Application that you have considered is pipe flow. Pipe flow can be assumes as isentropic flow. Isentropic equations are non-linear. (Non-linear i'm using here is algebraic non-linearity. Please note the governing equation of fluid mechanics is also non-linear PDE). So resulting gas equation will be non-linear in nature.

We know ideal gas relation is $p=\rho R T$ . This Ideal gas equation can be linearized or make similar to Ohms law if we consider either constant temperature process or constant density process else this is always non linear. I'm sorry to say that, I'm not aware of any easy experiments to visualize that, melting and evaporation are isothermal process. Its tough to do qualitative analysis in those process without equipment.

"Nature is non-linear. Linearity is a sub case of non-linearity".

Application that you have considered is pipe flow. Pipe flow can be assumes as isentropic flow. Isentropic equations are non-linear. (Non-linear i'm using here is algebraic non-linearity. Please note the governing equation of fluid mechanics is also non-linear PDE). So resulting gas equation will be non-linear in nature.

We know ideal gas relation is $p=\rho R_{specific} T$ . This Ideal gas equation can be linearized or make similar to Ohms law if we consider either constant temperature process or constant density process else this is always non linear. I'm sorry to say that, I'm not aware of any easy experiments to visualize that, melting and evaporation are isothermal process. Its tough to do qualitative analysis in those process without equipment.

"Nature is non-linear. Linearity is a sub case of non-linearity".