Analyzing high temperatures using the M-B distribution and

[Positron137]

I am planning on writing a research paper in my high-school physics journal on analysis of high temperatures, and possibly, a bound for an "absolute hottest temperature" (depending on the type of material). I have been using the Maxwell-Juttner speed distribution to analyze a few calculations under the assumption of monatomic gases (such as Hydrogen and Helium). So for example, calculating the temperature of one mol of H2 (assuming S.T.P. conditions) with the M-B distribution, where the most-probable speed would be v = 0.99c. I've been trying to see if there is a limit. I know some conventions have been the Planck Temperature, since our theories don't work beyond that. however, I've been trying to find a better way (or I guess, abetter justification) for analyzing perhaps bounds on extremely high temperatures attainable. I do know that at really high temperatures, quantum effects take place, and things like degenerate matter are prevalent, or stuff such as quark-gluon plasma. Additionally, I was wondering - how do I consider pressure under the Maxwell distribution? Does the equation change with pressure? Could anyone provide me with some suggestions as to how to proceed with these research ideas? Thanks, I really appreciate it.

 

[mfb]

Does the equation change with pressure?

It is a distribution for an ideal gas, where pressure does not change the distribution.

I've been trying to see if there is a limit.

Well, if you keep heating it, you get a plasma - the atoms lose more and more electrons.
At relativistic speeds, the collisions will begin to produce new particles, so at some point you don't increase the energy per particle significantly any more, you just produce more and more particles. The energy density has no known bound - at the Planck energy density, we just don't know what will happen.

 

[Positron137]

Ah ok. I understand. Maybe a good research would be to quantify exactly when the temperature is at when the energy per particle doesn't change significantly - or perhaps analyze other interesting properties (using theory alone) at that point. Do you think that could be a feasible high-school research project? Could you elaborate at the part where the collisions produce new particles? Is the energy (as heat from each collision) creating new particles (by E = mc^2), or some other phenomenon? Thanks.

 

[Vanadium 50]

I don't think a good research paper involves taking equations outside of their realm of validity, and drawing conclusions from them. Indeed, what you are talking about is not even internally consistent: STP means Standard Temperature and Pressure, and you're talking about very high temperatures. I think you should discuss this with your teacher before going further.

 

[Positron137]

Ok. Thanks! By the way, are there other equations relating particle speed distributions and varying temperatures (apart from the Maxwell-Juttner, which applies to STP)? I know a lot of people have done work dealing with high temperatures from a theoretical standpoint. But, could you suggest a good research question in your opinion that I could wok on as a high-school student? Thanks.

 

[mfb]

(apart from the Maxwell-Juttner, which applies to STP)

While it can be used there, it is not limited to STP.

Temperatures beyond the validity of Maxwell-Juttner are particle physics, probably not a good high-school project if you want to calculate anything.

 

[Positron137]

Ok. Thanks!