L2A The Second Law.pdf

# L2A The Second Law.pdf - Chapter 2A ENTROPY AND THE SECOND...

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Chapter 2A ENTROPY AND THE SECOND LAW

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Outline of this Chapter 1. Microstate, macrostate and multiplicity 2. Coin flipping model, two- state paramagnet and Einstein’s solid 3. The postulate of equal a priori probabilities 4. The most probable configuration 5. Energy exchange and irreversibility 6. Stirling’s approximation for large numbers 7. Sharpness of multiplicity for very large systems 8. Entropy and the Second Law of Thermodynamics PHYS4050 THERMODYNAMICS AND STATISTICAL PHYSICS 2
Mysterious Problems in Thermodynamics You might think about the possible answers of the following questions: Why does heat flow from a hotter object to a cooler object spontaneously? Why do so many processes that obey the 1 st law not happening naturally? Why is perpetual motion machine impossible (never-stop machine)? If energy is conserved in this universe, why should we worry about energy crisis (energy shortage)? Why does time flow only in the forward direction, but not the backward direction (the arrow of time)? PHYS4050 THERMODYNAMICS AND STATISTICAL PHYSICS 3

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Simple Model: Coin Flipping Toss three identical coins, each has two equally probable outcomes: Head (H) or Tail (T). Each of the 8 outcomes (e.g. HHT) is called a microscopic state or microstate . Each microstate is equally probable, with a probability of: PHYS4050 THERMODYNAMICS AND STATISTICAL PHYSICS 4 Coin A Coin B Coin C H H H H H T H T H T H H H T T T H T T T H T T T P(A,B,C)=P(A)P(B)P(C)=(1/2)(1/2)(1/2) = (1/8) What is the condition for this to hold?
Macrostate These are called the macroscopic states or macrostates . Knowing a microstate can determine the corresponding macrostate, but the reverse is not true . E.g. the microstate HHT corresponds to the macrostate 2H. However, the macrostate 2H may come from three possible microstates, i.e. HHT, HTH and THH. PHYS4050 THERMODYNAMICS AND STATISTICAL PHYSICS 5 Coin A Coin B Coin C #H H H H 3 H H T 2 H T H 2 T H H 2 H T T 1 T H T 1 T T H 1 T T T 0 Possible outcomes of the total number of Heads ( or Tails ): 3H, 2H, 1H or 0H.

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