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The Ehrenfest urn is a model for the mixing of gases in two chambers. Classic research deals with this system as a Markovian model with a fixed number of balls, and derives the steady-state behavior as a binomial distribution (which can be approximated by a normal distribution). We study the gradual change for an urn containing n balls from the initial condition to the steady state. We look at the status of the urn after kn draws. We identify three phases of kn: The growing sublinear, thedoi:10.1137/1.9781611973006.2 dblp:conf/analco/BalajiM10 fatcat:r6g7lncekjhi3bwjue2ilffeku