Compare diffusion of chlorine gas into air and into a vacuum
Answers
Answer:
I'm interested in solving the diffusion equation for gas in vacuum. I have a general question and a more specific questions.
What I know:
The Diffusion Equation: For density function ϕ(r⃗ ,t)ϕ(r→,t) the diffusion equation is:
∂∂tϕ(r⃗ ,t)=D∇2ϕ(r⃗ ,t)∂∂tϕ(r→,t)=D∇2ϕ(r→,t)
where D is the diffusion coefficient.
For a gas of two constituent atom types, Chapman-Enskog theory predicts that the Diffusion Coefficient - at 1 atm and 300 K - will be:
D=9.65445⋅1/M1+1/M2−−−−−−−−−−−√σ212ΩD=9.65445⋅1/M1+1/M2σ122Ω
where σ212σ122 is the average of the collision diameters for the two gasses (σ1σ1 and σ2σ2) in Angstroms and ΩΩ is a temperature-dependent collision integral (apparently, usually on order 1).
What I don't know
How would one calculate the diffusion coefficient if instead of a gas of two atoms, we have a gas of just one atom type diffusing?
General Question
Let's say we know that at time t=0 we have a gas of one type of atom confined to a volume