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I guess it depends on the heat or the type of the material but can you give some examples or formulas to calculate it ?

The best example would be the average speed of the air molecules (all types in the air) at room temperature or water molecules at human body temperature.

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It depends on the mass of the molecule in question. Here's a quick, back-of-the-envelope answer. In a body at thermal equilibrium, every energy mode has the same average amount of energy, $\frac12kT$, where $T$ is temperature and $k$ is Boltzmann's constant. One of the energy modes is the translational kinetic energy of a molecule in some direction $x$, $\frac12mv_x^2$. We can solve

$$\frac12kT=\frac12mv_x^2$$

to find

$$v_x=\sqrt{\frac{kT}m}$$

and then plug in $k=1.38×10^{-23}\rm{m^2 kg s^{-2} K^{-1}}$, $T=300\rm{K}$, and for $m_{\rm{N}_2}=2×14\rm{u}=2×14×1.66×10^{−27} \rm{kg}=4.65×10^{−26} \rm{kg}$ to get

$$v_x=298\rm{m/s}=667mph.$$

The molecule is also moving in the $y$ and $z$ axes, so the answer depends on what exactly you mean by average speed: mean spead vs. root-mean-square speed.

This ignores rotational and vibrational degrees of freedom. Similar calculations may be performed for other substances.

Some links: http://en.wikipedia.org/wiki/Root-mean-square_speed

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  • $\begingroup$ Thank you this is very helpful. By average speed, I meant the actual distance traveled in a specific period of time as we describe the speed of a car without thinking about axes. Ignoring rotation is fine for me but can you explain the vibration of gas molecules ? I thought they didn't vibrate by themselves (without colliding others) since they are not connected unlike liquid and solids molecules. $\endgroup$ – Xtro Jul 27 '14 at 18:31
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    $\begingroup$ Then you probably want $\langle v\rangle=\sqrt{\frac{8kT}{\pi m}}$=476m/s=1065mph. All molecules vibrate: the distance between the atoms in the molecule oscillates like a spring. Also see en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution and en.wikipedia.org/wiki/Molecular_vibration $\endgroup$ – Scott Centoni Jul 28 '14 at 16:25
  • $\begingroup$ Oh yeah you are right. When I was thinking about molecules, I forgot to think about atoms in them. Of-course they vibrate :) Can we say an hydrogen atom also vibrates by itself without colliding anything else ? Maybe because interaction between the proton and electron or maybe the interaction between quarks ? $\endgroup$ – Xtro Jul 28 '14 at 18:11
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    $\begingroup$ It's harder to apply classical concepts to electrons. See physics.stackexchange.com/questions/20187/… for a back-of-the envelope discussion. Quark vibrations should exist within a proton, but a proton is a very messy system because of the self-interaction of gluons. $\endgroup$ – Scott Centoni Jul 28 '14 at 20:49

protected by Qmechanic Feb 10 '15 at 21:03

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