Problem 36P

Consider an Einstein solid for which both N and q are much greater than 1. Think of each oscillator as a separate “particle.”

(a) Show that the chemical potential is

(b) Discuss this result in the limits N ≫ q and N ≪ q, concentrating on the question of how much S increases when another particle carrying no energy is added to the system. Does the formula make intuitive sense?

Calculus 1 Lecture 3 9/13/16 Professor’s Comments Free tutoring available at Rutgers Learning Centers Khan Academy has videos available on most topics Study groups are highly encouraged Limit Loose definition: The value a function approaches but does not reach Calculus was done for 250 years without any formal definition of a limit Limit has nothing to do with the value of the function at a specific point, it only tells us what value the function is approachi