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# 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...

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 XXXXXXXXXXg/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.

## Solution

Robert answered on Dec 29 2021
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/cm
3
.
(a) Determine its density upon heating to 800?C when only thermal expansion is considered.
In this portion of the problem we are asked to determine the density of gold at 800C on the basis of
thermal expansion considerations. The basis for this determination will be 1 cm3 of material at 20C; this
volume of gold has a mass of 19.320 g, which mass is assumed to...
SOLUTION.PDF