N-atom single-mode radiation field interaction system is regarded as an interacting quasi-boson-photon system and is treated as a grand canonical ensemble.The explicit expression for the thermodynamical potential of the system is obtained using cluster expansion method.Some thermodynamic quantities are derived in terms of the general thermodynamic formulas.The numerical calculation and diagrams exhibit the thermodynamic behavior of the system.The singularities appearing in the critical line and other places furnish evidences of existence of the second kind of phase transformation in this collective system.