The number of vacancies in some hypothetical metal increases...

Name: The number of vacancies in some hypothetical metal increases by a factor of 5 when the temperature is increased from 1050 K to 1160 K. Calculate the energy (in kJ/mol) for vacancy formation assuming that the density of the metal remains the same over this temperature range.
Uploaded: 2022-10-04T15:46:56-08:00
Duration: 6 min 51 s
Channel: Derrick Danso
Description: The number of vacancies in some hypothetical metal increases by a factor of 5 when the temperature is increased from 1050 K to 1160 K. Calculate the energy (in kJ/mol) for vacancy formation assuming that the density of the metal remains the same over this temperature range.

The number of vacancies in some hypothetical metal increases by a factor of 5 when the temperature is increased from 1050 K to 1160 K. Calculate the energy (in kJ/mol) for vacancy formation assuming that the density of the metal remains the same over this temperature range.

When a metal is heated its density decreases. There are two sources that give rise to this diminishment of $\rho:(1)$ the thermal expansion of the solid, and (2) the formation of vacancies (Section 4.2). Consider a specimen of gold at room temperature $\left(20^{\circ} \mathrm{C}\right)$ that has a density of $19.320 \mathrm{g} / \mathrm{cm}^{3}$. (a) Determine its density upon heating to $800^{\circ} \mathrm{C}$ 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 $0.98 \mathrm{eV} /$ atom, and that the volume coefficient of thermal expansion, $\alpha_{v}$ is equal to $3 \alpha_{i}$.