It is evident that you did not grasp the concept

For a real gas you must tweak the equation adding the van der Waals constants which depend on the type of gas
However also The Boltzman constant has a physical meaning since it defines the status of the system

The extra dimensions on the contrary , same as the parameters of the standard model have no physical meaning
Or better, their meaning , if any, is not known because we are dealing with entitities which are beyond the limit of our experience

Human beings reason by analogies

Humanity took some thousand years to realize that a gas is made of small particles however it is not hard to grasp this concepts because we have experience of similar entities
Consequently we can associate an " mental image " to each parameter of the the equations of classic physics
In atomic physics is not alwayes possible to reason by analogies consequently modern physics is bound to be, up to a certain extent, pure math