Molar heat capacities of the pure samples of acetone, methanol and the azeotropic mixture composed of acetone, cyclohexane and methanol were measured by an adiabatic calorimeter from 78 to 320 K. The solid-solid and solid-liquid phase transitions of the pure samples and the mixture were determined based on the curve of the heat capacity with respect to temperature. The phase transitions took place at (126.16±0.68) and (178.96±1.47) K for the sample of acetone, (157.79±0.95) and (175.93±0.95) K for methanol, which were corresponding to the solid-solid and the solid-liquid phase transitions of the acetone and the methanol, respectively. And the phase transitions occurred in the temperature ranges of 120 to 190 K and 278 to 280 K corresponding to the solid-solid and the solid-liquid phase transitions of mixture of acetone, cyclohexane and methanol, respectively. The thermodynamic functions and the excess thermodynamic functions of the mixture relative to standard temperature of 298.15 K were derived based on the relationships of the thermodynamic functions and the function of the measured heat capacity with respect to temperature.