# Unique characterization of Ideal gas

In Thermodynamic state - Wikipedia, it defines a thermodynamic state as:

A thermodynamic state of a system is its condition at a specific time, that is fully identified by values of a suitable set of parameters known as state variables.

In the part explaining state functions, it says

In the most commonly cited simple example, an ideal gas, the thermodynamic variables would be any three variables out of the following four: mole number, pressure, temperature, and volume. Thus the thermodynamic state would range over a three-dimensional state space.

I would think this is not a result in thermodynamics. Is this just an assumption made about ideal gas, or can it be derived from considering the model of the ideal gas statistically?

The ideal gas law reads $$p V = n R T$$ where $$R$$ is a constant or alternatively, $$p V = N k_B T$$, where $$k_B$$ is a constant. Thus, if three of the four variables are given, you can use this equation to determine the fourth variable.