Calculating isothermal copressibility and expansion coefficient

[Zcuttlefish]

Homework Statement

Calculate the isothermal compressibility and the expansion coefficient of a van der waals gas. Then show using Euler's chain relation that KR = alpha(Vm-b)

Homework Equations

isothermal compressibility K = (-1/V) (dv/dp)^t
isothermal expansion alpha= (1/v)(dv/dt)^p

The Attempt at a Solution

I realize it has to do with partial derivatives. But beyond this I'm lost.

 

[gabbagabbahey]

Hi Zcuttlefish, welcome to PF!

Hint: You might start by looking up the equation of state for a Van Der Waals gas!

 

[Zcuttlefish]

I did (p+ a/V2)(v-b) = RT
(not including n because it should be constant)

​

my answer for dv/dp ended up looking like
Then i used the product rule and took the derivative dv/dp of the terms. I'm still unsure of why or if I've even gotten closer to the answer.

V³(v-b)/(2a(v-b)²-RTV³)
I seem to be missing an R on top.