Question

How is the molar specific heat capacity of a gas at constant pressure = 7/2R

Answer 1

Continuing this logic, a diatomic molecule will add 2 rotational modes at normal temperatures. Technically there is also a vibrational mode that is added, but this takes high temperatures to be activated. So at room temperature, you will get cv=5/2Rcv=5/2R and therefore cp=7/2Rcp=7/2Rgiving the typical specific heat ratio of air as γ=7/5=1.4γ=7/5=1.4. At high temperature, if you assume the vibrational mode is fully excited, you get γ=8/6=1.3333γ=8/6=1.3333which can be used for calorically perfect, high temperature gases.