# Ideal 2-D Gas and Micro-Canonical Ensemble

1. Dec 8, 2008

### Fourier mn

1. The problem statement, all variables and given/known data
1.a. analyze an ideal gas in a two dimensional world using micro-canonical ensemble. Specifically, find the equation of state (surface tension and area will replace pressure and volume) and also the energy as a function of temperature. b. modify the equation to create a “van der Waal” – like equation for this two dimensional gas. c. compute the energy of this van der waal gas (assume a constant heat capacity at constant area).

2. Relevant equations
I know the obvious eqns for an ideal gas, but I dont know how to start this problem

3. The attempt at a solution

First, how can I apply micro-canonical ensemble to a gas with N particles, I thought that it should be canonical ensemble to a system with this order of magnitude? Second, what do they mean by a "in a 2-D world," besides the obvious that its 2-D, what kind of a system is it? Any suggestions on how to start the problem would be most welcome!

2. Dec 8, 2008

### turin

What order of magnitude are you talking about? AFAIR, the three ensebles considered in stat mech were:
1) micro-canonical: the easiest, defined as constant N, V, and E
2) canonical: more realistic version of mechanically contained ensemble, defined as constant N, but E (and V?) can vary
3) grand canonical: most general in the sense that N can also vary

I don't see any inconsistency in stating that the system is a micro-canonical ensemble; just think of it as a gas in a perfectly insulted, rigid container with no leaks.

This will effect the density of states (and, of course, the meaning of volume).