Perfect Gas

In principle, it is possible to do gas dynamic calculations with the general equation of state relations, for fluids. But in practice most elementary treatments are confined to perfect gases with constant specific heats. For most problems in gas dynamics, the assumption of the perfect gas law is sufficiently in accord with the properties of actual gases, hence it is acceptable.

For perfect gases, the pressure-density-temperature relation or the thermal equation of state, is given by:

(2.78)

where R is the gas constant and T is absolute temperature. All gases obeying the thermal state equation are called thermally perfect gases. A perfect gas must obey at least two calorical state equations, in addition to the thermal state equation. The cp, cv relations given below are two well-known calorical state equations:

where h is specific enthalpy and u is specific internal energy, respectively. Further, for perfect gases with constant specific heats, we have:

where cp and cv are the specific heats at constant pressure and constant volume, respectively, and Y is the isentropic index. For all real gases cp, cv and y vary with temperature, but only moderately. For example, cp of air increases about 30 percent as temperature increases from 0 to 3000 °C. Since we rarely deal with such large temperature changes, it is reasonable to assume specific heats to be constants in our studies.