This is just a summary of many of the definitions and identities I find useful when working with the basic thermodynamics of a system or process. It is not meant to be a comprehensive list.
Using the reasoning behind the notation used for derivatives of thermodynamic potentials, there are some useful identities given the following prototypical system
This equation represents a generic thermodynamic potential of an arbitrary system or process as a function of two implicitly extensive thermodynamic potentials. Adopting the notation
To denote the relationship between intensive variables, extensive variables, and the size of the system allows for the trivial conversion between system size dependent and system size agnostic thermodynamic relationships. The total differential for the extensive form of the thermodynamic potential for the prototypical system is given by