{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Fa08-MT1-SunRev1-Soln

# Fa08-MT1-SunRev1-Soln - Sterling’s approximation N is...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4. There are N /2 particles each of substances A and B . First, we want to ask how many ways are there of putting these N total particles into the N possible slots of the alloy. First, let’s look at the A particles. We want to put N /2 objects into N slots. There are N - choose- N /2 ways to do this. Remembering a little probability theory, this equals N N / 2 " # \$ % & = N ! ( N / 2)!( N / 2)! Now, we have N/2 empty spaces left, and exactly N /2 particles of B to fill them! There’s only one way of doing this, so the total number of microstates for the binary allow is: " = N ! ( N / 2)! [ ] 2 The entropy is S = k B ln Ω . The logarithm of the number of states is found using

This preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Sterling’s approximation ( N is very large!): ln " = ln N ! # 2ln( N /2)! \$ N ln N # 2 N 2 ln N 2 = N ln N # ln N /2 ( ) = N ln2 Therefore, the entropy of the binary alloy, with N = 10 23 is: S = Nk B ln2 = 7 " 10 22 k B Another way of seeing this is that there are 2 choices for each of the N slots! b) There is no work, heat transfer, or change in temperature, so the change in internal energy should be 0! c) If, on the other hand, A and B were not distinct from eachother, there would only be 1 way of putting all the particles into the N slots! So, S = 0....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern