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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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.
Anders Sandberg
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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.
M. Enns
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