The calcium looping (CaL) process, based upon the dry carbonation/calcination of CaO/CaCO3, is at the center of a potentially low‐cost, second‐generation technology for CO2 capture. This manuscript analyzes the energy penalty that arises from the integration of the CaL process into a coal‐fired power plant using cheap and abundantly available CaO precursors such as natural limestone, dolomite, and steel slag. Experimental results on their multicycle capture capacity behavior obtained from thermogravimetric analysis (TGA) at realistic CaL conditions for CO2 capture are used to this end. This work shows that the specific energy consumption for CO2 avoided (SPECCA) is reduced by using either dolomite or steel slag, whose carbonation kinetics in the diffusive phase are accelerated as compared to limestone. Thus, the use of dolomite as CaO precursor would yield a low SPECCA value of approximately 2 MJ kg−1 CO2 for a residence time of the solids in the carbonator of approximately 10 minutes, which is clearly below the SPECCA value usually reported for conventional amine‐based CO2 capture systems.