Intensive Variables: Equal Value for Equilibrium?

[Gear300]

Is it a necessary condition for intensive variables to have the same value for all points in a system that is in equilibrium?

 

[Mapes]

We can't just give you the answer, since then nobody would learn anything. But if you describe your reasoning, you'll likely get helpful comments.

 

[Gear300]

My reasoning is that they are said to be scale invariant. I read that electric and magnetic fields can be taken to be intensive, so I'm just trying to narrow down what is considered in an electromagnetic field in thermal equilibrium.