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1) Obtain expressions for the heat capacity due to longitudinal vibrations of a chain of identical atoms; (a) in the Debye approximation; (b) using the exact density of states (Eq. below). With the same constants K and M, which expression gives the greater heat capacity and why? Show that at low temperatures both expressions give the same heat capacity, proportional to T. g(c) = L (MY πα Κ ² sec (3ka) = (K) T - 2N (14-2²)-1². 7 M N ¹/2 2(K/M)¹/2 (4K/M-²)¹/2

1) Obtain expressions for the heat capacity due to longitudinal vibrations of a chain of identical atoms; (a) in the Debye approximation; (b) using the exact density of states (Eq. below). With the same constants K and M, which expression gives the greater heat capacity and why? Show that at low temperatures both expressions give the same heat capacity, proportional to T. g(c) = L (MY πα Κ ² sec (3ka) = (K) T - 2N (14-2²)-1². 7 M N ¹/2 2(K/M)¹/2 (4K/M-²)¹/2

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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1) Obtain expressions for the heat capacity due to longitudinal vibrations of a chain of identical atoms; (a) in the Debye approximation; (b) using the exact density of states (Eg. below). With the same constants Kand M, which expression gives the greater heat capacity and why? Show that at low temperatures both expressions give the same heat capacity, proportional to T. L (M\/2 2(K/M)2 (4K/M – w²)/² N (M\1/2 g(») : sec (įka): %3D naK 1/2 2N (4K M
Transcribed Image Text:1) Obtain expressions for the heat capacity due to longitudinal vibrations of a chain of identical atoms; (a) in the Debye approximation; (b) using the exact density of states (Eg. below). With the same constants Kand M, which expression gives the greater heat capacity and why? Show that at low temperatures both expressions give the same heat capacity, proportional to T. L (M\/2 2(K/M)2 (4K/M – w²)/² N (M\1/2 g(») : sec (įka): %3D naK 1/2 2N (4K M
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