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Unformatted text preview: Lecture 8 1 Partition Functions and Ideal Gases (Chapter 18.1, 2) As we discussed last time, for gases where the number of available eigenstates is greater than N we can write ( 29 ( 29 , , , indistinguishable! ! N q V Q N V N = We will explicitly determine the molecular partition function for an ideal gas, using our available knowledge from Q.M. For an ideal monatomic gas, there can only be two contributions to the energy: . trans elec = + These energies are independent, so: . trans elec q q q = ( 29 First, , i trans i q V e - = For an atom in a cube of side a : ( 29 2 2 2 2 , , 2 8 , , 1,2,3... x y z i n n n x y z x y z h n n n ma n n n = = + + = Lecture 8 2 ( 29 2 2 2 2 2 , , 1 2 2 2 2 2 2 2 2 2 1 1 1 exp 8 exp exp exp 8 8 8 x y z x y z trans x y z n n n y x z n n n h so q n n n ma h n h n h n ma ma ma = = = = =- + + =- - - Since the box is a cube, each sum is identical!...
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