Question

The average energy of particles in the early phase of the universe, when it was very
hot, was approximately 10 GeV. Calculate the corresponding temperature.

Answer 1

The average energy of particles $E=10 GeV = 1.6 \cdot 10^{10} J$

k = Boltzmann’s constant $=1.381 \cdot 10^{−23} J/K$

$E=kT\implies T=\frac{E}{k}$

$T = \frac{1.6\cdot 10^{10}}{1.38\cdot 10^{-23}}=1.15 \cdot 10^{14} K$

Answer $T = 1.15 \cdot 10^{14} K$