Abstract The thermodynamic behavior of carbon doped MgB 2 has been studied using a rigid ion model (RIM). The model potential consists of the long-range Coulomb, the short-range repulsive and the van der Waals interactions. This model has successfully explained the cohesive and thermodynamic properties of Mg(B 1− x C x ) 2 ( x=0.0, 0.02, 0.05, 0.075, 0.1, 0.2). The properties studied are the cohesive energy, molecular force constant, Restrahlen frequency, compressibility, Debye temperature and Gruneisen parameter. Our results on Restrahlen frequency and Debye temperature are in reasonably good agreement with the available experimental data. In addition, we have computed the specific heat C p for Mg(B 1− x C x ) 2 ( x=0.2) as a function of temperature T in the range 16 K⩽ T⩽1000 K. We have also shown the variation of specific heat C p with doping concentration at room temperature (300 K). The calculated specific heat C p for Mg(B 1− x C x ) 2 ( x=0.2) in the temperature range 16 K⩽ T⩽22 K for which experimental results are available, agrees pretty well with the experimental data.