# Statistical Mechanics: Phase Diagrams and Effusion

1. Oct 11, 2012

### ecastro

1. The problem statement, all variables and given/known data
There are two problems:
The first problem is to calculate the slope of a phase-equilibrium line of a substance given its properties (Helium, Water, etc.) as the temperature approaches a certain value (in this case, T approaches zero).
The second problem is the effusion of a gas into a slit to produce an atomic beam. The intensity of the beam is calculated from the number of molecules that leave the beam.

2. Relevant equations
For the first problem:
$\frac{dp}{dt} = \frac{\Delta S}{\Delta V}$
S is entropy and V is volume.

Second Problem:
$\frac{dN}{dt} = -\frac{1}{4}n\bar{v}A$

3. The attempt at a solution
I do not know how to move on for the first equation, considering that the density of the solid is greater than that of the liquid.
As for the second problem, I'm not sure if this is already I (the given equation). Differentiating it with respect to T, and
$n = \frac{pV}{kT}$
Considering no change in volume as T changes. Also, the velocities of the particles changes with temperature, I'm also not sure if this assumption is correct. Could you please guide me?