Thermodynamics/Statistical Mechanics Probability Questions

[cep]

Homework Statement

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?

Homework Equations

Equipartition theorem

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?

 

[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.

 

[vela]

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

 

[cep]

Cool, thanks guys :)