Thermal expansion, specific heat, and ultrasonic data are presented for several metals, alloys, ceramics, and polymers, in order to define the magnitude of energy changes which occur when the materials are heated or cooled. Thermal Gruneisen ratios were computed as a function of temperature and numerous ultrasonic and thermodynamic equations were derived from the thermal data combined with measured compressibility data. Attempts to relate the volume coefficient of expansion, &bgr;, to heat capacity at constant volume, Cv, and to the elastic properties of polymers are discussed. Correlations are made between the measured thermal Gruneisen coefficients and those obtained from the change of atomic vibrational frequency with the change of volume as defined ultrasonically.