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Table of Contents: 00:09 Lecture 2.2: Phonon Density of States 00:28 So, What is Temperature? 02:22 Phonon Density of States in 2D 05:52 Phonon Density of States in 3D 07:14 General Expressions for Number of States 08:38 Density of States in K-space 10:14 Density of States in Frequency Space 11:47 Debye Approximation This video is part of the nanoHUB-U course "Thermal Energy at the Nanoscale" (http://nanohub.org/courses/te) Thermal Energy at the Nanoscale, taught by Tim Fisher, is a five-week online course that develops a unified framework for understanding essential physics of nanoscale thermal energy and its important applications, trends, and directions. The course is designed to present this in a way that is accessible with only a very basic knowledge of heat transfer. The course will present an understanding of the fundamental elements of solid-state physics relevant to thermal transport, develop skills to derive continuum physical properties from sub-continuum principles, and apply statistical and physical principles to describe thermal energy transport in modern small-scale materials and devices.