# Thermo question on mean square of concentration

1. Oct 28, 2011

### go_ducks

This problem is from Callen. In the 1st edition it is 15.4-3. I am stuck on the last part of this problem. It also appears, in a slightly different form, in the second edition of Callen as problem 19.3-5.

1. The problem statement, all variables and given/known data

15.4-3 Consider a small volume V within a two-component simple system. Let x1= N1/(N1+N2), in which N1 and N2 are the mole numbers within V. Show that

$N^2{}$(δ$\hat{x1}$)^2 = (δ$\hat{N1}$)^2 - 2x1(δ$\hat{N1}$ $\hat{N}$) + x1^2 (δ$\hat{N}$)^2

and compute the mean square deviation of concentration <(δ$\hat{x1}$)^2>.

2. Relevant equations

Actually dont know. It is in a section of the book which is related to fluctuations and correlation moments. Nothing looks relevant to me.

3. The attempt at a solution

Done the "show that"..its just taking a derivative. Quite straightforward. But I dont know how to compute the mean square deviation of concentration based on this. Nobody in my peer group knows what to do. Took it to the TA and he was also unsure what to do with it. Just looking for how to get started.