The Dulong–Petit law states that the molar specific heat of solids is 3R at higher temperatures, where R is the gas constant. For metals, this law is obeyed at room temperature, 300 K. The absorption of energy appears as internal energy in the metal in two primary ways: (1) vibration of metal lattice ions locked into crystalline positions and (2) translational kinetic energy of free electrons. The number of free electrons in a metal is approximately proportional to k_BT/E_F ,  since only those electrons near the Fermi energy can be thermally excited into available states. From this information, work with your group to determine the percentage of the total molar specific heat that is attributed to free electrons in gold.