Thermodynamics/Statistical Mechanics Probability Questions

1. Feb 17, 2012

cep

1. The problem statement, all variables and given/known data
On this problem set, there are multiple questions regarding the probability of events:

1. Consider a box of volume V containing N molecules. Assume that the molecules in the box are free of all interactions, that is, that the equation of state is that of an ideal gas.
(a) What is the probability of finding all the molecules in a portion of the container having a volume
V/2?
(b) If N=1023, what is the numerical value of this probability?

2. A volume V contains NA molecules of type A and NB molecules of type B. A valve is opened and M molecules flow out. What is the probability that among the M molecules there are mA of species A and mB of species B?

3. Suppose that a volume V is subdivided into M sub-volumes. Let there be N molecules in V. What is the probability that some one sub-volume will contain N’ molecules?

2. Relevant equations

Equipartition theorem

3. The attempt at a solution

I missed class, and I know the material I missed was the equipartition theorem. I am unsure if these problems require application of the equipartition theorem, or if I can just logic at them. Conveniently, this lecture was taken from a textbook that was not assigned for the course. Thoughts?

2. Feb 17, 2012

gash789

I don't really think an understanding of equipartition theorem is required further than what Wikipedia can provide. Just consider it a big statistical problem (you have no interactions) and should be okay.

3. Feb 17, 2012

vela

Staff Emeritus
They don't. They're just probability problems.

4. Feb 17, 2012

cep

Cool, thanks guys :)