What does the fundamental equation of thermodynamics represent?

The fundamental equation of thermodynamics is represented by the expression (dU = TdS - pdV). This equation describes how the internal energy (U) of a system changes in response to changes in entropy (S) and volume (V).

In this equation, (T) is the temperature, and (p) is the pressure. Here, (TdS) signifies the portion of energy change associated with heat exchange at a constant temperature, while (-pdV) represents the work done by or on the system during a volume change. Essentially, this relationship encapsulates the first law of thermodynamics, which involves energy conservation, indicating that any change in internal energy is due to the heat added to the system minus the work done by the system on its surroundings.

This equation forms the cornerstone of thermodynamic relationships, leading to further developments such as the derivation of other thermodynamic potentials and processes, ultimately allowing one to understand various physical and chemical processes in terms of energy changes.