At the Large Hadron Collider (LHC) a temperature of 7.2 trillion kelvin is recorded(really?!)... We know that the speed of sound increases by 0.61m/s for 1°C.So if at the same instant sound is produced and it passes through the region of 7.2 trillion K temperature the speed of sound would be really high, much higher than that of light. Is it possible or are there some other things I am missing?
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asked Jan 29, 2019 at 15:47
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6$\begingroup$ Seems like you are using an equation outside of its range of validity! $\endgroup$– B. BrekkeCommented Jan 29, 2019 at 16:00
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3$\begingroup$ A good rule of thumb is anytime you calculate a speed greater than C, you've probably made a mistake. $\endgroup$– zeta-bandCommented Jan 29, 2019 at 20:14
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2 Answers
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The 0.61m/s for 1°C figure looks like it comes from an equation for the speed of sound in air. Even it did continue to be linear up to that extreme temperature I'm pretty sure there isn't much air in the LHC.
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$\begingroup$ But that does not mean that there will be no air. $\endgroup$ Commented Jan 29, 2019 at 16:09
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1$\begingroup$ there is absolutely no air in a accelerator's beam tube. $\endgroup$ Commented Jan 29, 2019 at 19:01
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This is what happens when you apply an equation outside its range of validity (as B Brekke pointed out). Equations for the speed of sound in air do not describe the speed of sound in nuclear plasma.
In fact, since thw involved particles travel close to the speed of light one needs to use relativistic fluid dynamics to derive a speed of sound, which turns out to be about $c/\sqrt{3}\approx 0.57c$ (note that that question had the opposite problem - misapplying the relativistic equation to non-relativistic velocities). See this pdf for more relativistic hydrodynamics.
Of course, it is not entirely clear that even this is applicable since the collision occurs in vacuum and the particles may be to sparse to form a "fluid" of any kind with a well defined speed of sound. In which case velocities may get arbitrarily close to lightspeed, and the total energy of the event is used to estimate a "temperature" in the sense that temperature is a measure of the energy in particle motion.
answered Jan 29, 2019 at 18:49
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$\begingroup$ Hi. Look at the second answer to this question. The new studies show the fastest speed of sound is about $36$ km/s. $\endgroup$ Commented Jul 24, 2023 at 20:51
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$\begingroup$ @SnackExchange - Yes, I know about that paper. But that result hinges on what kind of matter it is, and it assumes it is normal matter made out of protons and electrons. The relativistic hydrodynamics approach ignores the type of matter. $\endgroup$ Commented Jul 25, 2023 at 16:12