12.3 Most Probable Distribution
Assume that we have N distinguishable particles to occupy two energy levels 1 and 2, the probability to find N1 particles occupying at energy level 1 is given by the number of combinations of N particles taken N1 at a time
January 28, 2009
Condensed Matter Physics/Physics-335
Assignment #2Diffraction
Due on Moday February 8, 2010 @ 12:30PM sharp
(Suggestion: start immediately working on this assignment it is a bit more difficult than it looks. This is
particularly the case
Basic Principles of Classical and Statistical Thermodynamics
By
Thomas W. Leland, Jr.(*)
Preparation and editorial by
G.A. Mansoori
Department of Chemical Engineering, University of Illinois at Chicago
810 S. Clinton Street, Chicago, IL 60607-7000, <manso
Chapter 18 Bose-Einstein Gases (Part I)
18.1 Black-Body Radiationa perfect quantal gas
18.1.1 Introduction
First, one may ask: What is black-body radiation? A perfectly black body radiation
absorbs all radiation falling on it. This is very similar to the
12.6 Energy Levels and Quantum States
In quantum mechanics, the N-particle system contained in a
finite volume may exist in any one of an enormous number
of discrete states determined by the Schrdinger equation
r
r
(r , t ) = (r , t ).
H
j
Each energy ei
Chapter 12. Statistical Thermodynamics
12.1 System and ensembles
Introduction. Statistical mechanics deals with the following
problem: we have a system, that is, the part of the physical
world, in which we are interested. About this macroscopic
system, we
BISHOPS UNIVERSITY
Department of Physics
PHYSICS 107: THERMAL AND FLUID PHYSICS
FALL 2005
Instructor: Dr. Valerio Faraoni
Office: Molson 107, tel. (819) 822 9600 ext. 2490, fax (819) 822 9661,
electronic mail vfaraonicslinux.ubishops.ca
Office hours: Mond
Assignment # 1: Problems 12-1, 12-4, and 12-6 (due on Monday, January 18)
Assignment # 2: Problems 12-8, 12-9, 12-11 and 12-12 (due on Monday, January 25)
Assignment #9: Due on Wed, March 23.
1.
Use the simple model of the greenhouse-gas effect of the Earth given in Lecture
note 18.1.7 to address the following two issues.
(a)
Discuss the effect of increasing atmospheric CO2 concentrations from the current
v
Assignment #9: Due on Wed, March 23.
1.
Use the simple model of the greenhouse-gas effect of the Earth given in Lecture
note 18.1.7 to address the following two issues.
(a) Discuss the effect of increasing atmospheric CO 2 concentrations from the current
Assignment # 10. Due on Wed, March 30.
Problem 1. An atomic nucleus can be roughly modeled as a gas of nucleus with a number
density of 0.18 fm-3 (1 fm=10-15 m). Because nucleons come in two different types
(protons and neutrons), each with spin , each sp
Chapter 12. Statistical Thermodynamics
12.1 System and ensembles Introduction. Statistical mechanics deals with the following problem: we have a system, that is, the part of the physical world, in which we are interested. About this macroscopic system, we
19.3 Free Electron Model of Metals
In the free electron gas model, the outer valence electrons the free electron gas model the outer valence electrons of atoms move freely in a potential well. The free electrons occupy the lowest energy states up to the F
Chapter 18 Bose-Einstein Gases (Part II)
18.2 Bose-Einstein Condensation 18.2.1 Introduction In 1924, S. N. Bose sent to Einstein a paper, in which Planck formula was derived by entirely statistical argument, treating black-body radiation as a photon gas.
13.4 Dilute gases & Maxwell-Boltzmann Distribution
For a dilute gas, the occupation number at each energy level is much smaller than the available number of quantum states, i.e.,
Nj gj
This gives
< 1, for each j.
(13.27)
fj =
Nj gj
=
1 e
( j ) / kT
1
< 1,
16.3 Debye theory of the heat capacity of solids
The atoms in a crystal consisting of N atoms do not vibrate independently of each other about fixed sites. Instead, they execute very complicated coupled vibrations. From classical mechanics, however, one k
Chapter 13 Classical and Quantum Statistics
In this chapter, we are interested in determining the equilibrium configuration for a microcanonical ensemble subject to Eqs. (12.7) and (12.8), i.e., the total number of particles is N and the total energy of p
Chapter 15 The heat capacity of a diatomic gas
Introduction
For a diatomic gas, f=7, the equipartition of energy gives U=(7/2)NkT, Cv=(7/2)Nk, CP=(9/2)Nk, so that =CP/CV=1.28. This is inconsistent with the experimental observation. Moreover, the classical
Chapter 14 Application of MaxwellBoltzmann Statistics to an Ideal Gas
The Classical Statistical Treatment
As mentioned in Chapt 13, Maxwell-Boltzmann statistics is a good model for a real gas under most conditions (the classical limit condition holds for
13.2 Fermi-Dirac Statistics
We want to get the equilibrium configuration for a system consisting of fermion particles, such as electrons and protons. The number of ways to arrange Nj indistinguishable particles into energy level j with gj quantum states w
18.1.2 Derivation of Planck formula from the wave 18.1.2 Derivation of Plancks formula from the wave picture of EM radiation The wave-particle duality of EM radiation leads to two wave duality of EM radiation leads to two alternative statistical treatment
14.3 Condition of the Classical Limit-Applicability of M-B statiscs
M-B stat. is valid under the dilute gas condition:
fj = Nj gj = N j / kT e < 1. Z
Since j~kT, the above inequality is equivalent to
N N = < 1, Z V ( 2mkT ) 3 / 2 h2 V 1/ 3 h (14.12) dB .
Chapter 16 The Heat Capacity of Solids
16.1 Introductory remarks
In this chapter, we shall apply statistical methods to obtain the heat capacity (Cv) of solids, or more precisely, the heat capacity associated with the lattice vibrations of crystalline sol