i. From a knowledge of the partition function Z derived in class, write an expression for the entropy S of an ideal FD g

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I From A Knowledge Of The Partition Function Z Derived In Class Write An Expression For The Entropy S Of An Ideal Fd G 1 (118.32 KiB) Viewed 25 times

i. From a knowledge of the partition function Z derived in class, write an expression for the entropy S of an ideal FD gas. Express your answer solely in terms of nr, the mean number of particles in state r. ii. Write a similar expression for the entropy S of a BE gas. iii. What do these expressions for S become in the classical limit when ñr « 1? Use the above two results and S = k(In Z + aÑ + BĒ), which we found in class. , =
Show that the answer to (c)iii is what you would expect for an ideal gas with “fudged clas- sical” statistics (i.e., classical statistics with the correction factor for indistinguishability thrown in). [Start by finding the entropy of a single particle, which has probabilities Pr = ñy/N of being in stater. Then find the entropy of all Ñ indistinguishable particles.] -