Chem33-1, C-hour Problem Set 2

1. Which of the following involve an increase in the entropy of the system under consideration? a. melting of a solid b. evaporation of a liquid c. sublimation d. freezing ANSWER: e.f.g.mixing separation diffusion Of the three phases, solids are most ordered and gases are most disordered. Thus, a, b, c, e, and g involve an increase in entropy. All others decrease disorder and entropy. 2.Entropy can be calculated by a relationship proposed by Ludwig Boltzmann: S = kB ln Ω Where kB = 1.38 x 10-23 J/K and Ω is the number of ways a particular state can be obtained. (This equation is engraved on Boltzmann's tombstone.) Calculate S for the three arrangements of particles in Table 10.1 of our text book. ANSWER: Arrangement I: S = k ln Ω with Ω = 1 S = k ln 1 = 0 Arrangement II: Ω = 4: S = k ln 4 = 1.38 x 10-23 J/K ln 4 S = 1.91 x 10-23 J/K Arrangement III: Ω = 6: S = k ln 6 = 2.47 x 10-23 J/K Alternatively, you could have calculated the entropy based on the probabilities for each arrangement in table 10.1. In this case you would have gotten the probabilities 1/16, 4/16, and 6/16. As a consequence the absolute values of the entropy would have been shifted but the differences between them would remain unchanged.