A question for gas cloud physics gurus.....?

Question

I have a cloud. It is in thermodynamic equilibrium. I assume this means it is at the same temperature throughout. Now, what does this mean for the kinetic energy distribution of the particles? What are the populations of the bound energy states of the cloud in? And the ionisation states of the atoms. What abundances are there?

I am currently looking at Ekin = 1/2 mv^2 , Saha and Boltzmann equations but am getting nowhere.

Can anyone help?

Many thanks.

Answer 1

thermodynamic equilibrium does NOT mean same temp throughout (you use the word isothermal for that).  thermo eq. means that you have sufficient time so that all chemical reactions and all distributions of states of matter are dependent solely on the local temperature, and not on such non equilibrium processes as radiation from other parts of the gas cloud or shock waves..

if the gas is at thermal equilibrium, the speeds of the gas are distributed according to a Gaussian distribution, and so kinetic energies will have the same spread

without more information, i can only describe ratio of states...suppose you have two states, X and Y, that are at energies E(X) and E(Y) (where Y>X)

the probability of finding the particle in state Y compared to the probability of finding the particle in state X is:

p(Y)/p(X) = exp[-E(Y)/kT]/exp[-E(X)/kt]

where k is boltzman's cst and T is the local temp; this is Boltzmann's equation

for most astrophysical applications (and I am guessing you are doing astrophysics since you mention Saha), you likely want to include all possible degenerate states with energies E(X) and E(Y), in this case, the equation above becomes:

p(Y)/p(X) = g (Y)exp[-E(Y)/kT]/{g(X) exp[-E(X)/kt]}

whereg(Y) and g(X) are the degeneracies of each state.

Saha's equation will tell you ratio of particles in different ionized states; but to give any more specific guidance I would need to know things like the ionization energy, temperature and partition function.

If you can, get a copy of a basic astrophysics text like Carroll and OStlie or Zeilik and look for their examples.  

Let me know how I can givemore specific guidance if this is not what you were looking for.