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Chapter 3 Statistical Thermodynamics

Chapter 3 Statistical Thermodynamics. From another source: Statistical Thermodynamics: The basics. Nature is quantum-mechanical Consequence: Systems have discrete quantum states. For finite “closed” systems, the number of states is finite (but usually very large) Hypothesis

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Chapter 3 Statistical Thermodynamics

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  1. Chapter 3Statistical Thermodynamics

  2. From another source:Statistical Thermodynamics: The basics • Nature is quantum-mechanical • Consequence: • Systems have discrete quantum states. • For finite “closed” systems, the number of states is finite (but usually very large) Hypothesis In a closed system, every state is equally likely to be observed. Consequence ALL of equilibrium Statistical Mechanics and Thermodynamics

  3. …, but there are not many microstates that give these extreme results Each individual microstate is equally probable Basic Assumption If the number of particles is large (>10) these functions are sharply peaked

  4. Does the basic assumption lead to something that is consistent with classical thermodynamics? Systems 1 & 2 are weakly coupled such that they can exchange energy. These correspond to Reif’s systemsA & A'. Find the energy E1that is most probable. The probability of Ahaving a particular energy E1is proportional to the product of the number of accessible states of A times the number of accessible states of A' consistent with energy conservation: E = E1 + E2 Each configuration is equally probable; but the number of states that give a particular energy E1is not known. Find it by finding the energy where the left side of the above equation has a maximum.

  5. Energy is conserved! dE1=-dE2 This can be seen as an equilibrium condition Definition!! The physical interpretation of β is that it is a measure of a system’s temperature!

  6. Also, DEFIINE the EntropyS of a system: With kB= 1.380662 10-23 J/K = Boltzmann’s constant. In thermodynamics, the Kelvin temperature scale is defined such that But we just defined:

  7. So, this gives a “statistical” definition of temperature: SoEntropy and temperature are both related to the number of accessible states. • So, the fundamental postulate leads to: • An equilibrium condition. Two systems are in thermal • equilibrium when their temperatures are equal. • A maximum entropyfor the coupled systems when they • are at equilibrium.As we’ll see, this is related to the • 2nd Law of Thermodynamics. • The 3rd Law of Thermodynamics. We’ll see later.

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