All the terms you are referring to are the properties of the mixture in the ideal gas state at the given temperature and composition.swmmr1928 said:
Infinite specific volume refers to the ideal gas limit. You need to do the integration to get the correction for the property at finite specific volume.
The terms involving the chemical potentials are for the pure substances at temperature T relative to a specified reference state.
A thermodynamic property is a physical characteristic of a system that can be measured or calculated and is used to describe its state. Examples of thermodynamic properties include temperature, pressure, and energy.
The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or converted from one form to another. The second law states that the total entropy of a closed system will always increase over time. The third law states that the entropy of a perfect crystal at absolute zero temperature is zero.
Thermodynamic properties are related to each other through various equations and relationships, such as the ideal gas law and the laws of thermodynamics. These relationships allow us to understand how changes in one property can affect other properties of a system.
A derivation of a thermodynamic property is a mathematical process used to derive a relationship between different thermodynamic properties. This can involve manipulating equations and applying the laws of thermodynamics to find a new equation or relationship between properties.
Derivations of thermodynamic properties are important because they allow us to understand the underlying principles and relationships between different properties. This can help us to make predictions and solve problems in thermodynamics, and also provides a deeper understanding of how energy and matter behave in different systems.