Finding the equation of the adiabats.

[mateomy]

Working from Callen, Chapter 1:

Find the equation of the adiabats in the P-V plane given
$$U = AP^2V$$

Where A is defined as a positive constant of dimension $[P]^-1$.

I'm not sure what to do with this. I was thinking of solving the equation for P and then...no idea.

If I do that I (probably incorrectly) get something like this:

$$P = \frac{U}{V}$$

After plopping this into Mathematica I can see that it looks like an adiabatic curve, but there's no way the problem is that easy. So I think I'm not going about this correctly. Just looking for some pointers/guidance.

Thanks.

 

[member 553083]

The equation of the adiabats in the P-V plane can be found by rearranging the given equation to solve for V, resulting in the equation:V = \frac{U}{AP^2}This equation describes the relationship between Pressure (P) and Volume (V) and is the equation of the adiabats in the P-V plane.