A Brief Review of Thermodynamics
The importance of thermodynamics in the analysis and understanding of compressible flow was underscored in Section 7.1. Hence, the purpose of the present section is to review those aspects of thermodynamics that are important to compressible flows. This is in no way indended to be an exhaustive discussion of thermodynamics; rather, it is a review of only those fundamental ideas and equations that will be of direct use in subsequent chapters. If you have studied thermodynamics, this review should serve as a ready reminder of some important relations. If you are not familiar with thermodynamics, this section is somewhat self-contained so as to give you a feeling for the fundamental ideas and equations that we use frequently in subsequent chapters.
7.2.1 Perfect Gas
As described in Section 1.2, a gas is a collection of particles (molecules, atoms, ions, electrons, etc.) which are in more or less random motion. Due to the electronic structure of these particles, a force field pervades the space around them. The force field due to one particle reaches out and interacts with neighboring particles, and vice versa. Hence, these fields are called intermolecular forces. However, if the particles of the gas are far enough apart, the influence of the intermolecular forces is small and can be neglected. A gas in which the intermolecular forces are neglected is defined as a perfect gas. For a perfect gas, p, p, and T are related through the following equation of state:
where R is the specific gas constant, which is a different value for different gases. For air at standard conditions, R = 287 J/(kg • K) = 1716 (ft • lb)/(slug • °R).
At the temperatures and pressures characteristic of many compressible flow applications, the gas particles are, on the average, more than 10 molecular diameters apart; this is far enough to justify the assumption of a perfect gas. Therefore, throughout the remainder of this book, we use the equation of state in the form of Equation (7.1), or its counterpart,
where v is the specific volume, that is, the volume per unit mass; v — 1/p. (Please note: Starting with this chapter, we use the symbol v to denote both specific volume and the у component of velocity. This usage is standard, and in all cases it should be obvious and cause no confusion.)