How does increasing temperature increase modes?

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Homework Help Overview

The discussion revolves around understanding why the number of modes per particle in gases increases with temperature, specifically focusing on diatomic gases and excluding monatomic gases. The original poster is exploring the relationship between temperature, kinetic energy, and the accessibility of different modes of energy in gas molecules.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use an energy argument to explain the increase in modes with temperature but expresses confusion about the concepts of excited and ground states. Participants inquire about the types of modes present in gas molecules and discuss the degrees of freedom associated with diatomic gases, including translational, rotational, and vibrational modes.

Discussion Status

Participants are actively engaging with the concepts, questioning the nature of modes in gas molecules and the implications of temperature on energy states. Some guidance has been offered regarding the quantization of rotational and vibrational energies and their relation to temperature, but no consensus has been reached on the original poster's understanding.

Contextual Notes

There is a mention of the Boltzmann distribution and the conditions under which rotational and vibrational modes become excited, indicating a need for clarity on these concepts. The discussion highlights the complexity of energy states in diatomic gases and the assumptions involved in relating temperature to mode accessibility.

romantichero7
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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.
 
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What kind of modes posses a gas molecule?
 
ehild said:
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.
 
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 KBT> ΔE, the difference between the energy levels. The probability of a molecule to be at a certain energy level depends on the ratio ΔE/(KBT) You certainly have learned about Boltzmann distribution?
What do you think about the excitation energy of the rotational and vibrational modes, which are higher ?
 

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