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# ln22f07 - LECTURE 22 STATISTICAL THERMODYNAMICS So far we...

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L ECTURE 22. S TATISTICAL T HERMODYNAMICS So far we have discussed thermo in fairly simple terms that allowed us to do two useful things: Predict reaction spontaneity from Δ G = Δ H – T Δ S Perform simple calculations of Δ G, Δ H, Δ S, B.E., w This was all put together in worksheets and permitted the ability to quickly feel useful with thermodynamics. But--It really played fast and loose with the underlying theory of thermo. It is all fine, it was just sloppy. Kind of like you didn’t earn it. So now you will earn it, with more sophisticated lectures on thermodynamic theory Statistical thermodynamics Internal energy Entropy, equilibria, and free energy

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S TATISTICAL T HERMO To this point in thermo we have dealt entirely with bulk properties of a system Provides a bulk V, T, P, G, H, S, E of a system But what about if we deal with the system one molecule at a time and ask questions about is E or S one molecule at a time. This is the study of statistical thermodynamics. And the short answer to the question is this: To find internal energy: To find internal entropy: E = ½ kT S=k ln W Which is the energy per which is the absolute entropy molecule per degree per molecule in a of motion freedom system. in a system The constant, k, in both equations is the Boltzmann constant = 1.38x10 -23 J/K
The Origin of Internal Energy Consider an atom It can move 3 ways in a 3-D coordinate Now hook that atom up to other atoms to make a molecule.

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