Last edited by a moderator: May 6, 2017

[Dassinia]

Hello

Homework Statement

Show that for an ideal gas:

n(E)dE=2πn/(kπT)^3/2 *E^1/2 exp(-E/kT) dE

where n(E) is the number of particles for each element of volume whose energy is between E and E+dE

Homework Equations

The Attempt at a Solution

Really don't know where to start from
Thanks

 

[Simon Bridge]

Start by reviewing your recent coursework concerning density of states and distributions.
Is the gas confined to some sort of container? What sort? Do you have notes about energy levels and so on?
That stuff.

 

[Dassinia]

I have to start from
E=1/2 mv²
dE=mv dv

I found an expression on the internet n(E)dE=N/z exp(-E/kt) * g(E)
But how can I prove that to use it ?

 

[Simon Bridge]

I'm sorry - what is the course you are doing and what level?
I'd have expected you to start from some potential - i.e. "particles in a box".

 

[Simon Bridge]

You should have a textbook and lecture notes then.
1st cycle = undergraduate: is this a first-year paper or course?

Basically I cannot help you without giving you a couple of lectures on thermodynamics.
These are things you should already have had - so you have lecture notes for those.
You need to review your notes and give it your best shot.
If there is something you don't understand in your notes, I could help with that.

I have a crash-course review:
http://home.comcast.net/~szemengtan/ see: Statistical Mechanics.
particularly ch1 and ch4.
... but it may be more advanced than you need.

What you should not be doing is looking for equations online.
They won't help you. You need to understand the physics behind the equations.

aside:

n(E)dE=2πn/(kπT)3/2 *E1/2 exp(-E/kT) dE

... reads like:
$$n(E)dE = \frac{2\pi n}{(k\pi T)^{\frac{3}{2}}}\frac{E}{e^{-E/kT}} $$
... seems funny: is this verbatim for how it was given to you?
... do you know what all the symbols mean?
... is the n(E) on the LHS the same as the n on the RHS?