# Thermodynamics Questions

1. Jan 17, 2010

### mmmboh

1. The problem statement, all variables and given/known data

Hi, I got a set of problems to do and there are a few I am having trouble with: (edit: I had more questions before but I figured them out)

1. A hypothetical substance has an isothermal compressibilty $$\kappa$$=a/v and an expansivity $$\beta$$=2bT/v, where a and b are constants, and v is the specific volume.
a) Show that the equation of state is given by v-bt2 + aP=constant
b) If at a pressure P0 and temperature T0, the specific volume is v0, evaluate the constant.

3. The attempt at a solution

1. Ok I figured out 2a), but I don't know how to evaluate the constant for 2b)...what I did was just replace v, T, and P with v0, t0, and P0, but I don't think that is right.

I think it may be something with an exact differential equation, I am not sure though. I have ($$\beta\nu$$/$$\partial$$P)$$\partial$$T = -($$\kappa\nu$$/$$\partial$$T)$$\partial$$P

Btw how do you make the kappa symbol on the same level as everything else?

Last edited: Jan 18, 2010
2. Jan 17, 2010

### mmmboh

Ok number 3 I figured out

3. Jan 18, 2010

Any help?