Physical significance of chemical potential and fugacity I'm studying equilibria and thermodynamics and came across these two terms.
My problem is, unlike other thermodynamic properties that I can understand physically like volume, pressure, enthalpy etc. do these two quantities have physical significance or, is it just that we define fugacity (without any physical meaning) just to make sure the equation
$$\mu - \mu_0 = RT\ln\frac{p}{p_0}$$
looks the same for real gases? If yes, then what is the motivation for the name “fugacity” meaning literally “escaping tendency”?
Similarly, do we just define chemical potential randomly, since it's extremely useful in various calculations when the composition varies, or does it have some physical significance?
Also, why do we call it chemical potential?
The chemical potential is the partial derivative of the Gibbs free energy with respect to the number of moles of the specified species at constant T, P, and numbers of moles of all other species.  The equation you wrote is the what this partial derivative reduces to for a species in an ideal gas mixture, where P is the partial pressure of the species in the mixture.  For a real gas, the fugacity of the species replaces the partial pressure of the species in the same equation for the chemical potential.