Physics-based battery models can predict not only voltage behaviors of a cell but also internal electrochemical variables such as lithium concentrations and electrical potentials. Knowledge of these variables will be critical in future battery management systems to be able to devise controls that extract the maximum performance from a cell while also slowing down its degradation, since available performance and degradation are both direct functions of the values of these internal electrochemical variables. This paper and its Part-1 companion concern themselves with simple but accurate models of lithium-ion cells having electrodes that are composed of a blend of multiple active materials. In this paper, we show how to create a physics-based reduced-order model (ROM). This ROM not only gives better voltage predictions than the equivalent-circuit models proposed in the Part-1 paper, but is also able to predict all cell internal electrochemical variables. Additionally, its computational complexity is similar to that of the circuit model.