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ANSWERED on Tue 15 Aug 2017 - 1:18 pm UTC by Roger Browne

Question: gases at the speed of light

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yaffle 

Customer

 14 Aug 2017 19:09 UTCMon 14 Aug 2017 - 7:09 pm UTC 

Now I believe, but correct me if I'm wrong - that the temperature of a gas is determined by how fast its molecules or it's atoms are moving, absolute zero being the temperature when all movement stops.

Now in this universe, if I understand correctly NOTHING AT ALL CAN TRAVEL FASTER THAN THE SPEED OF LIGHT.

So, does this mean that there is a theoretical "absolute maximum temperature" where the atoms are moving at the speed of light.  That's my reckoning but am I right?

This is just for ,my own scientific interest.  I have a degree in applied chemistry btw.

Don't recall hearing question asked before.

 

Roger Browne 

Answer

 15 Aug 2017 13:18 UTCTue 15 Aug 2017 - 1:18 pm UTC 

Hello yaffle, welcome back to Uclue. And what an interesting question!

The thermodynamic temperature of a gas is proportional to the average kinetic energy of the particles of that gas. The Boltzmann constant defines the relationship between the energy and the temperature, in units of Joules per Kelvin. [1]

According to the equations of Special Relativity, the mass of a particle increases as its speed increases towards the speed of light, according to the formula
m = \frac{m0} {\sqrt{ 1 - v^2 / c^2}}
where m is the "relativistic mass"[2], m0 is the rest mass, v is the velocity, and c is the speed of light.

Therefore, we can keep on pumping energy into something to increase its temperature. As the kinetic energy of the particles increases, they become more massive, and their velocity will increase less for each infusion of energy. Since the relativistic mass tends towards infinity as the velocity approaches the speed of light, the particles will never reach the speed of light no matter how much energy we pump in. Therefore, the speed of light does not define an upper bound to the temperature of a gas.

[1] Wikipedia - Boltzmann constant
https://en.wikipedia.org/wiki/Boltzmann_constant

[2] Wikipedia - Mass in special relativity
https://en.wikipedia.org/wiki/Mass_in_special_relativity#Relativistic_mass

 

David Sarokin 

Researcher

 15 Aug 2017 14:38 UTCTue 15 Aug 2017 - 2:38 pm UTC 

yaffle...interesting question indeed. Though not totally on target, this discussion of the Planck Temperature might be an interesting read as well:

https://futurism.com/coldest-hottest-temperatures-known-universe-infographic/
The Coldest and Hottest Temperatures in the Known Universe

 

Roger Browne 

Researcher

 15 Aug 2017 15:25 UTCTue 15 Aug 2017 - 3:25 pm UTC 

Although my previous post answers the question as asked, I have some further comments to add (I accidentally hit "post" too early).

We are talking about very high temperatures before the relativistic mass of a gas becomes significant. Suppose we measure the mass of something at absolute zero. If we heat the thing to 3.6 Terakelvins (3.6 x 10^12 K) its mass will double due to the increased relativistic mass of the particles comprising that thing. [3]

When a warm body gives off "black body radiation", the highest frequency of that radiation increases as the object gets hotter. If we start with an object at room temperature, it will emit black body radiation in the infra-red spectrum. As we heat up the object, it will start to radiate in the visible spectrum (first it will glow red, then yellow, then it will become white-hot when all visible colors are being radiated). If we heat it further, it will start to radiate in the ultra-violet spectrum, and so on. As the frequency of the black body radiation increases, its wavelength decreases. Visible light has a smaller wavelength than infra-red radiation, for example.

There comes an interesting point at around 1.42 x 10^32 K (known as the Planck temperature) where the wavelength of the black body radiation equals one Planck length (1.6 x 10^-35 meters). That might be the maximum possible temperature, but we can't say for sure because we don't have a working theory of quantum gravity - and that's what we would need to describe what happens at wavelengths less than or equal to the Planck length. [4][5]

At the Planck temperature, each particle has such an enormous relativistic mass that it would be its own black hole - and we don't yet know how a black hole of one particle would behave. Interestingly, when a black hole "evaporates" by emitting Hawking radiation, the "temperature" of that radiation when it is emitted can be the Planck temperature. And the Planck temperature is thought to have been the temperature of the universe a mere 10^-45 of a second after the big bang.

If we confine our investigation to ordinary matter (made of protons, neutrons and electrons) there is indeed a maximum possible temperature, of around 2 × 10^12 K, known as the Hagedorn temperature. At the Hagedorn temperature, a particle of ordinary matter has so much energy that it will spontaneously create a quark-antiquark pair. And if we keep adding energy, in an attempt to increase the temperature further, it will keep spitting out more quark-antiquark pairs, without the original particle rising in temperature. But all the quarks and antiquarks could be heated beyond the Hagedorn temperature. For this reason, the Hagedorn temperature is sometimes loosely described as the boiling point of Hadronic ("ordinary") matter, because above that temperature we can only have quark matter. [6]

In theoretical physics, if enormous amounts of high-energy photons are concentrated into a small space, they will create such an energy density that it warps spacetime enough to create a black hole from the radiation (rather than from matter). This is known as a Kugelblitz, and exceeds the Planck temperature. [7]

In chemistry, we consider thermodynamic temperature with respect to the movement of particles within the three dimensions of physical space. But particle physicists must also consider other degrees of freedom - quantum spin, electron energy levels, etc. This leads to some fascinating and bizarre outcomes whereby the available energy levels can become saturated - meaning that as you add more energy to the system, the entropic temperature at first increases until it becomes infinite, then it becomes negatively infinite and gradually becomes less negative and moves towards zero! [8]

Finally, let me draw your attention to a research paper which carefully examines the interaction of black holes with the maximum possible temperature in a thermodynamical system, and concludes that black hole formation will in practice limit the achievable temperature to about one-third of the Planck temperature. The authors conclude their paper with a brief review of other research related to maximum possible temperatures. [9]

[3] Wikipedia - Orders of magnitude (temperature)
https://en.wikipedia.org/wiki/Orders_of_magnitude_(temperature)

[4] Wikipedia - Planck temperature
https://en.wikipedia.org/wiki/Planck_temperature

[5] Wikipedia - Planck length
https://en.wikipedia.org/wiki/Planck_length

[6] Wikipedia - Hagedorn temperature
https://en.wikipedia.org/wiki/Hagedorn_temperature

[7] Wikipedia - Kugelblitz
https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics)

[8] Wikipedia - Negative temperature
https://en.wikipedia.org/wiki/Negative_temperature

[9] Maximal temperature in a simple thermodynamical system [PDF]
De-Chang Dai, Shanghai Jiao Tong University, and Dejan Stojkovic, SUNY at Buffalo NY
https://arxiv.org/abs/1601.07563

 

yaffle 

Customer

 15 Aug 2017 20:55 UTCTue 15 Aug 2017 - 8:55 pm UTC 

Yes I understand completely-   as the mass of the particles increases with their speed one would never actually reach a limit to the amount of energy ie temperature - I was a bit wrong there- but one often is wrong in science.  I know, I used to do it for a living.

 

Roger Browne 

Researcher

 15 Aug 2017 21:30 UTCTue 15 Aug 2017 - 9:30 pm UTC 

Thank you for your kind comments and tip, yaffle.

 

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