Compression and Expansion of Gases

When gases are compressed or expanded, the relationship between pressure and density depends on the nature of the process.

• Isothermal process:

$$\frac{p}{\rho }=\text{constant}$$

• Isentropic process:

$$\frac{p}{{\rho }^k}=\text{constant}$$

where $k=c_p/c_v$, which are the specific heats at constant pressure and constant volume. The two specific heats are related by the gas constant, $R=c_p-c_v$.