[genghis___khan]

I'm trying to solve the reversible, isothermal compression of one mole of a Van Der Waal's gas from "state (P1, V1) to (P2, V2)". The question wants me to identify if q, w, deltaH, deltaU and deltaS are positive, negative, or zero.
My first instinct is to use the w = ∫ P dV from V2 to V1 equation to solve for the work. I do so, coming up with -RTln((V2-b)/V1-b)) + a(1/V2 - 1/V1).
V2 < V1, as it is a compression, and as such (1/V2 - 1/V1) > 0.
From here, I used the (∂U/∂V)constantT = a/V2 function for a Van Der Waal's gas. I then took the integral of the right side (not sure how to integrate the left side properly!), and found it to be -a/V.
I know -a/V is also equal to T(∂P/∂T)constantV - P. I solved (∂P/∂T) to get (R/V-b) - (a/V2), and substituted in RT/V-b - (a/V2) for P to get this:
T[(R/V-b) - (a/V2)] - RT/V-b + (a/V2) = -a/v
I simplified this down until I got T-1/V = 1 and then T-1 = V.
I'm not sure that this is the right path to take to solve this.
From here, I took T-1 = V and attempted to shove it back into the integrated work function from earlier, in both places for V2 and V1, which brought me to w=0. (I know, this makes absolutely no sense!)
So, if I my work was correct up until that last step, how do I use the T-1 = V to solve properly? Or was my work entirely wrong anyways?

[mjc123]

Can't you see that it's wrong? How can you get T - 1 = V? T, V and 1 all have different dimensions. That should alert you at once.

I know -a/V is also equal to T(∂P/∂T)constantV - P.

No it isn't - it's a/V². (Again, dimensions; a/V² has the same units as P.)

I solved (∂P/∂T) to get (R/V-b) - (a/V2)

No - where does the second term come from?
P = RT/(V-b) - a/V²
(dP/dT)_v = R/(V-b)
T(dP/dT)_v - P = a/V²