A system for reducing carbon dioxide emissions from a flue gas generated via combusting a fossil fuel is provided. The system includes a carbonator and a classifier. The carbonator is configured to receive the flue gas and carbon absorbing particles. The classifier is fluidly connected to the carbonator and configured to receive a mixture that includes heat-transferring particles and the carbon absorbing particles. The mixture is fluidized within the classifier via the flue gas at a velocity such that the flue gas entrains and transports the carbon absorbing particles to the carbonator while the heat-transferring particles are not entrained nor transported to the carbonator.