Degrees of freedom affect on heat capacity ratio

In summary, the heat capacity ratio is affected more by the vibrational and rotational degrees of freedom for heavier molecules such as N2 and CO2 compared to lighter molecules like He and Ar. This is because the heavier molecules have more active vibrational degrees of freedom. This can result in a larger change from the expected heat capacity ratio as predicted by the equipartition theorem. However, this is only an issue at high temperatures and not at room temperature. Helium and argon, being monatomic, do not have vibrational or rotational degrees of freedom, so they only partition energy among their three translational degrees of freedom.
  • #1
jaejoon89
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Homework Statement



Why would vibrational and rotational degrees of freedom affect the heat capacity ratio more for N2 and CO2 than He or Ar? Would this occur at room temperatures?

Homework Equations



d.o.f.: 3N
vibrational d.o.f., linear molecule: 3N - 5
nonlinear: 3N - 6

The Attempt at a Solution



My book says that the vibrational d.o.f. will be more active for heavier molecules. Why is this? Does this mean there would be a larger change from the expected heat capacity ratio as predicted by the equipartition theorem? I don't understand whether it would negatively or positively affect it, or why. Also, I thought it was only an issue for REALLY high temperatures, not room temperature. A little clarification would be helpful.
 
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  • #2
Helium and argon are monatomic. They do not have vibrational or rotational degrees of freedom. All they can do when you add energy to them is move faster, i.e. partition the energy among the three translational degrees of freedom.
 

1. What is the concept of degrees of freedom in relation to heat capacity ratio?

The concept of degrees of freedom refers to the number of independent ways in which molecules in a substance can move and store energy. In the context of heat capacity ratio, it refers to the number of ways in which a molecule can store and transfer energy through its motion and vibration.

2. How does the number of degrees of freedom affect the heat capacity ratio of a substance?

The number of degrees of freedom has a direct impact on the heat capacity ratio of a substance. In general, a substance with a higher number of degrees of freedom will have a higher heat capacity ratio, meaning it can store more energy in the form of heat.

3. Why do substances with more degrees of freedom have a higher heat capacity ratio?

This is because molecules with more degrees of freedom have more ways to store and transfer energy. This means they can absorb more heat before their temperature increases, resulting in a higher heat capacity ratio.

4. How does the heat capacity ratio change with temperature for substances with different degrees of freedom?

For substances with the same number of degrees of freedom, the heat capacity ratio remains constant with changing temperature. However, for substances with varying degrees of freedom, the heat capacity ratio can change with temperature due to changes in the molecules' ability to store and transfer energy.

5. Can the heat capacity ratio of a substance be used to determine the number of degrees of freedom?

Yes, the heat capacity ratio can be used to calculate the number of degrees of freedom for a substance. This calculation involves knowing the molecular weight, heat capacity ratio, and other properties of the substance. However, this method is not always accurate and may only provide an estimate of the degrees of freedom.

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