# is there an absolute highest temperature that can be achieved?

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This is an interesting question. Actually there is an absolute highest temperature that can be (theoretically) achieved by any material particle/system of objects. It is called the Hegedorn temperature.

Hagedorn temperature:

The Hagedorn temperature is the maximal allowed temperature (of certain systems) above which the partition sum diverges.

Depending on the system in consideration, the Hagedorn temperature may be different.

In string theory, for an ensemble of strings, if we try to heat the ensemble past a limiting temperature T_H , the Hagedorn temperature, the number of states of string theory at a specific energy level increases exponentially with the energy.If more energy is pumped into the system, the energy goes into producing longer and longer pieces of string – which also actually interact with each other a great deal at this temperature – rather than raising the temperature.

As a result, the partition, function is infinite for T > T_H due to the competition between the entropy and the Boltzmann factor e^(−βE), where β is the inverse of the temperature . At Hagedorn temperature, the energy density is much larger than the Planck scale and the Einstein equation is no longer valid. What happens when we try to increase the temperature past this is not known.

The formula for T_H is (for strings)

T_H ~ 1/l_s

where l_s is the string length scale, which is not precisely known. However it is believed that the strings are of the order of Planck length long.

This gives an estimate of the Hagedorn temperature of

T_H ~ T_P = Planck temperature

~ 1.41679 × 10^(32) K

Highest temperature in the universe:

The highest temperature in the universe was at the Big Bang which is believed to be 1.4×10^(32) K, the Planck temperature of micro black holes; a temperature 5×10^(−44) seconds after the Big Bang.

Cheers.

Source(s): Credits: http://en.wikipedia.org/wiki/Hagedorn_temperature Original work: R. Hagedorn, Nuovo Cimento Suppl. 3 (1965) 147. Article: http://ph-dep-th.web.cern.ch/ph-dep-th/content2/wo... Highest temperature: http://en.wikipedia.org/wiki/1_E2_K

There is no highest temperature in principle, the way there is a lowest temperature (absolute zero). The temperature of a substance at a particular place and time is the average kinetic energy of the particles making up the substance, and in principle there is no highest kinetic energy the particles can have. The reason there is no highest kinetic energy is that kinetic energy is proportional to mass and velocity squared, and although velocity is limited to the speed of light, mass increases as velocity approaches light-speed. Thus velocity can increase until it approaches the speed of light, while mass can increase without bound to increase kinetic energy. But in practice, temperature can never be greater than is made possible by the sum total of the mass-energy in the universe. Even if there was only one moving particle, and the rest of the universe was at absolute zero, the amount of energy the moving particle could have absorbed from the rest of the universe is finite. Thus, because the mass-energy of the universe if finite, there is a highest possible temperature a body could ever achieve, in practice.

The highest temperature created by humans is 905 million deg F - 30 times hotter than the center of the sun - on May 27, 1994, at the Tokamak Fusion Test Reactor at the Princeton Plasma Physics Laboratory in New Jersey, using a Deuterium-Tritium plasma mix.

Source(s): Guinness World Records 2000 - Millenium Edition
• Anonymous

No, but sort of.

Microscopic temperature (i'll use that definition loosely) is actually the inverse of what we call regular temperature.

So something can get up to infinite temperature when the microscopic temp (derivative of entropy wrt energy) is zero.

Even hotter than super large positive temp is superlarge negative temp. And a less negative temperature is even hotter still. The very hottest something could be would be to have a macroscopic temp just under zero.

Wrap your mind around all that. Take stat thermo if you actually want to understand.

Infinitely high temperature is routinely achieved in

nuclear demagnetization refrigerators.

Ironically, they are used to achive lowest possible

temperatures, microkelvins and less.