# Thermodynamical fluctuations, mean square deviation help!

1. Nov 12, 2008

### EvilLost

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

Recalling that k=R/Na (Na is Avogadro's number), show that the density of fluctuations of an ideal gas are given by :

<(dp)^2> / p^2 = 1 / (N*Na) where p is the density (mass/V)

That is, the relative mean square density deviation is the reciprocal of the number of molecules in the subsystem.

2. Relevant equations

<(dN)^2> = <N^2> - <N>^2 from my book

3. The attempt at a solution

I have no idea where to even begin with this..I have a whole series of problems that ask me to find the "mean square deviation of ____". I understand what an expectation value is, and that i have the given equation for the value.

But HOW do I find <P> or <P^2> ?? Normally I would take the value*probability (sum of X*P(X) right?) but in this case....what is my probability? what is my value??

Where do I even start!?!?

Plz help I have 4 problems like this and am stuck in the exact same place on all 4.

2. Nov 13, 2008

### weejee

You may look up "grand canonical ensemble" or "grand partition function" in any thermodynamics textbook. It'll help.