They all come from the equations of adiabatic processes of an ideal gas. Wikipedia explains better than me: https://en.wikipedia.org/wiki/Ideal_gas https://en.

They all come from the equations of adiabatic processes of an ideal gas. Wikipedia explains better than me: https://en.wikipedia.org/wiki/Ideal_gas https://en.wikipedia.org/wiki/Ideal_gas https://en.wikipedia.org/wiki/Adiabatic_process https://en.wikipedia.org/wiki/Adiabatic_process (Especially the section "Derivation of discrete formula" in the latter) It's only a first approximation, but meh.