STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SOLUTIONS
PROBLEM 1
a. NA = 6.02 1023 nucleons/gram, tells us how many nuclear particles (protons and neutrons)
1 gram of matter contains. One of my favorite formulas is therefore:
NA
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SET 1:
This Homework is due on Wednesday of the second week of classes,
in class just before the lecture.
A. THERMAL PHYSICS REVIEW
PROBLEM 1
A dilute gas such as air can be described
Chapter 4
The Methodology of Statistical
Mechanics
c 2010 by Harvey Gould and Jan Tobochnik
9 January 2015
We develop the basic methodology of statistical mechanics and provide a microscopic foundation
for the concepts of temperature and entropy.
4.1
Intr
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SET 2:
This Homework is due on Wednesday of the third week of classes,
in class just before the lecture.
PROBLEM 6
The equations of state for an ideal monoatomic gas
pv = kB T
;
u=
3
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SET 3:
This Homework is due on Wednesday of the fourth week of classes,
in class just before the lecture.
C. THE SECOND LAW
PROBLEM 9
a. Recall problem 5, where we throw water onto a
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SET 4:
This Homework is due on Wednesday of the fth week of classes,
in class just before the lecture.
REMINDER: the MIDTERM takes place on MONDAY Nov 02
It covers Chapters 2 and 3 of
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SET 5:
This Homework is due on Friday November 06
D. RANDOM WALK PROCESSES
PROBLEM 17
Consider the Master equation for a random walker on a one dimensional lattice of sites
with m = 0
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SOLUTIONS
PROBLEM 6
The equations of state for an ideal monoatomic gas
pv = kB T
;
u=
3
kB T
2
(where v = V /N is the volume per particle and u = U/N the internal energy per particle)
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SOLUTIONS
PROBLEM 9
(a). The water thrown on the wall evaporation process is a non quasi-static process and is irreversible. The time reversed movie of the collision when interpreted
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SOLUTIONS
PROBLEM 13
This problem resembles more an assisted reading assignment and literature (WEB) search
than a conventional homework problem Find in GT the sections about the Joul
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SET 6:
This Homework is due on Monday November 16.
F. MICRO CANONICAL ENSEMBLE
PROBLEM 21
a. Consider the Gaussian integral
I=
2
1
dx eax =
a
dx ex
2
(1)
Find its value by squaring i
Chapter 3
Concepts of Probability
c 2011 by Harvey Gould and Jan Tobochnik
3 June 2014
We introduce the basic concepts of probability and apply them to simple physical systems and
everyday life. We discuss the universal nature of the central limit theorem
Chapter 2
Thermodynamic Concepts and
Processes
c 2011 by Harvey Gould and Jan Tobochnik
3 June 2014
We introduce the concepts of temperature, energy, work, heating, entropy, engines, and the laws
of thermodynamics and related macroscopic concepts.
2.1
Int
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SET 3:
This Homework is due on Wednesday of the fourth week of classes,
in class just before the lecture.
C. THE SECOND LAW
PROBLEM 9
a. Recall problem 5, where we throw water onto a
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SET 1:
This Homework is due on Wednesday of the second week of classes,
in class just before the lecture.
A. THERMAL PHYSICS REVIEW
PROBLEM 1
A dilute gas such as air can be described
STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
HOMEWORK SET 2:
This Homework is due on Wednesday of the third week of classes,
in class just before the lecture.
PROBLEM 6
The equations of state for an ideal monoatomic gas
pv = kB T
;
u=
3
YOUR NAME:
PRACTICE FINAL EXAM STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
PROBLEM 1: (100 points)
(a). [15] Consider a particle living on the line segment 1 x < . Write down the definition
of the Boltzmann-Shannon entropy of the probab
YOUR NAME:
SOLUTIONS - PRACTICE MIDTERM, STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
PROBLEM 1 [25 points]
A small cube of ice, of mass M = 100 gr, at its freezing temperature T = 0 C, is dropped
into a large bath tub filled with water,
YOUR NAME:
PRACTICE FINAL EXAM STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
PROBLEM 1: (100 points)
(a). [15] Consider a particle living on the line segment 1 x < . Write down the definition
of the Shannon-Boltzmann entropy of the probab
THERMODYNAMICS
Marcel den Nijs
ENGINES, REFRIGERATORS, AND THE SECOND LAW.
1. REVERSIBLE AND IRREVERSIBLE CYCLE PROCESSES
a. ideal gas cycles
The (ir)-reversibility of cycle processes is the central issue in macroscopic thermodynamics
discussions of the 2
THERMODYNAMICS
Marcel den Nijs
ELEMENTS OF KINETIC GAS THEORY
1. PRESSURE
a. pressure tensor
In solids, the tensor character of pressure is important. The same is true in non-equilibrium
liquids and gases (viscosity). However, in static gases and liquids,
R
EVI EWS
Ofi'
MOD ERN
:3escription
PH
YSI CS
VOLUME
29, NUMBER
1957
JANUARY,
States in Quantum .V. :ec.zanies
:Density .'V. :atrix anc Operator . . ec.~niques
o1
vy
U. FAwo
National BNreaN, of Standards, Washimgtoe,
1. INTRODUCTION
Contents
'0
1. Introdu
Chapter 1
From Microscopic to Macroscopic
Behavior
c 2010 by Harvey Gould and Jan Tobochnik
3 June 2014
We explore the fundamental dierences between microscopic and macroscopic systems, note that
bouncing balls come to rest and hot objects cool, and discu
YOUR NAME:
PRACTICE MIDTERM, STATISTICAL MECHANICS
PHYSICS 328, Instructor: Marcel den Nijs
PROBLEM 1 [25 points]
A small cube of ice, of mass M = 100 gr, at its freezing temperature T = 0 C, is dropped
into a large bath tub filled with water, at Tw = 30