Handbook of Compressible Aerodynamics

Chapter 3

Review of Thermodynamics

3.1. Macroscopic systems, basic state variables, and absolute temperature

The systems studied in thermodynamics are macroscopic material systems containing a large number of material particles. They are defined in space and time and can be described by a finite number of functions of space and time: these are the state variables of the system that can be dependent. Their set at a given moment constitutes the macroscopic state of the system. The state of a system evolves over time under the influence of other systems forming the exterior, this influence manifests in various forms: temperature differences, electromagnetic potential, acceleration, deformation, etc. The interaction can also happen through microscopic exchanges of matter (diffusion) without an apparent macroscopic transport or differences in the temperature or the potential. It is agreed that a measurable physical quantity, called energy, can be associated with all these forms of action. This quantity is transported and exchanged between the systems like matter.

The macroscopic state of a system is formed by the following properties:

– the system occupies a certain volume (ϑ) in space at each moment t, (ϑ) being measurable and always positive,

– it has a measurable and positive mass m,

– a positive density ρ can be associated to the mass m and the volume (ϑ) (see the concept of continuous medium in section 4.1),

– a position and a velocity can be associated with each element of the ...