ALL 8 CHAPTERS COVERED
,Contents
Chapter 1 Energy in Thermal Physics . . . . . . . . . . . . . . . . . . 1
Chapter 2 The Second Law . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter 3 Interactions and Implications . . . . . . . . . . . . . . . . . 59
Chapter 4 Engines and Refrigerators . . . . . . . . . . . . . . . . . . 82
Chapter 5 Free Energy and Chemical Thermodynamics . . . . . . . . 104
Chapter 6 Boltzmann Statistics . . . . . . . . . . . . . . . . . . . . 169
Chapter 7 Quantum Statistics . . . . . . . . . . . . . . . . . . . . . 202
Chapter 8 Systems of Interacting Particles . . . . . . . . . . . . . . 284
Appendix A Elements of Quantum Mechanics . . . . . . . . . . . . . 320
Appendix B Mathematical Results . . . . . . . . . . . . . . . . . . 333
iii
,Preface
This Instructor’s Solutions Manual contains solutions to all 486 problems in An Introduction to
Thermal Physics. The solutions are not just hints or outlines—I have tried to include as many
algebraic steps as a typical student would need to write out, plus enough prose to explain both the
method of solution and the meaning of the results. Of course, one can always say more about almost
any question or calculation; I’m sure that many students and instructors can add further insight to
what is written here.
About 75 of the problems in the book require some sort of automatic computation, beyond
what can be done with a simple pocket calculator. Although the problems themselves do not assume
any particular computing environment, their solutions do. In this manual I have used three different
microcomputer-based computing environments: the Excel spreadsheet program for making tables
of numbers and some graphs; Mathematica for plotting formulas, for numerical integration and root
finding, and for occasional symbolic computation; and True BASIC for the Monte Carlo simulations
in Problems 8.26 through 8.32. I recognize that no computing environment is perfect in all respects,
and that others will make different choices, for excellent reasons. My own choices were determined
by trade-offs among such factors as personal familiarity, ease of use, readability of the printed
record, portability between operating systems, apparent stability over time, and consistency within
this manual. I would be interested to hear from instructors or students who have solved the more
intricate problems using other computing environments.
If you haven’t already, please browse the web site for the book, which (for the foreseeable future)
is at the URL “http://physics.weber.edu/thermal/”. There you will find some instructions on
getting started with Excel, Mathematica, and True BASIC, plus a variety of other information
about the book and about thermal physics. Perhaps most importantly, you will find a page listing
corrections to the book, and a similar page for this manual. If you find errors in either that are not
listed on the web pages, please let me know.
I am extremely grateful to the many instructors and students who have already used An
Introduction to Thermal Physics and sent comments and suggestions. This manual has benefited
from several corrections that were contributed by instructors using draft chapters. I am also indebted
to Deb Badger for the use of her Macintosh G4 computer, which allowed me to run the True BASIC
simulations in a reasonable amount of time.
DVS
Ogden, Utah
November 1, 2000
Note on this corrected edition: I have taken the opportunity to correct all of the known errors
in the original edition of this manual. It is a pleasure to thank B. Blakie, L. Cominsky, M. Davis, A.
Gavrin, J. Lockhart, and G. Wiegerinck for bringing many of these errors to my attention. I have
also redrawn and improved a number of the illustrations, including all of the spreadsheet-generated
graphs. Further corrections and suggestions are always welcome.
August 5, 2016
iv
, 1 Energy in Thermal Physics
c 2001, 2016 Pearson Education, Inc. All rights reserved. No portion of this material may be
reproduced, in any form or by any means, without permission in writing from the publisher.
Problem 1.1. (Fahrenheit temperature scale.)
(a) To take Celsius to Fahrenheit, we want a linear function that takes 0 to 32 and 100
to 212. Imagining a graph of this function, the vertical intercept must be 32 and the
slope must be (212 32)/(100 0) = 9/5; therefore the function is
9
(T in F) = (T in C) + 32.
5
Inverting this function is now just a matter of algebra:
5
(T in C) = [(T in F) 32].
9
(b) Plugging 273.15 C into the first formula gives the value 459.7 for absolute zero in
degrees Fahrenheit.
Problem 1.2. To convert from Fahrenheit to Rankine, you would simply add 460, which
raises the value of absolute zero (see the previous problem) to zero as desired. Rankine
and kelvin temperatures are both measured from the same zero-point, so the conversion
between them is just the factor of 9/5 found in the previous problem, with no constant
term added. A kelvin degree is bigger than a Rankine degree, so the conversion is
9
(T in R) = (T in K),
5
which is equivalent to
5
K. 1 R=
9
9
Room temperature, about 300 K, would therefore be 5
· 300 = 540 on the Rankine scale.
Problem 1.3. (Kelvin temperature examples.)
(a) Human body temperature is “officially” 37 C, or 310 K. (In the U.S., this official
temperature is traditionally converted to 98.6 F—a classic example of failing to round
off insignificant digits.)
(b) Water is supposed to boil at 100 C, so that would be 373 K.
(c) I remember a night in Minnesota when the temperature was reported as 29 F. That
converts to 34 C, which is 239 K.
(d) 196 C would be 77 K, so liquid nitrogen is about four times closer to absolute zero
than room temperature is.
(e) 327 C would be 600 K, to three significant figures.
1
,Contents
Chapter 1 Energy in Thermal Physics . . . . . . . . . . . . . . . . . . 1
Chapter 2 The Second Law . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter 3 Interactions and Implications . . . . . . . . . . . . . . . . . 59
Chapter 4 Engines and Refrigerators . . . . . . . . . . . . . . . . . . 82
Chapter 5 Free Energy and Chemical Thermodynamics . . . . . . . . 104
Chapter 6 Boltzmann Statistics . . . . . . . . . . . . . . . . . . . . 169
Chapter 7 Quantum Statistics . . . . . . . . . . . . . . . . . . . . . 202
Chapter 8 Systems of Interacting Particles . . . . . . . . . . . . . . 284
Appendix A Elements of Quantum Mechanics . . . . . . . . . . . . . 320
Appendix B Mathematical Results . . . . . . . . . . . . . . . . . . 333
iii
,Preface
This Instructor’s Solutions Manual contains solutions to all 486 problems in An Introduction to
Thermal Physics. The solutions are not just hints or outlines—I have tried to include as many
algebraic steps as a typical student would need to write out, plus enough prose to explain both the
method of solution and the meaning of the results. Of course, one can always say more about almost
any question or calculation; I’m sure that many students and instructors can add further insight to
what is written here.
About 75 of the problems in the book require some sort of automatic computation, beyond
what can be done with a simple pocket calculator. Although the problems themselves do not assume
any particular computing environment, their solutions do. In this manual I have used three different
microcomputer-based computing environments: the Excel spreadsheet program for making tables
of numbers and some graphs; Mathematica for plotting formulas, for numerical integration and root
finding, and for occasional symbolic computation; and True BASIC for the Monte Carlo simulations
in Problems 8.26 through 8.32. I recognize that no computing environment is perfect in all respects,
and that others will make different choices, for excellent reasons. My own choices were determined
by trade-offs among such factors as personal familiarity, ease of use, readability of the printed
record, portability between operating systems, apparent stability over time, and consistency within
this manual. I would be interested to hear from instructors or students who have solved the more
intricate problems using other computing environments.
If you haven’t already, please browse the web site for the book, which (for the foreseeable future)
is at the URL “http://physics.weber.edu/thermal/”. There you will find some instructions on
getting started with Excel, Mathematica, and True BASIC, plus a variety of other information
about the book and about thermal physics. Perhaps most importantly, you will find a page listing
corrections to the book, and a similar page for this manual. If you find errors in either that are not
listed on the web pages, please let me know.
I am extremely grateful to the many instructors and students who have already used An
Introduction to Thermal Physics and sent comments and suggestions. This manual has benefited
from several corrections that were contributed by instructors using draft chapters. I am also indebted
to Deb Badger for the use of her Macintosh G4 computer, which allowed me to run the True BASIC
simulations in a reasonable amount of time.
DVS
Ogden, Utah
November 1, 2000
Note on this corrected edition: I have taken the opportunity to correct all of the known errors
in the original edition of this manual. It is a pleasure to thank B. Blakie, L. Cominsky, M. Davis, A.
Gavrin, J. Lockhart, and G. Wiegerinck for bringing many of these errors to my attention. I have
also redrawn and improved a number of the illustrations, including all of the spreadsheet-generated
graphs. Further corrections and suggestions are always welcome.
August 5, 2016
iv
, 1 Energy in Thermal Physics
c 2001, 2016 Pearson Education, Inc. All rights reserved. No portion of this material may be
reproduced, in any form or by any means, without permission in writing from the publisher.
Problem 1.1. (Fahrenheit temperature scale.)
(a) To take Celsius to Fahrenheit, we want a linear function that takes 0 to 32 and 100
to 212. Imagining a graph of this function, the vertical intercept must be 32 and the
slope must be (212 32)/(100 0) = 9/5; therefore the function is
9
(T in F) = (T in C) + 32.
5
Inverting this function is now just a matter of algebra:
5
(T in C) = [(T in F) 32].
9
(b) Plugging 273.15 C into the first formula gives the value 459.7 for absolute zero in
degrees Fahrenheit.
Problem 1.2. To convert from Fahrenheit to Rankine, you would simply add 460, which
raises the value of absolute zero (see the previous problem) to zero as desired. Rankine
and kelvin temperatures are both measured from the same zero-point, so the conversion
between them is just the factor of 9/5 found in the previous problem, with no constant
term added. A kelvin degree is bigger than a Rankine degree, so the conversion is
9
(T in R) = (T in K),
5
which is equivalent to
5
K. 1 R=
9
9
Room temperature, about 300 K, would therefore be 5
· 300 = 540 on the Rankine scale.
Problem 1.3. (Kelvin temperature examples.)
(a) Human body temperature is “officially” 37 C, or 310 K. (In the U.S., this official
temperature is traditionally converted to 98.6 F—a classic example of failing to round
off insignificant digits.)
(b) Water is supposed to boil at 100 C, so that would be 373 K.
(c) I remember a night in Minnesota when the temperature was reported as 29 F. That
converts to 34 C, which is 239 K.
(d) 196 C would be 77 K, so liquid nitrogen is about four times closer to absolute zero
than room temperature is.
(e) 327 C would be 600 K, to three significant figures.
1
