# Homogeneity criteria (Thermodynamics)

## Homework Statement

The problem is this one:

Consider a monocomponent fluid, isolated and in equilibrium,

a) Find the homogeneity criteria that must fulfill the number of microstates Ω(U,V,N).

b) If Ω(U,V,N)=exp(a*Vα*Uβ) when a>0 use the result in a to find the condition that have to fulfill α and β.

c) Find the Helmholtz energy expresion and study the stability of the system depending of α and β

I don't knok how to find the 1º part, so I cannot continue, if you Can help me, I'll be very grateful,

2. Homework Equations [/B]

S=Kb·ln(Ω) (And possible Much More)

## The Attempt at a Solution

I don't have any idea on how to solve this problem, because i don't find any information in the web, but i think that probable, this homogeneity criteria means Criteria for equilibrium in statistical thermodynamics, that I find some information in the web, but this criteria only arrives that in a isoltated sistem, all the parts of the system must have the same Temperature, and I think that the problem shoud not focus in this way.

I see that possible one criteria is that Ω(λU,λV,λN)=λ*Ω(U,V,N)

A little help, can help me to solve this problem[/B]