A model is developed to predict the evolution of the particle size distribution for batch impact attrition, resulting in a transfer from larger to smaller particles. This model allows the fate of individual particles to be described in terms of impact attrition and the effects of operating parameters, i.e., number of impact cycles, particle velocity upon impact and temperature. The model provides good agreement with experimental results for two limestones striking a target at temperature from 25-580 degrees C and particle impact velocities from 9 to 64 m/s with model fitting parameters estimated using nonlinear least squares based on experimental sieve analysis data. The exchange of mass between different particle size intervals is assumed to be first-order with respect to the mass of original particles, proportional to the square of particle velocity, and following an Arrhenius relationship with respect to temperature, but with quite different activation energies for the two limestones. A simplified model with only one fitted parameter provides almost as goad agreement as the multi-parameter model and is suggested for practical applications. (C) 2010 Elsevier B.V. All rights reserved.