MATLS 1M03 Lecture Notes - Lecture 4: Heat Capacity, Latent Heat, Thermal Conduction
20 May 2018
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MATLS 1M03: Follow-along Notes: Module 3 Winter 2017
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Module 4: Transport Phenomena in Solids
The transport of physical quantities affects every part of life around us. Consider the cells
within the human body: mass is transported in and out to provide fuel and eliminate waste,
heat is transported to regulate temperature, and electricity provides communications. In this
module we will explore the transport of mass, heat, and electricity in solids, a mode that is
generally called diffusion. We will assume steady-state conditions and one-dimensional flow.
This leads to: Fick’s First Law, Fourier’s Law, and Ohm’s Law. Although they were discovered by
different individuals, all three share the identical form. Note – we will return to the topic of
Electronic materials later in the course.
Chapters Covered: 5,18,19
Vocabulary
Chapter 5: Mass diffusion coefficient, Vacancy diffusion, Interstitial diffusion, Fick’s First Law
Chapter 18: Resistivity, Conductivity, Electronic conduction, Ionic conduction, Ohm’s Law
Chapter 19: Specific heat capacity, Latent heat, Thermal conductivity, Diffusivity, Fourier’s Law
At the end of this module, you should be able to
Name and describe the underlying mechanisms of mass, heat, and electrical conduction
Identify the factors that influence mass, heat, and electrical conduction
Calculate the mass diffusion coefficient for a material at a specified temperature, given
appropriate constants
Write Fick’s First Law, and define all parameters
Write Fourier’s Law, and define all parameters
Write Ohm’s Law, and define all parameters
Apply the above laws in an engineering context to determine specific parameters.
Follow-along Notes
Mass Diffusion: Diffusion is the process in which atoms or molecules move through a substance.
This is not the same as flow. Flow implies that a bulk fluid is moving through space. In diffusion,
individual atoms or molecules move individually through the bulk of another material.
Consider the case of H2 gas moving through a thin but solid Ni sheet. On one side of the metal
the gas has pressure PL, on the other side pressure PR. Answer the following questions:
• Which side has the greater H2 pressure, L or R?
• Which side has the greater H2 concentration, L or R?
• Based on the figure, which way does the H2 move through the Ni, to the right or to the left?
• If the concentration of H2 were greater on side R than side L, which way would the H2
diffuse?
• If the concentration of H2 were equal on sides R and L, which way would the H2 diffuse?
MATLS 1M03: Follow-along Notes: Module 3 Winter 2017
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• What is the driving force for H2 diffusion through the metal sheet?
• Consider two situations, both with PL>PR. If PL increases from double PR to triple PR, will the
rate of diffusion change?
There are two main mechanisms of diffusion; vacancy diffusion and interstitial diffusion.
Vacancy diffusion is called this because you can think of it occurring by the motion of vacancies
(even though it is really atoms that are moving). Interstitial diffusion is called this because
atoms jump between successive interstitial sites.d
The questions below will help you to explore the concepts of vacancy and interstitial diffusion.
• Circle the substitutional impurity in the figure.
• Circle the vacancy in the figure.
• If the impurity atom were going to diffuse, where could it move to?
• Can the impurity atom continue to move further away from its original position based only
on what you see in the figure? Is there anywhere else that it could go other than back to
where it was?
• If the impurity atom were going to move further away from its original position, what would
have to be present?
• Circle the interstitial atom in the figure.
• Put an X through the vacant interstitial sites in the figure.
• If the impurity atom were going to diffuse, where could it move to?
• Can the impurity atom continue to move further away from its original position based on
what you see in the figure? Is there anywhere else it can go other than back to where it was?
• Which is faster, diffusion of substitutional or interstitial impurity atoms?
PL>PR
Document Summary
The transport of physical quantities affects every part of life around us. Consider the cells within the human body: mass is transported in and out to provide fuel and eliminate waste, heat is transported to regulate temperature, and electricity provides communications. In this module we will explore the transport of mass, heat, and electricity in solids, a mode that is generally called diffusion. We will assume steady-state conditions and one-dimensional flow. This leads to: fick"s first law, fourier"s law, and ohm"s law. Although they were discovered by different individuals, all three share the identical form. Note we will return to the topic of. Chapter 5: mass diffusion coefficient, vacancy diffusion, interstitial diffusion, fick"s first law. Chapter 18: resistivity, conductivity, electronic conduction, ionic conduction, ohm"s law. Chapter 19: specific heat capacity, latent heat, thermal conductivity, diffusivity, fourier"s law. At the end of this module, you should be able to. Name and describe the underlying mechanisms of mass, heat, and electrical conduction.
