKWKSLBYDKWPQ
• Lower entropy string of characters (English)
• IWONDERABOUTTHETREES
• English is so redundant that you could rewrite
  any sentence using only two letters (if youre
  clever)

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File Compression

• A compressed file is a shortened version of a
  file with maximum entropy (random characters)
• As a consequence of the 2nd law, no computer
  program can compress every file
• English language files can be compressed by about
  a factor of 8

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The Direction of Time

• If time ran backwards, the ink in colored water
  would eventually reassemble into a drop
• Three reasons time runs forward
• Entropy always increases (2nd law)
• Cant remember the future
• Kaons (a subatomic particle) behave differently
  when time is reversed

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Self Assembly

• Simple molecules can and do self-assemble into
  more complex molecules
• Much of the energy in this process is wasted
  (converted to heat)
• Self-assembly does not violate the 1st or 2nd law
  of thermodynamics

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Non-isolated Systems

• Entropy can be decreased by supplying energy from
  an external source
• Example One can remove ink from water (e.g.
  through distillation) and reassemble it into a
  drop by doing work on the system
• This does not violate the 2nd law because entropy
  must increase only in isolated systems

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The Big Picture

• The surface of the earth is provided with
  external energy

Sun
Earth
Radioactive Decay
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Entropy and Evolution

• Evolution Total entropy of earth decreases while
  total entropy of Earth solar system increases
• Sun, geological heating and Earths gravity all
  supply energy to the biosphere
• Thus, the biosphere is not an isolated system