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 :)

 

[paranormal]

As a scientist, it is important to understand the material that you missed in class. The equipartition theorem is a fundamental concept in thermodynamics and statistical mechanics, and it is likely that you will need to apply it to these problems. However, it is also possible to use logical reasoning to solve these problems, but it may be more difficult without a solid understanding of the equipartition theorem. I recommend reviewing the material on your own or seeking help from your instructor or classmates to better understand the concept before attempting these problems. It is important to have a strong understanding of all the concepts in your course in order to effectively solve problems and advance your knowledge in the field of science.