Continuum Mayer |work| Guide

To understand why this relation holds, one must look at the First Law of Thermodynamics:

Using Mayer's relation, one can derive the specific entropy change for an ideal gas: $$\Delta s = c_p \ln\left(\fracT_2T_1\right) - R \ln\left(\fracP_2P_1\right)$$ continuum mayer

$$c_p - c_v = R$$

Without Mayer's relation linking $c_p$ and $c_v$, we could not close the system of equations needed to solve for pressure and density changes in high-speed aerodynamic flows. To understand why this relation holds, one must