Absolute zero is the lowest temperature but is there an upper limit?

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There are a number of arguments as to why there should be an upper bound on the value of temperature. The simplest is that temperature is related to energy (via Boltzmann’s constant). So if we believe that the energy in the universe is finite (a reasonable supposition), then that gives us the highest temperature.

This can be estimated as follows: the mass of the visible universe is about 1054 kilograms. From this, the energy of the universe can be calculated using the equation, E = mc2, where energy (E) equals mass (m) multiplied by the square of the speed of light (c2). Then divide this sum by Boltzmann’s constant to get the temperature. This comes out to about 1094 kelvin. While this is a large number, it certainly isn’t infinite.

“It is possible that neither the lowest nor highest temperature will ultimately have any fundamental significance”

The second argument comes from quantum physics and gravity. They imply that there is a smallest possible distance that can be defined in the universe, known as the Planck length. This gives us the highest possible frequency, which when multiplied by the Planck constant gives us the highest possible quantum of energy. If you divide this by Boltzmann’s constant, you get a temperature of 1032 kelvin. This is sometimes called the Planck temperature.

Another way of thinking about this concerns the Planck mass, thought to be the highest mass that a hypothetical elementary particle could have. Multiply this by c2 to get the energy of this particle, then divide by Boltzmann’s constant and you again get the Planck temperature, 1032 kelvin. This is much smaller than the first estimate I presented, but some cosmological models take it to be the initial temperature of the universe.

However, temperature isn’t a fundamental entity. It is really an emergent concept that tells us about the average chaotic kinetic energy of an object. In that sense, it is perfectly possible that neither the lowest nor the highest temperature will ultimately have any fundamental significance. Only time will tell.

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