Re: Why isn't there a highest possible temperature of matter?

Hello, Ariean. This is a very interesting question that I have wondered about as well. There does not seem to be any limitations on the temperature that objects can attain. Temperature is usually explained using gas in a container. The pressure of a gas is directly proportional to its temperature. A scientist named Boltzmann showed that the average kinetic energy of the gas molecules was directly proportional to the pressure. Therefore, the average kinetic energy of the molecules is directly related to temperature.

Average kinetic energy = 3kT/2 = (mv²)/2

k = Boltzmann's constant = 1.38x10^-23J/K

T = Temperature in Kelvin

m =Mass

v = velocity (random mean velocity)

As the temperature increases, so does the average kinetic energy of the molecules increases. Since the kinetic energy increases, so does the velocity of the molecules. As molecules go faster their mass also increases. In the equations below, something to the .5 power is the square root.

m = (m₀)/(1-(v²/c²))^.5

(m₀) = mass at rest

m = mass in motion

v = object velocity

c = velocity of light

As the molecule approaches the speed of light, its mass approaches infinity. This may not be the best wording to a mathematician. You could put all of the energy in the universe in the molecule and it would never reach the speed of light. I suppose that to find the highest possible temperature, you could calculate all of the energy in the universe and then cram it into the lightest particle possible.

[note added by MadSci Admin: because the limit of the mass of the particle approaches infinity as its speed approaches the speed of light, its energy also approaches the limit of infinity. The maximum possible temperature therefore approaches the limit of infinity!]

I hope that this answers your question. If you have any more problems, please write back to MadSci.

Kevin