a very direct consequence may be the highest temperature.
According to the kinetic theory, the temperature of a gas depends entirely on the speed of its particles.
number of mole * a constant * Temperature = one and half * mass * square of speed
Thus, the highest speed set a upper bound of temperature.
when we put the number in it, the highest temperature for 1 mole of the heaviest atom ( ununoctium, a mole is weight 294 gram) is:
4.767 x 10^15 degree ~ 5 x 10^15 degree = 5,000,000,000,000,000 degree
a very huge number!!
To see how hot it is, we can compare this with some known temperature.
Boiling Point of Gold is about 3,000 degree
Melting Point of diamond is about 3,500 degree
Boiling Point of diamond is about 5,000 degree
The core of earth is about 7,000 degree
The sun's surface is about 6,000 degree
The sun's core is about 5,000,000 degree
Notices that at the sun core, nuclear fusion is taking place. This is one of the violent reaction is the universe.
However, this is the classical view.
If we review the theory of getting the temperature. the temperature is proportional to K.E. instead of speed square. Since according to the special relativity, the Kinetic energy is corrected and not just the square of speed. Other speaking, the classical kinetic energy, which is equal to half of mass times speed square is for low speed. For high speed, the classical formula is not correct. Thus, the kinetic energy is not limited by the special relativity, but the speed. Therefore, there is no highest temperature.
The story does not stop in here, if we look a more closer look on what happen under high temperature. First, when temperature getting higher and higher, the pack of particle hits each others more frequently, and harder. Around 9,000 degree, atom no longer exist because the electrons are kicked out, and we called this, plasma. around 20,000 degree, plasma no longer exist because nuclear are broken, only protons and neutrons are left. At even higher temperature, protons and neutrons fall part and quark is left. Although we not really observed quark, we believe its existence. At very very high temperature, a hit of quark may produce many other particles as well. So, how to treat this ? what physics law should be use?
2nd, if we treat it like classic physic (i.e. no interaction between quark), the mass term is greatly reduced by replacing a heaviest atom by a quark. 100 times lesser the temperature will be. If we use electrons, also very fundamental particle, the mass term will be deduced 2000 times.
3rd, we so far believe the quark and electron cannot be broken because they are fundamental particles, What if it is wrong?
4th, What is the definition of temperature? only by the kinetic theory? If we have only 1 particle, is there any meaning for temperature? if no, what is the minimum number of particle to define a temperature? That are all testing our understanding.
Another definition of temperature is giving by thermodynamic. The concept of entropy.
entropy = Boltzmann constant * Log ( combination of the system )
1/ Temperature = change of entropy per unit energy
In human language, which means, if we inject 1 unit of energy, How many entropy or how the change of possible combination of the system. And the change is equal 1 over temperature. Which mean, if the change is minimum or zero, we have the highest temperature. Thus, when you cannot change the system by inject more energy, the temperature is highest and equal to infinite. Make sense!!!
According to this definition, even a single particle or an empty space has temperature! But the discussion is already out of topic.
Another way to find out the highest temperature is by the uncertainty principle, which stated that
the change of energy * the change of time must be grater or equal to the Planck constant.
In this case, the highest temperature is around 15 x 10^31 degree.
So far, the highest temperature is still an open question.
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