A linear correlation between the specific heat C P and the thermal expansion α p is established here for constant temperatures close to the melting pressure in ammonia solid III. For this correlation, the experimental data for the isothermal compressibility κ T is analysed according to a power-law formula with the critical exponent γ and, the C P and α p are calculated as a function of pressure near the melting point in ammonia solid III.Values of the entropy changes with the temperature, which are extracted from linear plots of C P against α p , decrease as the temperature increases for the ammonia solid III prior to melting.