How does increasing temperature increase modes?

[romantichero7]

Homework Statement

Explain why the number of modes per particle increases with increasing temperature for all gases (except monatomic gases).

Homework Equations

The Attempt at a Solution

I am trying to use an energy argument but to be honest, I don't understand the excited state vs rest state stuff in this context. My answer would be: increasing temperature by definition increases the average kinetic energy of the substance and also increases the energy in each existing mode. If the substance has more energy, it can more easily navigate between its excited and ground state which (somehow) leads to the ability to access more modes.

 

[ehild]

What kind of modes posses a gas molecule?

 

[romantichero7]

What kind of modes posses a gas molecule?

A diatomic gas has 3 KEtranslational modes, 2 KErotational modes. I know some diatomic gases have 2 vibrational modes too.

 

[ehild]

A diatomic gas molecule has one mode of vibration, but it counts twice with regard the energy. Molecules containing N atoms have 3N degrees of freedom, from those 3 is translational, 3 (2) are rotational, the others are vibrational.
You certainly know that the rotation and vibration energies are quantised. They are excited at temperatures when K_BT> ΔE, the difference between the energy levels. The probability of a molecule to be at a certain energy level depends on the ratio ΔE/(K_BT) You certainly have learned about Boltzmann distribution?
What do you think about the excitation energy of the rotational and vibrational modes, which are higher ?