The present work investigates the entropy and the excitation inversion of a coupled system that consists of a qubit represented by a Cooper pair box (CPB) interacting with a transmission line working as a circuit quantum electrodynamics (CQED). The proposed scheme uses the Buck-Sukumar model with a time dependent frequency in the presence of losses to study the evolution of the entropy and the excitation inversion of the system. We have shown that the CQED is much more sensitive to the presence of losses than the CPB. The results also show that it is possible to monitor properties of the subsystems through appropriate choices of the time-dependent parameters.