- #1
Telemachus
- 820
- 30
Homework Statement
Hi there. I have this problem which I'm trying to solve. Its from callen, it says:
Two ideal van der Walls fluids are contained in a cylinder, sparated by an internal moveable piston. There is one mole of each fluid, and the two fluids have the same values of the van der Waals constants b and c; the respective values of the van der Waals constant "a" are a1 and a2. The entire system is in contact with a thermal reservoir of temperature T. Calculate the Helmholtz potential of the composite system (V is the total volume of the composite system).
So, I've found the fundamental equation for a van der Waals gas in Helmholtz representation before. This is it:
f=-\frac{a}{v}+cRT-TR \ln{[(v-b)(cRT)^c]}+s_0
Now, for the composite system, the mole numbers and the temperature are constants, right? I'm not sure how to work this out.
I also have V=V_1+V_2 being the V at the left of the equality the total volume, and the others the volume for each part of the piston, divided by the cylinder in two.
The pressure must be the same all over the walls I presume, because I suppose the system is at equilibrium, so: P_1(T_r,V_1,N_1)=P_2(T_r,V_2,N_2)
Is this right. How should I go from here?