Thermodynamic energy of vibration

[Boltzmann2012]

I have read that every body possesses some energy of vibration due to the thermodynamic character and it is equal to 1/2 kT. Does this mean that we can detect the vibrations of bodies?
Or ,as it is, does it ultimately end up as heat?

Regards,
Boltzmann2012

 

[Ken G]

All types of energy that connect to a T are considered heat (although some places will restrict "heat" to mean thermal energy in transit between objects, while others will also talk about "heat content"). The way it works is, any thermal reservoir at some T is more or less "happy" to bestow any "mode" with which it comes into contact with with kT of energy, so to know how much energy passes from the reservoir to the system when placed in thermal contact, you need only count the modes. Each vibrational mode counts as one mode, so a 3D oscillator has 3 such modes, so a total of 3kT per oscillator. Free particles only count a "half" a mode for each dimension, so 3kT/2 for a free particle in 3D. A molecule with two atoms has 3kT/2 from its free motions, and two more kT/2 from its two free rotational modes around the axes not between the atoms, for a total of 5kT/2. At very high T, it would also get kT from its vibrational mode between the atoms, for a total of 7kT/2, but you don't generally see this because at such high T, the molecule breaks up. So you see, it's all about counting modes, when you are talking about thermal energy.

 

[Boltzmann2012]

Does that mean we can never detect these vibrations?
Please explain.

Regards,
Boltzmann2012

 

[Ken G]

Does that mean we can never detect these vibrations?

Whether or not we can detect it, and whether or not it is considered "heat", are two very different issues. Our ability to detect just depends on the quality of our technology, whether or not it is counted as heat depends on how statistically distributed is the energy over all the accessible modes. So in some situations, we can detect heat directly, in other situations, we indirectly infer its presence.

 

[sardar]

I can clarify that the thermodynamic energy of vibration is a type of kinetic energy that is associated with the random movement of atoms and molecules in a body. This energy is a result of the body's temperature, and it follows the principles of thermodynamics, which state that energy cannot be created or destroyed but can only be converted from one form to another.

The equation you have mentioned, 1/2 kT, is known as the equipartition theorem, which states that at a given temperature, each degree of freedom of a molecule (such as its ability to vibrate in a certain direction) has an average energy of 1/2 kT, where k is the Boltzmann constant and T is the temperature in Kelvin. This means that as the temperature increases, so does the energy of vibration of the molecules in a body.

To answer your question, yes, we can detect the vibrations of bodies, but it depends on the sensitivity of our instruments. For example, vibrations in the audible range can be detected by our ears, while more subtle vibrations may require specialized equipment. However, it is important to note that the energy of vibration ultimately ends up as heat due to the transfer of energy from one molecule to another. This is known as thermalization, and it is a fundamental concept in thermodynamics.

In summary, the thermodynamic energy of vibration is a type of kinetic energy associated with the random movement of atoms and molecules in a body. While we can detect these vibrations, they ultimately contribute to the overall heat energy of the body. I hope this explanation helps to clarify any confusion. Keep exploring the fascinating world of thermodynamics!