The behaviour of gases

In the study of the flight of aircraft, we are really only interested in the behav­iour of one particular gas, air. The most important relationship that we need to know is called the gas law, which can be written as:

= RT

where p is the pressure, p is the density, T is the temperature measured relative to absolute zero (i. e. in degrees Kelvin in the SI system), and К is a constant called the gas constant.

If the gas is compressed its density increases, so either or both the other quantities, temperature or pressure, must change. The way that they change depends on how the compression takes place. If the compression is very slow, and the gas is contained in a poorly insulated vessel so that heat is trans­ferred out of the system, then the temperature will stay constant, and the pressure change will be directly proportional to the density change. This is called an isothermal process, and it involves a heat transfer from the gas to its surroundings. In this case the relationship between pressure and density is given by:

a constant

If the compression takes place with no transfer of heat, which commonly occurs when compression is very rapid, then the change is said to be adiabatic. If the change also takes place without any increase in turbulence, so there is no increase in the disorder (entropy) of the system, then the process is called isentropic, and the relationship between pressure and density is given by:

P

рУ = a constant

where у is the ratio of the specific heat at constant pressure to the specific heat at constant volume, and has a value of approximately 1.4 for air.

We cannot go much further down this path without becoming embroiled in the complexities of thermodynamics, however, and as the relationships above are the only ones that are relevant to the understanding of the contents of this book, we will not pursue the subject any further.