a) Assume that a dielectric crystal consists of atomic planes that do not interact with each other, and thus the motion of the atoms remains in plane layers. Show that the low temperature Debye approximation is proportional to the phonon heat capacity.

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
icon
Related questions
Question
a) Assume that a dielectric crystal consists of atomic planes that do
not interact with each other, and thus the motion of the atoms
remains in plane layers. Show that the low temperature Debye
approximation is proportional to the phonon heat capacity.
(b) Assume that the monolayer atoms are on the surface of the
simple cubic structure (100) to form a two-dimensional array. If the
lattice constant of the cubic weave and the sound velocity over the
layer is m/s, determine how many Kelvin the Debye temperature is.
Transcribed Image Text:a) Assume that a dielectric crystal consists of atomic planes that do not interact with each other, and thus the motion of the atoms remains in plane layers. Show that the low temperature Debye approximation is proportional to the phonon heat capacity. (b) Assume that the monolayer atoms are on the surface of the simple cubic structure (100) to form a two-dimensional array. If the lattice constant of the cubic weave and the sound velocity over the layer is m/s, determine how many Kelvin the Debye temperature is.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Units and Dimensions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Process Dynamics and Control, 4e
Process Dynamics and Control, 4e
Chemical Engineering
ISBN:
9781119285915
Author:
Seborg
Publisher:
WILEY
Industrial Plastics: Theory and Applications
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The