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Q2. The free energy of vacancy formation in aluminum is 0.76eV per vacancy. Estimate the vacancy concentration in this material just below the melting temperature (660°C).

Q2. The free energy of vacancy formation in aluminum is 0.76eV per vacancy. Estimate the vacancy concentration in this material just below the melting temperature (660°C).

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Q2. The free energy of vacancy formation in aluminum is 0.76eV per vacancy. Estimate the vacancy concentration in this material just below the melting temperature (660°C).
Transcribed Image Text:Q2. The free energy of vacancy formation in aluminum is 0.76eV per vacancy. Estimate the vacancy concentration in this material just below the melting temperature (660°C).
Expert Solution
Step 1: Explaining

To enter the reactive state all the elements need minimum amount of thermal energy to overcome the barrier of activation energy. The equation for the number of vacancies present in a metal at equilibrium at a particular temperature is:-

n subscript v equals N C e to the power of fraction numerator negative E subscript v over denominator k T end fraction end exponent

Where,

  •  n subscript v= number of vacancies per cubic meter of metal
  • N = total number of atom sites per cubic meter of metal
  • E subscript v= activation energy to form a vacancy (eV)
  • T = absolute temperature (K)
  • k = Boltzmann's constant = 8.62 cross times 10 to the power of negative 5 end exponent e V divided by K
  • C = constant
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