Colorless quark-gluon gas in the limit of large $N_c$

A quark-gluon gas in a finite volume with global internal symmetry group $SU(N_c)$ on the states of which the condition of being colorless is imposed is studied in the limit $N_c\to\infty$. It is shown that without allowance for the conservation law of the baryon charge this system undergoes a phase transition of the third kind. However, in the more realistic situation in which this conservation law is taken into account there is no phase transition.