# Temperature Limits

Please excuse my lack of proper terminology, I've only just graduated high school so I'm by no means an expert on anything regarding physics.

My question is this: since there is a natural limit to the velocity of an object, the speed of light, and temperature is measured by kinetic energy of molecules of a substance, does that mean that the speed of light imposes a limit on how fast the molecules can move, and thus imposes a limit on the temperature? I'm not looking at it from a relativistic point of view, and I haven't really considered any of the consequences of the molecules approaching the speed of light, is this perhaps more important than I suspected?

On a semi-related note, is absolute zero a limit on the other end of the temperature spectrum? The way I see it, if all particle motion stops, this violates the uncertainty principle. So absolute zero cannot be reached, correct?

## Answers and Replies

Vanadium 50
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Neither of those statements is true. Absolute zero refers to the state of minimum motion, not a state of zero motion. Temperature is more accurately described as a function of energy, not velocity, and while there is an upper limit to an object's velocity, there is no such limit for energy.

The temperature of a substance depends on the average kinetic energy of the molecules in the substance, (which depends on the square of the average velocity blah blah blah). While there is a limit on the velocity of the molecules (the speed of light), the theory of special relativity shows that there is no limit to an object's kinetic energy, thus there is no limit to temperature (for all we know). What I'm trying to say is that you shouldn't put a burrito in the microwave for more than seven minutes...

As for absolute zero, listen to Vanadium, he's more experienced than I.

... Temperature is more accurately described as a function of energy, not velocity, and while there is an upper limit to an object's velocity, there is no such limit for energy.

I think there's such a limit, at least in the gas phase. Consider the temperature of a mixture of gas. The temperature is expressed in term of gas molecule (or electrons & nuclei if it's too hot) velocity. The particles' velocity is limited so the temp is also limited isn't it?

My understanding is the maximum temperature possible is Planck temperature.

Vanadium 50
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I think there's such a limit, at least in the gas phase. Consider the temperature of a mixture of gas. The temperature is expressed in term of gas molecule (or electrons & nuclei if it's too hot) velocity. The particles' velocity is limited so the temp is also limited isn't it?

No. As I said, temperature is a function of energy: it's proportional to kinetic energy, so while there is a velocity limit in SR, there is no kinetic energy limit.

Vanadium 50
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My understanding is the maximum temperature possible is Planck temperature.

Why would this be true?

No. As I said, temperature is a function of energy: it's proportional to kinetic energy, so while there is a velocity limit in SR, there is no kinetic energy limit.

We have this formula: T = (2/3)*(1/k)*(mv^2)/2
v has a limit so you mean m can rise?

Vanadium 50
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You have the non-relativistic expression for kinetic energy in there and are attempting to use it to draw relativistic conclusions.