Consider an isolated gas-like system consisting of a

Chapter 20, Problem 20.58

(choose chapter or problem)

Consider an isolated gas-like system consisting of a boxthat contains N = 10 distinguishable atoms, each moving atthe same speed v. The number of unique ways that these atomscan be arranged so that NL atoms are within the left-handhalf of the box and NR atoms are within the right-handhalf of the box is given by Nl/Ni)Nr\, where, for example, thefactorial 4! = 4-3-2-1 (the only exception is that 0! = 1).Define each unique arrangement of atoms within the box tobe a microstate of this system. Now imagine the followingtwo possible macrostates: state A where all of the atoms arewithin the left-hand half of the box and none are within theright-hand half; and state B where the distribution is uniform(that is, there is the same number in each half). SeeFig. 20-21. (a) Assume the system is initially in state A and,at a later time, is found to be in state B. Determine thesystems change in entropy. Can this process occur naturally?(b) Assume the system is initially in state B and, at a latertime, is found to be in state A. Determine the systemschange in entropy. Can this process occur naturally?FIGURE 20-21 58.