• id: JTHERM-01-N09
• title: C_p - C_v = R and the Role of Degrees of Freedom
• tags: mayer, degrees-of-freedom, gamma

Mayer's relation: $C_p - C_v = R$ for one mole of ideal gas. The extra R in $C_p$ accounts for work done during expansion at constant pressure. $C_v = (f/2)R$, $C_p = ((f+2)/2)R$, $\gamma = (f+2)/f$. Monatomic (He, Ne, Ar): f = 3, $\gamma = 5/3$. Diatomic (N2, O2, H2 at moderate T): f = 5, $\gamma = 7/5$. Polyatomic (CO2, H2O): f = 6, $\gamma = 4/3$. At very high temperatures, vibrational modes activate, increasing f and decreasing $\gamma$.