# At what temperature does the vibrational degree of freedom becomes significant for an ideal diatomic molecule?

For ideal diatomic molecules such as $\text{H}_2$, $\text{N}_2$ and $\text{O}_2$, at what temperature does the vibrational degree of freedom significantly contributes to the calculations such as that of the specific molar heat capacity? Please explain without using statistical mechanics.

P.S. What I meant is how do I find $T_{vib}$ in the graph below.

The kinetic energy of the gas molecules is of order $kT$, so when two gas molecules collide there is up to around $2kT$ of energy available. If the spacing of the vibrational energy levels is less than or equal to $2kT$ then there is a non-zero probability that the kinetic enegry could be used to excite a vibrational transition. This would cool the gas molecules, because it reduces their kinetic energy, so extra heat is required to return the gas to its original temperature and the end result is to increase the specific heat.
So vibrational transitions start to contribute to the specific heat when the temperature rises to the point where $kT$ is roughly equal to the spacing of the vibrational energy levels.
There isn't a precise point where the vibrational modes cut in because the gas molecules have a spread of energies. Vibrational transitions will start to be excited at below $kT$ and won't fully contribute to the specific heat until above $kT$. However it's a good guideline as to when they become important.