# Thermodynamic energy of vibration

1. Apr 15, 2012

### 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

2. Apr 15, 2012

### 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.

3. Apr 15, 2012

### Boltzmann2012

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

Regards,
Boltzmann2012

4. Apr 16, 2012

### Ken G

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.

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