The Second Law of Thermodynamics

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The Second Law of Thermodynamics
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Coin Flip Problem

• You have two pennies

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• What combinations of these pair of pennies are
  possible?

One way to get 2 Heads, 2 ways to get H and T,
one way to get 2 Tails
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• The likely state of this system will be one Head
  and one Tail.
• Now imagine having 3 pennies. What are the
  combinations?
• 1 HHH N!/(n!(N-n)!
• 3 HTT N of pennies
• 3 HHT n of heads, etc.
• 1 TTT

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• Extend this analysis to 50 pennies. The chance
  that you could get 50 heads or 50 tails is
  vanishingly small.
• The most likely combination will be those with
  the most variations.

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• Natural processes proceed toward those states
  that have the greatest number of chances to get
  equivalent outcomes.
• For four pennies there is 6 ways to get two heads
  and two tails, but only one way to get 4 heads.
• For 50 pennies there are 12.6 Million different
  combinations 25 head or 25 tails.

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Entropy

• A measure of disorder.
• Natural processes proceed to increasing disorder.
• Disorder means lack of predictability.
• Those states that have the most order are the
  least likely for the system to end up in.

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• Question? Would conservation of energy allow the
  process whereby a cup of hot water sitting on
  your kitchen table would suddenly freeze?
• A. Yes
• B. No

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Why doesnt it happen?

• Because the frozen liquid represents a more
  ordered state than the liquid state.
• There are many more probable states available for
  the system to be in and so thats where it will
  go.

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• Lord Kelvin used Carnots concepts to analyze the
  heat flow into and out of Carnots engine.
• He discovered that the ratio of Q/T was constant
  and called this state function entropy, S.
• The change in entropy became a measure of whether
  a reaction was spontaneous or not, DS gt 0 meant
  spontaneous.