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In chemistry we use ultrasonication for cleaning vessels ,synthesis of chemical compounds (sonochemistry) etc.I know that during ultrasonication high temperature and pressure is formed "locally".But I want to know whether there is any equations which relates between ultrasonication and temperature .

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    $\begingroup$ I'm not sure whether I oversimplify things here but in the process of ultrasonification the atoms and molecules are highly accelerated leading to high velocities. And since the velocity is linked to the kinetic energy via $E_{\text{kin}} = \frac{1}{2} m v^{2}$ which is in turn linked to the temperatur, you have a direct connection between $v$ and $T$. Example: for a free particle inner energy = kinetic energy, so via equipartition theorem: $U = E_{\text{kin}} = \frac{3}{2} k_{\mathrm{B}} T$ and thus the average quadratic velocity is $\sqrt{<v^{2}>} = \sqrt{\frac{3 k_{\mathrm{B}} T}{m}}$. $\endgroup$ – Philipp Aug 28 '13 at 20:05
  • $\begingroup$ @Eka, as you mentioned, pressure is also important. I can't remember the numbers now, but if you do some research there are some examples of average temperatures caused by cavitation bubbles bursting at specific frequencies / power. Not sure about a formula, though. $\endgroup$ – Alex Aug 28 '13 at 23:26
  • $\begingroup$ scs.illinois.edu/suslick <BR> Publications list, re "The Sonochemistry of Materials and Biomaterials" $\endgroup$ – Uncle Al Apr 26 '14 at 23:08
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The temperature is highly nonlinear with sound pressure and dependent on external pressure, tensile strength of liquid etc. Cavitation, http://en.wikipedia.org/wiki/Cavitation, can produce local shock waves and temperatures of thousands of K, causing sonoluminescence. See also http://www.scs.illinois.edu/suslick/sonochembrittanica.html.

Because of that nonlinearity and all the dependencies, I do not know if any equation for calculating the peak temperatures exists, and there is still research going on to see how much of sonoluminescence is due to black-body radiation, the recombination of radicals etc.

BTW, you can view a mantis shrimp with a sonoluminescent punch at https://www.youtube.com/watch?v=sNzI8K-lCqo and https://www.youtube.com/watch?v=ti2Uoc1RXuQ, and another species at https://www.youtube.com/watch?v=QXK2G2AzMTU.

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