Equipartition Theorem (Thermal Physics)

In summary, the conversation discusses the relationship between the average kinetic energy per atom in a monatomic gas and the average kinetic energy per diatomic molecule, as well as the breakdown of the equipartition theorem at low temperatures.
  • #1
NATURE.M
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I just wanted to know whether the following formula 3/2kT=K (ave) demonstrates the average kinetic energy per atom in a monatomic gas.
And then if 5/2kT=K (ave) demonstrates the average kinetic energy per diatomic molecule.

This comes from the fact that the average energy per degree of freedom is 1/2kT.

Note k(lowercase) denotes Boltzmann Constant, and K (uppercase) denotes kinetic energy.
 
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  • #2
Yes, you are correct. The equipartition theorem breaks down at low temperatures when the energy kT is smaller than the energy spacing in a degree of freedom. It doesn't have enough energy to make that jump, so that degree of freedom becomes frozen out.
 

1. What is the Equipartition Theorem in thermal physics?

The Equipartition Theorem states that in thermal equilibrium, the total energy of a system is equally distributed among all degrees of freedom. This means that each degree of freedom, such as translational, rotational, and vibrational motion, will have an average energy of kT/2, where k is the Boltzmann constant and T is the temperature of the system.

2. How does the Equipartition Theorem apply to gases?

In gases, the Equipartition Theorem applies to the translational degrees of freedom, which are the three dimensions of movement in space. Each degree of freedom will contribute kT/2 to the total energy of the gas, resulting in a total energy of 3kT/2 per molecule.

3. Does the Equipartition Theorem only apply to gases?

No, the Equipartition Theorem can be applied to any system in thermal equilibrium, including solids and liquids. However, its application may vary depending on the system's specific degrees of freedom and the laws of thermodynamics.

4. Can the Equipartition Theorem be used to predict the behavior of particles in a system?

Yes, the Equipartition Theorem can be used to predict the average energy of particles in a system. This can be helpful in understanding the behavior of particles and their interactions, as well as in calculating thermodynamic properties of the system.

5. Are there any limitations to the Equipartition Theorem?

Yes, there are limitations to the Equipartition Theorem, especially at low temperatures and for systems with quantum mechanical properties. In these cases, the distribution of energy among degrees of freedom may not follow the predictions of the theorem, and other theories, such as quantum mechanics, must be used.

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