# Is there a highest temperature?

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I've read that there is a lowest temperature which is absolute zero where nothing happens, i.e. no vibrational activity from atoms.

Is there also a highest temperature, i.e. an absolute max temperature?

Last edited:
Arman777

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lekh2003
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We posed this question to Sam Gregson, High Energy Particle Physicist at the University of Cambridge... Sam - The temperature of a system is simply related to the amount of energy in that system. Because the system can't have a negative energy, there is only so much heat you can remove from it and so a limit to how cold you can get. This is called absolutely zero. We've got very close to it. Scientists in Finland have cooled rhodium atoms to a 10th of a billionth of a degree above absolute zero. On the other hand, an absolute maximum temperature would require there to be a limit to the amount of energy you can give to a particle. As far as we know, there is no such limit. Although the speed of light is the universal speed limit, the reason you can't get there is that this would require an infinite amount of energy. So this speed limit does not limit the amount of energy and therefore, the temperature of an individual particle. The most energetic particle ever observed was a cosmic ray over Utah, travelling at 99.999999999985% of the speed of light. Probably a single proton with about 50 joules of energy. This is equivalent to about 5 trillion trillion degrees Celsius and there is no evidence that this is the hottest you could get to.

As far as we know, you are just limited by the amounts of energy you can give to a particle. So you could say that the absolute maximum temperature is a temperature equivalent to all the energy in the universe, concentrated onto one particle. But that limits more accounting than basic physics. Hannah - Thanks, Sam Gregson from Cambridge and CERN. So temperature is related to thermal energy and Einstein's theory of relativity means that although a particle has a universal speed limit, it doesn't have an energy limit. If you took all of the energy in the universe and put it into one particle, you'd essentially run out of energy before you run out of capacity for energy which is why we have no absolute maximum temperature.
I got this from this website: https://www.thenakedscientists.com/articles/questions/there-absolute-maximum-temperature

HRubss and Serra Nova
MathematicalPhysicist
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On the other hand no one really knows or at least according to the third law of Nernest you cannot achieve zero absolute temperature within a finite number of irreversible steps (or was it reversible steps, check for the third postulate of Thermodynamics, I am typing my answer from my memory).

But it's a postulate, as in empirical law, which might be invalid in the future under some different conditions, in physics most laws or empirical laws don't necessarily hold forever.

Serra Nova
jbriggs444
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jim mcnamara
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Negative temperatures are hotter than the hottest positive temperature. The [unobtainable] limit for how "hot" you can get is absolute zero -- approached from below.

https://en.wikipedia.org/wiki/Negative_temperature
How do you explain that?

Can you even achieve negative temperatures in an experiment?

jbriggs444
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Can you even achieve negative temperatures in an experiment?

lekh2003
Gold Member
I am a bit confused about the ideas written on the website. I believe there is nothing like temperature of a particle. Temperature is a macroscopic variable and has meaning for a system which may be consisting of particles and has an element of disorder in it.
Temperature of a particle ideally means it's motion and disorder.

Temperature of a particle ideally means it's motion and disorder.
You mean its other properties such as spin are uncertain.

lekh2003
Gold Member
You mean its other properties such as spin are uncertain.
No I wouldn't think so. It would be the motion of the particles.

No I wouldn't think so. It would be the motion of the particles.
But motion and energy are related so disorder could be in direction of motion and may be this kind of disorder is possible fpr bosons.

mfb
Mentor
Temperature of a particle ideally means it's motion and disorder.
A single particle cannot have disorder.
You can ask about the temperature of a hypothetical set of particles all with the energy of this particle (but unordered).

MathematicalPhysicist
Gold Member
Not only this, I read it from the textbook of Kardar's and the princeton's problems book.

But I still find it difficult to grasp that we can achieve negative temperature but we cannot achieve absolute zero temperature.

I mean if I were to cool a system from T>0, until I get T->0+, how can I come to negative temperatures?

lekh2003
Gold Member
Not only this, I read it from the textbook of Kardar's and the princeton's problems book.

But I still find it difficult to grasp that we can achieve negative temperature but we cannot achieve absolute zero temperature.

I mean if I were to cool a system from T>0, until I get T->0+, how can I come to negative temperatures?
Celsius is an arbitrary scale.

MathematicalPhysicist
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Celsius is an arbitrary scale.
I was referring to Kelvin.

jbriggs444
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I mean if I were to cool a system from T>0, until I get T->0+, how can I come to negative temperatures?
You would not cool the system to obtain a negative temperature. You would need to prepare the system in a different way. But before attempting the feat, you would have to discard the definition of "temperature" that relates to the average kinetic energy [per degree of freedom] of the molecules in a substance and adopt a different definition.

Thermodynamics uses a definition of temperature which is more subtle than that. For ordinary everyday conditions the thermodynamic definition matches the kinetic energy definition quite well. But the thermodynamic definition extends to exotic situations where the kinetic energy definition definition ceases to behave properly.

If you had read the link I posted, you would have seen a section where the concept of temperature is defined in terms of energy and entropy. Some Wiki articles can go right over one's head, so I understand the urge to post without having fully understood the content first. However, rather than responding to this thread again immediately, please take time to examine the link I had provided. Pay particular attention to how temperature is defined as the derivative of thermal energy with respect to entropy, ##\frac{dq}{dS}##

I like to think of the definition of thermodynamic temperature as arising from two principles. First, that heat flows from high temperature to low and second, that in a closed system, entropy always increases. [It also helps to think in terms of inverse temperature ##\frac{1}{T}##, but let us not go there now].

Suppose that we have one reservoir where removing thermal energy results in an increase in entropy. This is an exotic situation, but achievable. This reservoir has a negative temperature by the thermodynamic definition. Suppose that we have another reservoir where adding thermal energy results in an increase in entropy. Now put the two reservoirs in thermal contact and allow heat to flow. In which direction will it flow?

If heat were to flow from normal reservoir to exotic reservoir, that would decrease the entropy of both reservoirs. That would violate the second law of thermodynamics. Instead, heat flows from the exotic reservoir to the normal reservoir, increasing the entropy of both reservoirs. Since heat flows from hotter to colder, the exotic, the negative temperature reservoir is hotter than any positive temperature.

nasu
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