Wednesday 14 August 2019

thermodynamics - Maximum Temperature?



I have been reading a lot about wavelengths of light and Planck's law and such. Curious as to whether a minimum wavelength of $h$ (Planck's Constant) indicates that there is in some way an absolute maximum temperature.


Any thoughts or suggestions are appreciated.



Answer



Planck temperature is the maximum temperature on the Planck scale. Some sources call it absolute hot.


The Planck temperature is defined as $$T_P = \frac{m_P c^2}{k} = \sqrt{\frac{\hbar c^5}{G k^2}} = 1.416833(85)\times10^{32} \text{K}$$ where $m_P$ is the Planck mass, $c$ is the speed of light, $\hbar = h/2\pi$ is the reduced Planck constant, $k$ is Boltzmann's constant, and $G$ is the universal gravitational constant.


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