When a metal is heated its density decreases. there are two sources that give rise to this decrease of rho: (1) the thermal expansion of the solid and (2) the formation of vacancies (section 5.2). consider a specimen of gold at room temperature (20°c) that has a density of 19.320 g/cm3 . (a) determine its density upon heating to 800°c when only thermal expansion is considered. (b) repeat the calculation when the introduction of vacancies is taken into account. assume that the energy of vacancy formation is 0.98 ev/atom, and that the volume coefficient of thermal expansion, αv is equal to 3αl .