where k is the ratio of the specific heat at constant pressure, to the specific heat at constant volume,
The two specific heats are related to the gas constant, R, through the equation
As was the case for the ideal gas law, the pressure in both Eqs. 1.14 and 1.15 must be expressed
as an absolute pressure. Values of k for some common gases are given in Tables 1.7 and 1.8,
and for air over a range of temperatures, in Appendix B 1Tables B.3 and B.42. The pressure–density
variations for isothermal and isentropic conditions are illustrated in the margin figure.
With explicit equations relating pressure and density, the bulk modulus for gases can be determined
by obtaining the derivative from Eq. 1.14 or 1.15 and substituting the results into
Eq. 1.13. It follows that for an isothermal process