Characterizing Volume in Equilibrium Thermodynamics

[pt176900]

from callen, equation 16.10 reads Z = sum(e^-BE)

the text later says that F = -kT ln Z, and states that it gives the helmholtz potential as a function of B, V, N
where B = 1/kT

my question is, what part of this relationship characterizes the volume?

 

[dextercioby]

Since the canonical Zustandsumme "Z" is not an integral in the phase space,for statistical systems in the quantum canonical ensemble it's not that obvious why the dependence on the extensive mechanical paramters like V & N needs to appear.
It comes up from the contraints we imposed upon the systems from the ensemble.Specifically,the systems exchange heat thus keeping the temperature constant,and that's it.They do not suffer other types of interactions,viz.NO MECHANICAL INTERACTIONS,therefore,in it's macroscopical description the extensive mechanical parameters are assumed constant and given.That's how u explain the dependence of 1/T,V,N,... for the Massieu function Phi or for Helmholtz potential F...

Daniel.

 

[pt176900]

ok, so if it's a constant, then why would you take the derivative of the helmhotlz potential with respect to volume to determine the pressure of the system?

 

[dextercioby]

That's a question not in the realm of stat.mechanics,but in the one of EQUILIBRIUM THERMODYNAMICS.Ask yourself what is the point of taking the derivatives (all of them partial due to multiple variable dependence) in EQUILIBRIUM thermodynamics...

HINT:the key word is thermoDYNAMICS...

Daniel.