EXAMPLE $4-1$ The Effect of Temperature on Vacancy Concentrations

Calculate the concentration of vacancies in copper at $25C.$ What temperature

will be needed to heat treat copper such that the concentration of vacan$-$

cies produced will be $1000$ times more than the equilibrium concentration of

vacancies at room temperature? Assume that $20,000$cal are required to produce

a mole of vacancies in copper.