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We can calculate other mechanical thermodynamic properties M j. Stat. Mech. Postulate: If you can calculate a mechanical property X i consistent with the macroscopic parameters, then, <X i > =macroscopic thermodynamic X. Using the postulate.

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## Using the postulate

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**We can calculate other mechanical thermodynamic properties**Mj Stat. Mech. Postulate: If you can calculate a mechanical property Xi consistent with the macroscopic parameters, then, <Xi> =macroscopic thermodynamic X Using the postulate Now that we know the probability of finding the quantum state with Ej at a given N,V**Going back to the calculation of mechanical properties…**Pressure With these tools in hand , we can now combine mechanical properties with thermodynamics and extract information about nonmechanical functions (like S or T)**A**A A A A B B B B B heat bath(T) Consider 2 ensembles A and B that become in thermal contact, with no change in volume dV = 0 ; dA = 0 dB = 0 Derivation of b Initially W({a,b}) = W({a*}) x W({b*}) Ensemble A bA Ensemble B bB What are the b values at the new equilibrium?**The sum of the changes in energy in each system yields the**infinitesimal change in the total energy**Derivation of b**Approaching equilibrium, there is an increase in the value of EA, heat is transferred from B to A. bA>bB At equilibrium bA =bB any change in W({a}) will be canceled by a similar change in W({b}) 1st law: equilibrium means TA =TB, and approaching equilibrium heat will be transferred from B to A when TA<TB**and since**and we obtain heatrev exchange workrev E and p relations**From thermodynamics, we already know that**or Gibbs Entropy Entropy**in the limit of T0**So far we worked with energy states, but we can easily change to levels, by counting how many times each “state” is repeated degeneracy= W(N,V) States vs levels in the limit of T Q(N,V,T) constant = number of states

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