Thermodynamical Properties of Elementary Particles

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In the mid-forties G.A. Gamov proposed the idea
of the "hot" origin of the World. Therefore thermodynamics
was introduced into cosmology, and nuclear physics too.
Before him the science of the evolution of Universe
contained only dynamics and geometry of the World.
A.D.Chernin.

The Standard Model particles and their properties.
Particles Mass Number of states $g$ (particles and anti-particles)
spin color
Photon ($\gamma$) 0 2 1 2
$W^+,W^-$ $80.4\, GeV$ 3 1 6
$Z$ $91.2\,GeV$ 3 1 3
Gluon ($g$) 0 2 8 16
Higgs boson $>114\, GeV$ 1 1 1
Bosons 28
$u,/,\bar{u}$ $3\, MeV$ 2 3 12
$d,/,\bar{d}$ $6\, MeV$ 2 3 12
$s,/,\bar{s}$ $100\,MeV$ 2 3 12
$c,/,\bar{c}$ $1.2\,GeV$ 2 3 12
$b,/,\bar{b}$ $4.2\, GeV$ 2 3 12
$t,/,\bar{t}$ $175\,GeV$ 2 3 12
$e^+,\,e^-$ $0.511\, MeV$ 2 1 4
$\mu^+,\,\mu^-$ $105.7\,MeV$ 2 1 4
$\tau^+,\,\tau^-$ $1.777\, GeV$ 2 1 4
$\nu_e,\,\bar{\nu_e}$ $<3\,eV$ 1 1 2
$\nu_\mu,\,\bar{\nu_\mu}$ $<0.19\,MeV$ 1 1 2
$\nu_\tau,\,\bar{\nu_\tau}$ $<18.2\, MeV$ 1 1 2
Fermions 90

Problem 1

Find the energy and number densities for bosons and fermions in the relativistic limit.

Problem 2

Find the number densities and energy densities, normalized to the photon energy density at the same temperature, for neutrinos, electrons, positrons, pions and nucleons in the relativistic limit.

Problem 3

Calculate the average energy per particle in the relativistic and non-relativistic limits.

Problem 4

Find the number of internal degrees of freedom for a quark.

Problem 5

Find the entropy density for bosons end fermions with zero chemical potential.

Problem 6

Find the effective number of internal degrees of freedom for a mixture of relativistic bosons and fermions.

Problem 7

Generalize the results of the previous problem for the case when some $i$-components have temperature $T_i$ different from the CMB temperature $T$.

Problem 8

Find the effective number of internal degrees of freedom for the Standard Model particles at temperature $T>1TeV$.

Problem 9

Find the change of the number of internal degrees of freedom due to the quark hadronization process.

Problem 10

Find the relation between the energy density and temperature at $10^{10}\, K$.

Problem 11

Find the ratio of the energy density at temperature $10^{10}\, K$ to that at $10^8\, K$.

Problem 12

Determine Fermi energy of cosmological neutrino background (CNB) (a gas).