Why Does the Ideal Gas Law Only Have Two Independent Variables?

[ehrenfest]

Homework Statement

http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/7A20B047-A049-44D6-96D2-75602F179856/0/notes_dfnitns.pdf
There it says tht the number of independent variables of a simple fluid is 2 (see the "Complete Specification" section). But the ideal gas law is PV=NkT which has 4 variables, so why are there not 3 independent variables for an ideal gas which is an example of a simple fluid?

Homework Equations

The Attempt at a Solution

 

[Mapes]

There is another equation of state for ideal gases, $U=Nc_vT$. The constraint from this additional equation reduces the number of independent variables to two.

 

[ehrenfest]

There is another equation of state for ideal gases, $U=Nc_vT$. The constraint from this additional equation reduces the number of independent variables to two.

That equation will only work if V is constant.

 

[Mapes]

No. Every student of thermo (including me) claims that at first, but no. It applies to all ideal gases under all processes.

EDIT: To give a little more explanation, $c_v$ is a constant. $U=Nc_vT$ is an equation of state that uses that constant; it's not a process subject to constraints. We could just as well write $U=N(c_p-R)T$.