This study gives our predictions for the thermal expansivity alpha(p), isothermal compressibility kappa(T), and specific heat Cp near the melting point for ice Ih. We calculate those thermodynamic quantities as functions of temperature and pressure near the melting point using the experimental data for the thermal expansivity as a function of pressure from the literature. The Pippard relations are validated by plotting C-p against alpha(p) and also alpha(p) against kappa(T) linearly close to the melting point in ice Ih. We deduce the values of the slope partial derivative P-m/partial derivative T from those linear plots, which are very close to the experimental value obtained from the P-T phase diagram of ice Ih along the melting curve.