ProbSet7_solutions(2)

# 4 ln 04 032 ln 032 024 ln 024 004 ln 004 kb p0

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: et 7 UC Berkeley Page 7 (ii) What is the ratio of the multiplicity for the two distributions? (iii) Calculate the difference in the entropy of the two distributions in units of J mol-1 K-1. Answer: Because the number of molecules is large enough, this question is best answered using the probabilistic definition of entropy, rather than trying to calculate factorials. For the first distribution: N total = 10000 + 8000 + 6000 + 1000 = 25000 10000 8000 = 0.4 p1 = = 0.32 25000 25000 6000 1000 p2 = = 0.24 p3 = = 0.04 25000 25000 S = − N total × [ 0.4 ln 0.4 + 0.32 ln 0.32 + 0.24 ln 0.24 + 0.04 ln 0.04 ] kB p0 = = − N total × [ −0.367 − 0.365 − 0.343 − 0.129 ] = N total × 1.204 For the second distribution: N total = 10000 + 7000 + 5000 + 3000 = 25000 10000 7000 = 0.4 p1 = = 0.28 25000 25000 5000 3000 p2 = = 0.20 p3 = = 0.12 25000 25000 S = − N total × [ 0.4 ln 0.4 + 0.28 ln 0.28 + 0.20 ln 0.20 + 0.12 ln 0.12 ] kB p0 = = − N total × [ −0.367 − 0.356 − 0.322 − 0.254 ]...
View Full Document

Ask a homework question - tutors are online