Determine its density upon heating to 800?C

When a metal is heated its density decreases. There are two sources that give rise to this diminishment of ρ: (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, α_v is equal to 3α_l.