Introduction to Theoretical and Mathematical Fluid Dynamics

12 Review of Thermodynamics

Thermodynamics is a phenomenalogical theory of equilibrium states and transitions among them. This is based on the concept of energy and identification of the Laws governing the conversion of one form of energy into another, and the use of various media to produce such transformations. The Laws of Thermodynamics establish the relation between the changes in the thermodynamic state of a system and its interactions with the environment. The First Law postulates the conservation of energy, while the Second Law establishes the trend toward equilibrium, as dictated by the existence of entropy S. These Laws are concerned with connecting the initial and final states of a system undergoing a process rather than the detailed evolution of the system during the process. Equilibrium Thermodynamics is directly applicable to the mechanics of ideal fluids. In contrast, the mechanics of real fluids has to include the various transport phenomena which disturb the state of thermodynamic equilibrium.

12.1 Thermodynamic System and Variables of State

A thermodynamic system is a quantity of matter isolated from its surroundings for the purpose of observation. The system we consider is a simple, homogeneous one composed of a single fluid.

An isolated system reaches a state of equilibrium, i.e., the macroscopic state becomes steady. Variables of state determine the state of the system. A variable of state is uniquely defined for any equilibrium state of the system and ...