Question: Given a standard reference system with axes x y z representing a 3 dimensional space and given a magnet whose north and south pole are at points $P\_N=(x\_N,y\_N,z\_N)$ and $P\_S=(x\_S,y\_S,z\_S)$ what is the law that describes the vector field of the magnet at any other point of the space? I'm interested in the law that associates to each point $P=(x,y,z) $ the direction and modulus of the vector of the magnetic field.

Answer: 
If the external pressure is constant, you will get a straight graph parallel to the V axis in the p-V-diagram. Yes, the external pressure is constant if it is related to atmospheric pressure.

The internal pressure will give you a curved graph in the p-V diagram. The area between this curved graph and the other graph in p-V diagram will give you the work that is done to the system.
Consider the case of a block moving on a frictionless surface with a force $\mathbf F$ acting on it for a displacement $\mathbf d$ then work done by the external force is $W = \mathbf F \cdot \mathbf d$. Now you may ask why didn't we considered the internal force for this? The reason being that they both represent the same exchange of energy i.e., from the pusher to the block. 
![Block on a frictionless surface](https://i.stack.imgur.com/jFr8N.jpg)

Now consider the case of a force pushing a piston which itself is pushing a gas. Here you may see that for every instance (other than the equilibrium state) $P\_{ext} = P\_{int} + \Delta P$ i.e., they don't form a action reaction pair and unless the piston is at rest at start and end this $\Delta P$ dissipates some of the this energy. So to find out the work done on the system by the external force we consider $\int P\_{ext} \cdot dV$ and not $\int P\_{int} \cdot dV$.