# Stat Mech Question

#### latentcorpse

An ideal gas of N molecules in a volume V. Write down the mean and standard deviation of the number of molecules n to appear in a volume V/3. Sketch the probability distribution of n and of n/N. Indicate how the curves change as N increases.

ok. $\bar{n}=\sum_i n_i P_i$

do i use $P_i$ form the grand canonical distribution or from teh canonical distribution here? i was going to go with the former as the subsystem of volume V/3 is an open system i.e. it can exchange energy AND particles with the rest of the system - but i wanted to check??

for the variance, do i just use

$\bar{\Delta n^2}= \bar{n^2} - \bar{n}^2$???

what would the graphs look like?

cheers

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