Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
à phonons is approximately Gak.

à phonons is approximately Gak.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
See similar textbooks
icon
Related questions
Question

Show that 22.12 imples 22.14

Please thanks!

Exercise 22.3. Debye theory of the lattice heat capacity of solids. At low temperatures, the heat capacity of dielectric solids is known to be pro- portional to T³, just as the heat capacity of the radiation field as derived from (22.10) is proportional to T8. We call a quantized elastic wave a phonon, in analogy to a photon as a quantized electromagnetic wave. The dispersion relation for long-wavelength phonons is approximately w = C,k, where c, is the velocity of sound. (a) If c, is taken as constant for all three longitudinal and transverse modes of vibration, show that the heat capacity per unit volume (22.12) с, 3D (12тЧkN /5)(T/Ө), where the Debye temperature O is given by (22.13) kO = hc,(6m*N)½, N being the number of atoms per unit volume. It is instructive to rewrite (22.12) for a cube of side L au 272 (22.14) C. 5 hc,L
Transcribed Image Text:Exercise 22.3. Debye theory of the lattice heat capacity of solids. At low temperatures, the heat capacity of dielectric solids is known to be pro- portional to T³, just as the heat capacity of the radiation field as derived from (22.10) is proportional to T8. We call a quantized elastic wave a phonon, in analogy to a photon as a quantized electromagnetic wave. The dispersion relation for long-wavelength phonons is approximately w = C,k, where c, is the velocity of sound. (a) If c, is taken as constant for all three longitudinal and transverse modes of vibration, show that the heat capacity per unit volume (22.12) с, 3D (12тЧkN /5)(T/Ө), where the Debye temperature O is given by (22.13) kO = hc,(6m*N)½, N being the number of atoms per unit volume. It is instructive to rewrite (22.12) for a cube of side L au 272 (22.14) C. 5 hc,L
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Buckling of Columns
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS