Thermodynamics and Statistical Mechanics: An Integrated Approach

282 Pages·2015·10.11 MB·English

by  Scott Shell

Thermodynamics and Statistical Mechanics: Table of Contents
An Integrated Approach
Reference Tables
Preface
M. Scott Shell
Chapter 1: Introduction and guide to this text
draft manuscript: 01-12-15 Chapter 2: Equilibrium and entropy
Chapter 3: Energy and how the microscopic world works
Chapter 4: Entropy and how the macroscopic world works
Chapter 5: The fundamental equation
Chapter 6: The first law and reversibility
Chapter 7: Legendre transforms and other potentials
Chapter 8: Maxwell relations and measurable quantities
Chapter 9: Gases
Chapter 10: Phase equilibrium
Chapter 11: Stability
Chapter 12: Solutions – fundamentals
Chapter 13: Solutions – advanced and special cases
Chapter 14: Solids
Chapter 15: The third law
Chapter 16: The canonical partition function
Chapter 17: Fluctuations
Chapter 18: Statistical mechanics of classical systems
Chapter 19: Other ensembles
Chapter 20: Reaction equilibrium
Chapter 21: Reaction coordinates and rates
Chapter 22: Molecular simulation methods

copy: MSS 07-22-14
formula (cid:1866)!(cid:1842)= (cid:3038)(cid:3041)((cid:1866)−(cid:1863))! (cid:1866)!(cid:1829)= (cid:3038)()(cid:1863)!(cid:1866)−(cid:1863)! (cid:3038)(cid:1866) ()(cid:1863)+(cid:1866)−1! ()(cid:1863)!(cid:1866)−1! ()∑(cid:1866)!(cid:1863)!(cid:3036)(cid:3036)= ∏∏!!(cid:1863)(cid:1863)(cid:3036)(cid:3036)(cid:3036)(cid:3036)
(cid:3041)
(cid:1866) (cid:1866)
Reference tables List of tables Table A: Counting and combinatorics formulae Table B: Useful integrals, expansions, and approximations Table C: Extensive thermodynamic potentials Table D: Intensive per-particle thermodynamic potentials for single-component systems Table E: Thermodynamic calculus manipulations Table F: Measurable quantities Table G: Common single-component statistical-mechanical ensembles Table H: Fundamental physical constants T-1 Table A: Counting and combinatorics formulae description example (cid:1863)number of ways to pick ordered (cid:1863)How many ways are there to put distinctly-colored marbles in separate buckets, with at most one marble per bucket? (cid:1866)objects from without replacement (cid:1863)number of ways to pick unordered (cid:1863)(cid:1866)How many ways are there to put identical blue marbles in separate buckets, with at most one marble per bucket? (cid:1866)objects from without replacement (cid:1863)number of ways to pick ordered (cid:1863)How many ways are there to put distinctly-colored marbles in separate buckets, with any number of marbles per bucket? (cid:1866)objects from with replacement (cid:1863)number of ways to pick unordered (cid:1863)(cid:1866)How many ways are there to put identical orange marbles in separate buckets, with any number of marbles per bucket? (cid:1866)objects from with replacement (cid:1863)(cid:1863)ways to pick objects of type 1, (cid:2869)(cid:2870)(cid:1863)(cid:1863)(cid:1863)How many ways are there to put blue, orange, and red (cid:2869)(cid:2870)(cid:2871)(cid:1866)=(cid:1863)+(cid:1863)+of type 2, etc., out of (cid:2869)(cid:2870)(cid:1863)+(cid:1863)+(cid:1863)marbles in buckets, with at most one marble per (cid:2869)(cid:2870)(cid:2871)⋯ in an unordered manner and bucket? without replacement T-2
(cid:1840) (cid:3036) (cid:1840) (cid:3036) (cid:2020)(cid:1840) (cid:3036)(cid:3036)
m (cid:2020)(cid:1840)(cid:3036)(cid:3036) (cid:1846) (cid:2020)(cid:1840) (cid:3036)(cid:3036) (cid:3533)(cid:2020)(cid:3036) (cid:3036) (cid:3533)(cid:2020)(cid:3036) (cid:3036) =(cid:3533) (cid:3036)
d for −(cid:3533) (cid:3036) +(cid:3533) (cid:3036) (cid:1846)(cid:1845)+ (cid:1842)(cid:1848)+ −(cid:1846)(cid:1845)
) ate (cid:1842)(cid:1848) (cid:1846) (cid:1842)(cid:1848) = =− (cid:1846)(cid:1845) (cid:1834)
((cid:1866) even integr (cid:1831)+=(cid:1846) =(cid:1846)(cid:1845)− (cid:1831)+(cid:1842)(cid:1848) (cid:1831)−(cid:1846)(cid:1845) +(cid:1842)(cid:1848)− +(cid:1842)(cid:1848)=
⁄(cid:2998)(cid:2869)(cid:2870)(cid:2024)(cid:3118)(cid:2879)(cid:3030)(cid:3051)(cid:1856)(cid:1876)=(cid:3505)(cid:1857) ⁄(cid:2869)(cid:2870)2(cid:1855)(cid:2868) (cid:2998)1(cid:3118)(cid:2879)(cid:3030)(cid:3051)(cid:1856)(cid:1876)=(cid:3505)(cid:1876)(cid:1857) 2(cid:1855)(cid:2868) ⁄(cid:2998)(cid:2869)(cid:2870)(cid:2024)(cid:3118)(cid:2870)(cid:2879)(cid:3030)(cid:3051)(cid:3505)(cid:1876)(cid:1857)(cid:1856)(cid:1876)= ⁄(cid:2871)(cid:2870)4(cid:1855)(cid:2868) (cid:2998)1(cid:3118)(cid:2871)(cid:2879)(cid:3030)(cid:3051)(cid:3505)(cid:1876)(cid:1857)(cid:1856)(cid:1876)= (cid:2870)2(cid:1855)(cid:2868) (cid:2998)(cid:2869)/(cid:2870)3(cid:2024)(cid:3118)(cid:2872)(cid:2879)(cid:3030)(cid:3051)(cid:1857)(cid:1856)(cid:1876)=(cid:3505)(cid:1876) (cid:2873)/(cid:2870)8(cid:1855)(cid:2868) ⁄(cid:2998)(cid:2869)(cid:2870)()(cid:2024)(cid:1866)−1‼(cid:3118)(cid:3041)(cid:2879)(cid:3030)(cid:3051)(cid:1857)(cid:1856)(cid:1876)= (cid:3505)(cid:1876)()⁄⁄(cid:3041)(cid:2878)(cid:2869)(cid:2870)(cid:3041)(cid:2870)(cid:2878)(cid:2869)(cid:1855)2(cid:2868) T-3 differential form (cid:1842)(cid:2020)1(cid:3036)(cid:1845)(cid:1856)(cid:1831)+(cid:1856)(cid:1848)−(cid:3533)(cid:1856)(cid:1840) (cid:3036)(cid:1846)(cid:1846)(cid:1846)(cid:3036) =(cid:1846)(cid:1856)(cid:1845)−(cid:1842)(cid:1856)(cid:1848)+(cid:3533)(cid:2020)(cid:1856)(cid:1840)(cid:1831) (cid:3036)(cid:3036) (cid:3036) =(cid:1846)(cid:1856)(cid:1845)+(cid:1848)(cid:1856)(cid:1842)+(cid:3533)(cid:2020)(cid:1856)(cid:1840)(cid:1834)= (cid:3036)(cid:3036) (cid:3036) −(cid:1845)(cid:1856)(cid:1846)−(cid:1842)(cid:1856)(cid:1848)+(cid:3533)(cid:2020)(cid:1856)(cid:1840)(cid:1827)= (cid:3036)(cid:3036) (cid:3036) (cid:1833)=(cid:1831)−(cid:1845)(cid:1856)(cid:1846)+(cid:1848)(cid:1856)(cid:1842)+(cid:3533)(cid:2020)(cid:1856)(cid:1840) (cid:3036)(cid:3036)(cid:1827)=(cid:3036) T-4
= = =
(cid:1856)(cid:1845) (cid:1856)(cid:1831) (cid:1856)(cid:1834) (cid:1856)(cid:1827) (cid:1856)(cid:1833)
sions, and approximations ln(cid:1866)!≈(cid:1866)ln(cid:1866)−(cid:1866) (cid:3041)(⁄)(cid:1866)!≈(cid:1866)(cid:1857) (cid:2998)(cid:3041)(cid:1876)(cid:3051)(cid:1857)=(cid:3533) (cid:1866)!(cid:3041)(cid:2880)(cid:2868) (cid:3041)(cid:1866)!(cid:3041)(cid:3038)()=(cid:3533)(cid:1876)1+(cid:1876) ()(cid:1863)!(cid:1866)−(cid:1863)!(cid:3038)(cid:2880)(cid:2868) (cid:2998)(cid:3041)(cid:2879)(cid:3051)(cid:3505)(cid:1876)(cid:1857)(cid:1856)(cid:1876)=(cid:1866)!=Γ((cid:1866)+1) (cid:2868) ()ln1+(cid:1876)≈(cid:1876) (cid:1876)for small (cid:2879)(cid:2869)()≈1−(cid:1876) (cid:1876)1+(cid:1876)for small mic potentials independent variables (cid:4668)(cid:4669)(cid:1845)((cid:1831),(cid:1848),(cid:1840)) (cid:4668)(cid:4669)(cid:1831)((cid:1845),(cid:1848),(cid:1840)) (cid:4668)(cid:4669)(cid:1834)((cid:1845),(cid:1842),(cid:1840)) (cid:4668)(cid:4669)(cid:1827)((cid:1846),(cid:1848),(cid:1840)) (cid:4668)(cid:4669)(cid:1833)((cid:1846),(cid:1842),(cid:1840))
an na y
B: Useful integrals, exp C: Extensive thermody name entropy energy enthalpy Helmholtz free energ Gibbs free energy
e e
bl bl
a a
T T
(cid:1842)
−
(cid:3017)
(cid:3440)
(cid:1845) (cid:1848)
(cid:2034) (cid:2034)
integrated relations (cid:2020)(cid:1857)(cid:1842)(cid:1874)=−(cid:1871)++ (cid:1846)(cid:1846)(cid:1846) (cid:2020)=(cid:1857)−(cid:1846)(cid:1871)+(cid:1842)(cid:1874) ℎ=(cid:1857)+(cid:1842)(cid:1874) (cid:2020)=ℎ−(cid:1846)(cid:1871) (cid:1853)=(cid:1857)−(cid:1846)(cid:1871) (cid:2020)=(cid:1853)+(cid:1842)(cid:1874) (cid:1859)=(cid:1857)+(cid:1842)(cid:1874)−(cid:1846)(cid:1871) =(cid:1853)+(cid:1842)(cid:1874)=ℎ−(cid:1846)(cid:1871)(cid:2020)=(cid:1859) example (cid:2034)(cid:1842)(cid:2034)(cid:1845)(cid:3436)(cid:3440)= 1(cid:3436)(cid:3440)(cid:3415) (cid:2034)(cid:1845)(cid:2034)(cid:1842)(cid:3021)(cid:3021) (cid:2034)(cid:1842)(cid:2034)(cid:1845)(cid:2034)(cid:1845)(cid:3436)(cid:3440)=−(cid:3436)(cid:3440)(cid:3436)(cid:3440)(cid:3416) (cid:2034)(cid:1846)(cid:2034)(cid:1846)(cid:2034)(cid:1842)(cid:3020)(cid:3017)(cid:3021) (cid:2034)(cid:1834)(cid:2034)(cid:1834)(cid:2034)(cid:1848)(cid:3436)(cid:3440)=(cid:3436)(cid:3440)(cid:3436)(cid:3440)(cid:3416) (cid:2034)(cid:1848)(cid:2034)(cid:1846)(cid:2034)(cid:1846)(cid:3017)(cid:3017)(cid:3017) (cid:2034)(cid:1831)(cid:2034)(cid:1845)(cid:2034)(cid:1831)(cid:3440)(cid:3436)(cid:3440)+(cid:3436)(cid:3440)=(cid:1846)(cid:3436)(cid:2034)(cid:1845)(cid:2034)(cid:1848)(cid:2034)(cid:1848)(cid:3023)(cid:3017)(cid:3020) (cid:2034)(cid:1831)(cid:1827)(cid:3436)(cid:3440)=− (cid:2870)(cid:2034)(cid:1846)(cid:1846)(cid:1846)(cid:3023) (cid:2034)(cid:1845)(cid:2034)(cid:1848)(cid:3436)(cid:3440)=−(cid:3436)(cid:3440) (cid:2034)(cid:1842)(cid:2034)(cid:1846)(cid:3021)(cid:3017)
(cid:3436)
=
(cid:3017)
(cid:3440)
(cid:1831) (cid:1848)
al form (cid:1842)+(cid:1856)(cid:1874) (cid:1846) −(cid:1842)(cid:1856)(cid:1874) +(cid:1874)(cid:1856)(cid:1842) (cid:1846)−(cid:1842)(cid:1856)(cid:1874) (cid:1846)+(cid:1874)(cid:1856)(cid:1842) (cid:2034)(cid:3436)(cid:2034)
stems differenti 1(cid:1856)(cid:1857)(cid:1856)(cid:1871)=(cid:1846) (cid:1856)(cid:1857)=(cid:1846)(cid:1856)(cid:1871) (cid:1856)ℎ=(cid:1846)(cid:1856)(cid:1871) (cid:1856)(cid:1853)=−(cid:1871)(cid:1856) (cid:1856)(cid:1859)=−(cid:1871)(cid:1856) (cid:2034)(cid:1852)+(cid:3436)(cid:3440) (cid:2034)(cid:1851)(cid:3025) (cid:2034)ℬ(cid:3436)(cid:3440) (cid:2034)(cid:1851)(cid:3025)
Table D: Intensive per-particle thermodynamic potentials for single-component sy name independent variables entropy per particle (cid:1871)((cid:1857),(cid:1874)) energy per particle (cid:1857)((cid:1871),(cid:1874)) enthalpy per particle ℎ((cid:1871),(cid:1842)) Helmholtz free energy per particle (cid:1853)((cid:1846),(cid:1874)) Gibbs free energy per particle(cid:1859)((cid:1846),(cid:1842)) T-5 Table E: Thermodynamic calculus manipulations name applies to... functional form (cid:2034)(cid:1850)(cid:2034)(cid:1851)inversion anything (cid:3436)(cid:3440)=1(cid:3436)(cid:3440)(cid:3415) (cid:2034)(cid:1851)(cid:2034)(cid:1850)(cid:3027)(cid:3027) (cid:2034)(cid:1850)(cid:2034)(cid:1852)(cid:2034)(cid:1851)triple product anything (cid:3436)(cid:3440)(cid:3436)(cid:3440)(cid:3436)(cid:3440)=−1 rule (cid:2034)(cid:1851)(cid:2034)(cid:1850)(cid:2034)(cid:1852)(cid:3027)(cid:3026)(cid:3025) (cid:2034)(cid:1850)(cid:2034)(cid:1850)(cid:2034)(cid:1851)addition of anything (cid:3436)(cid:3440)=(cid:3436)(cid:3440)(cid:3436)(cid:3440)(cid:3416) variable (cid:2034)(cid:1851)(cid:2034)(cid:1849)(cid:2034)(cid:1849)(cid:3027)(cid:3027)(cid:3027) (cid:2034)(cid:1852)(cid:2034)(cid:1852)(cid:2034)(cid:1850)non-natural anything ()(cid:1852)(cid:1850),(cid:1851) → (cid:3436)(cid:3440)=(cid:3436)(cid:3440)(cid:3436)(cid:3440)derivative (cid:2034)(cid:1851)(cid:2034)(cid:1850)(cid:2034)(cid:1851)(cid:3024)(cid:3026)(cid:3024) (cid:2034)(cid:1832)(cid:1832)potential potentials (cid:2869)(cid:2870)(cid:3436)(cid:3440)=− transformation (cid:2870)(cid:2034)(cid:1850)(cid:1850)(cid:1850)(cid:3026) (cid:2870)(cid:2870)Maxwell potential second (cid:1832)(cid:1832)(cid:2034)(cid:2034)(cid:2267)(cid:2034)(cid:3440)==→(cid:3436)(cid:4679)(cid:4678)(cid:4679)(cid:4678)relations derivatives (cid:2034)(cid:1850)(cid:2034)(cid:1851)(cid:2034)(cid:1851)(cid:2034)(cid:1850)(cid:2034)(cid:1850)(cid:3026) NOTES: The term “anything” indicates any complete state function. T-6
(cid:2879)(cid:3081)(cid:3017)(cid:3023) )(cid:1848),(cid:1840) ) (cid:1840))(cid:1856)(cid:1848)
particle or per mole version Δℎ latent (cid:2034)(cid:1857)(cid:2034)(cid:1871)(cid:1855)≡(cid:3436)(cid:3440)=(cid:1846)(cid:3436)(cid:3440) (cid:3023)(cid:2034)(cid:1846)(cid:2034)(cid:1846)(cid:3049)(cid:3049) (cid:2034)ℎ(cid:2034)(cid:1871)(cid:1855)≡(cid:3436)(cid:3440)=(cid:1846)(cid:3436)(cid:3440) (cid:3017)(cid:2034)(cid:1846)(cid:2034)(cid:1846)(cid:3017)(cid:3017) isothermal-isobaric (cid:1846),(cid:1842),(cid:1840) (cid:1831),(cid:1848) (cid:2879)(cid:3081)(cid:3006)(cid:2879)(cid:3081)(cid:3017)(cid:3023)(cid:1857)(cid:3288)(cid:3288)=℘ (cid:3040)()Δ(cid:1846),(cid:1842),(cid:1840) (cid:3091)(cid:3015)(cid:2879)(cid:3081)(cid:3006)()Δ(cid:1846),(cid:1842),(cid:1840)=(cid:3533)(cid:3533)(cid:1857) (cid:3289) (cid:3041)(cid:3023) (cid:2879)(cid:3081)(cid:3017)(cid:3023)()(cid:1843)(cid:1846),(cid:1848),(cid:1840)Δ=(cid:3533)(cid:1857) (cid:3023) (cid:2879)(cid:3081)(cid:3006)(cid:2879)(cid:3081)(cid:3017)(cid:3023))((cid:1840)=(cid:3533)(cid:3533)(cid:1857)Ω(cid:1831), (cid:3006)(cid:3023) (cid:1833)=−(cid:1863)(cid:1846)lnΔ((cid:1846),(cid:1842),(cid:1840)(cid:3003)(cid:2998)1(cid:2879)(cid:3081)(cid:3017)(cid:3023)(cid:3505)(cid:1857)(cid:1852)((cid:1846),(cid:1848),Δ=(cid:2871)(cid:3015)(cid:1840)!Λ(cid:2868)
Table F: Measurable quantities per name notation and definition pressure (cid:1842) temperature (cid:1846) volume (cid:1848) (cid:1861)total mass of species (cid:1865) (cid:3036) (cid:1861)total moles of species (cid:1866) (cid:3036) (cid:1861)molecular weight of species ℳ(cid:3036) ⁄(cid:1861)molecules of species (cid:1840)=(cid:1865)ℳ (cid:3036)(cid:3036)(cid:3036) (cid:1861)(cid:1876)(cid:1877)(cid:1878)mole fraction of species , , or (cid:3036)(cid:3036)(cid:3036) enthalpy or latent heat of phase change Δ(cid:1834) latent (cid:2034)(cid:1831)(cid:2034)(cid:1845)constant volume heat capacity (cid:1829)≡(cid:3436)(cid:3440)=(cid:1846)(cid:3436)(cid:3440) (cid:3023)(cid:2034)(cid:1846)(cid:2034)(cid:1846)(cid:3023),(cid:3015)(cid:3023),(cid:3015) (cid:2034)(cid:1834)(cid:2034)(cid:1845)constant pressure heat capacity (cid:1829)≡(cid:3436)(cid:3440)=(cid:1846)(cid:3436)(cid:3440) (cid:3017)(cid:2034)(cid:1846)(cid:2034)(cid:1846)(cid:3017),(cid:3015)(cid:3017),(cid:3015) 1(cid:2034)(cid:1848)(cid:2034)ln(cid:1848)(cid:2034)ln(cid:1874)isothermal compressibility (cid:2018)≡−(cid:3436)(cid:3440)=−(cid:3436)(cid:3440)=−(cid:3436)(cid:3440) (cid:3021)(cid:1848)(cid:2034)(cid:1842)(cid:2034)(cid:1842)(cid:2034)(cid:1842)(cid:3021),(cid:3015)(cid:3021),(cid:3015)(cid:3021) 1(cid:2034)(cid:1848)(cid:2034)ln(cid:1848)(cid:2034)ln(cid:1874)thermal expansivity ≡(cid:3436)(cid:3440)=(cid:3436)(cid:3440)=(cid:3436)(cid:3440)(cid:2009) (cid:3017)or thermal expansion coefficient (cid:1848)(cid:2034)(cid:1846)(cid:2034)(cid:1846)(cid:2034)(cid:1846)(cid:3017),(cid:3015)(cid:3017),(cid:3015)(cid:3017) T-7 Table G: Common single-component statistical-mechanical ensembles property microcanonical canonicalgrand canonical constant (cid:1831),(cid:1848),(cid:1840)(cid:1846),(cid:1848),(cid:1840)(cid:1846),(cid:1848),(cid:2020) conditions fluctuations none (cid:1831)(cid:1831),(cid:1840) (cid:2012)(cid:2879)(cid:3081)(cid:3006)(cid:2879)(cid:3081)(cid:3006)(cid:2878)(cid:3081)(cid:3091)(cid:3015)microstate (cid:1857)(cid:1857)(cid:3288)(cid:3288)(cid:3288)(cid:3006),(cid:3006)(cid:3288)=℘ ℘= ℘= probabilities (cid:3040)(cid:3040)(cid:3040)()Ω(cid:1831),(cid:1848),(cid:1840)()()(cid:1843)(cid:1846),(cid:1848),(cid:1840)Ξ(cid:1846),(cid:1848),(cid:2020) partition (cid:2879)(cid:3081)(cid:3006)(cid:2879)(cid:3081)(cid:3006)(cid:2878)(cid:3081)()()()(cid:1843)(cid:1846),(cid:1848),(cid:1840)=(cid:3533)(cid:1857)Ξ(cid:1846),(cid:1848),(cid:2020)=(cid:3533)(cid:3533)(cid:1857)Ω(cid:1831),(cid:1848),(cid:1840)=(cid:3533)(cid:2012) (cid:3289)(cid:3289)(cid:3006),(cid:3006)function (cid:3289)(cid:3041)(cid:3015)(cid:3041)(cid:3041) relations to --- (cid:2879)(cid:3081)(cid:3006)(cid:3015)()()Ω(cid:1831),(cid:1848),(cid:1840)Ξ=(cid:3533)(cid:2019)(cid:1843)(cid:1843)=(cid:3533)(cid:1857)(cid:1846),(cid:1848),(cid:1840)other (cid:3006)(cid:3015)partition functions (cid:3015)(cid:2879)(cid:3081)(cid:3006)((cid:1857)Ω(cid:1831),(cid:1848),=(cid:3533)(cid:3533)(cid:2019) (cid:3006)(cid:3015) (cid:2019)≡exp[(cid:2010)(cid:2020)]where potential lnΩ((cid:1831),(cid:1848),(cid:1840))(cid:1827)=−(cid:1863)(cid:1846)ln(cid:1843)((cid:1846),(cid:1848),(cid:1840))(cid:1842)(cid:1848)=(cid:1863)(cid:1846)lnΞ((cid:1846),(cid:1848),(cid:2020))(cid:1845)=(cid:1863) (cid:3003)(cid:3003)(cid:3003)(cid:2998)1()classical (cid:1852)(cid:1846),(cid:1848),(cid:1840)(cid:3015)(cid:2019)(cid:1852)((cid:1846),(cid:1848),(cid:1840))(cid:3015)(cid:3015)(cid:3015)(cid:3015)(cid:3505)(cid:2012)[(cid:1834)((cid:1816),(cid:1818))−(cid:1831)](cid:1856)(cid:1816)(cid:1856)(cid:1818)Ω= (cid:1843)= Ξ=(cid:3533) partition (cid:2871)(cid:3015)ℎ(cid:1840)!(cid:2871)(cid:3015)Λ(cid:1840)!(cid:2871)(cid:3015)Λ(cid:1840)!function (cid:3015)(cid:2880)(cid:2868) (cid:3263) (cid:3439)(cid:3435)(cid:2879)(cid:3081)(cid:3022)(cid:1818)(cid:3015)(cid:1852)≡(cid:3505)(cid:1857)(cid:1856)(cid:1818) (cid:2019)≡exp[(cid:2010)(cid:2020)]where (cid:2869)(cid:2870)⁄)(2(cid:2024)(cid:1865)(cid:1863)(cid:1846)Λ≡ℎ(cid:2870)(cid:3003)NOTES: (cid:1866)(cid:1848)(cid:1840)Sums over are sums over all microstates at a given and . (cid:1840)∞(cid:1848)∞(cid:1831)−∞∞Sums over are from 0 to , over are from 0 to , and over are from to . Classical partition functions are given for a monatomic system of indistinguishable, structureless particles. T-8
s
notation and definition (cid:2879)(cid:2870)(cid:2871)⁄=1.38065×10JK(cid:1863)(cid:3003) ⁄K(cid:1844)=8.31446Jmol⋅ (cid:2870)(cid:2871)(cid:2879)(cid:2869)(cid:2280)=6.02214×10mol (cid:3002) (cid:2879)(cid:2869)(cid:2877)Cℯ=1.60218×10 (cid:2879)(cid:2871)(cid:2872)J⋅sℎ=6.62607×10 (cid:2879)(cid:2871)(cid:2872)⁄J⋅=ℎ2(cid:2024)=1.05457×10 (cid:2870)⁄(cid:1859)=9.80665ms (cid:2879)(cid:2869)(cid:2870)(cid:2870)⁄=8.8542×10CJ⋅m(cid:2035)(cid:2868)
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Preface physical behaviors. As such, I have tried to streamline notation and focus on
simple qualitative models (e.g., lattice models) for building basic physical
intuition and student confidence in model-development and refinement. By the
same token, this narrative does not try to be comprehensive in covering many
applied thermodynamic property models, which I feel are best left in existing
Like so many texts, this book grew out of lecture notes and problems that I
and specialist texts. I also deliberately use a straightforward, casual voice for
developed through teaching, specifically, graduate thermodynamics over the
clarity.
past seven years. These notes were originally motivated by my difficulty in
finding a satisfactory introductory text to both classical thermodynamics and I have included a number of problems at the end of each chapter, most
statistical mechanics that could be used for a quarter-long course for first-year of which are entirely original. Many of these are guided and multi-step problems
chemical engineering graduate students. However, as the years pressed forward, that walk students through the analysis of different kinds of systems, including
it became apparent that there was a greater opportunity to construct a new modern problems in biophysics and materials, for example. These are divided
presentation of these classic subjects that addressed the needs of the modern into three categories: conceptual and thought problems that address the basic
student. Namely, few existing books seem to provide an integrated view of both origins, behaviors, and trends in various thermodynamic quantities;
classical and molecular perspectives on thermodynamics, and at a sufficient fundamentals problems that develop classic and general thermodynamic
level of rigor so as to address graduate-level problems. relations and equations; and finally, applied problems that develop and analyze
simple models of specific systems.
It has become clear to me that first year graduate students respond best
to a molecular-level “explanation” of the classic laws, at least upon initial I owe tremendous thanks to the many students over the years in my
discussion. For them this imparts a more intuitive understanding of group and course that have provided great amounts of feedback on my notes.
thermodynamic potentials and, in particular, the entropy and second law. Perhaps unbeknownst to them, it has been their questions, discussions, and
Moreover, students’ most frequent hurdles are conceptual in nature, not epiphanies that have shaped this text more than anything else—inspiring a
mathematical, and I sense that many older presentations are inaccessible to seemingly unending but happy circumstance of repeated revisions and
them because concepts are buried deep under patinas of unnecessarily complex improvements. I am also deeply indebted to my mentors Pablo, Thanos, Frank,
notation and equations. and Ken, who not only chaperoned my own appreciation for thermodynamics,
but who provided immaculate examples of clear and concise communication.
With this book, therefore, I aim for a different kind of storytelling than
Finally, I am profoundly fortunate to have the love and support of my family, and
the conventional classical first, statistical second approach. Namely, I have
it is returned to them many times over.
endeavored to organize the material in a way that presents classical
thermodynamics and statistical mechanics side-by-side throughout. In a As with any first edition, I am under no illusion that this book will be
manner of speaking, I have thus eschewed the venerable postulatory approach entirely free of errors, typographical or otherwise, despite the repeated edits it
that is so central to the development of the classical theory, instead providing a has received from many different eyes. I am grateful to future readers for
bottom-up, molecular rationale for the three laws. This is not to say that I reject pointing these out to me, and I welcome any form of feedback, positive or
the former and its impressive elegance, or that I view it as an unnecessary negative.
component of a graduate-level education in thermodynamics. It is merely a

pedagogical choice, as I strongly believe one can only truly appreciate the
postulatory perspective once one has a “gut feel” and a solid foundation for MSS
thermodynamics, and this is best served by a molecular introduction. Moreover, December 31, 2013 · Santa Barbara, CA
the topics of modern graduate research are increasingly focused on the
nanoscale, and therefore it is essential that all students understand exactly how
macroscopic and microscopic thermodynamic ideas interweave.
At the same time, this book seeks to provide a contemporary exposure
to these topics that is complementary to classic and more detailed texts in the
chemical thermodynamics canon. Here, I place heavy emphasis on concepts
rather than formalisms, mathematics, or applications. My experience has been
that complex notation and long analyses of intricate models at the outset gets in
the way of students’ understanding of the basic conceptual foundations and
P-1 P-2
Chapter 1  basic statistics and probability: familiarity with the concepts of
probability, probability distributions (including multivariate), and
Introduction and guide for this text combinatorics.
 introductory exposure to thermodynamic concepts and terminology:
familiarity with the concepts of a system, surroundings, boundary,
absolute temperature, pressure, heat, work, and processes.
Thermodynamics is a remarkable subject, both in its pervasiveness throughout
the pure and engineering sciences, and in the striking simplicity and elegance of It is very likely that any reader with at least three or four years of undergraduate
its principles. Indeed, it is hard to underestimate the significance of coursework in physics, chemistry, or engineering will be sufficiently prepared for
thermodynamics to virtually any physical problem of interest, even if its role this book. Regardless, most of the requisite background material is reviewed or
appears only indirectly through derivative theories or models. As a testament to explained with examples in an as-you-go manner.
its importance, Einstein made the rather potent statement that thermodynamics
is “the only physical theory of universal content, which I am convinced, that The most distinguishing feature of this text is that it integrates
within the framework of applicability of its basic concepts will never be macroscopic principles (classical thermodynamics) and molecular aspects of
overthrown.” thermodynamics (statistical mechanics) throughout. This constitutes a different
perspective than many traditional treatments of the material that begin purely at
At the same time, thermodynamics can be surprisingly difficult to grasp the macroscopic level with the so-called postulatory approach. The latter gives a
at a fundamental level, even for the experienced student. Unlike many other beautiful formulation of classical thermodynamics that makes no reference to
advanced scientific subjects, its main challenges are not mathematical in nature; the molecular world and hence is independent of the particular nature of
a working knowledge of multivariate calculus is usually quite sufficient. Instead, microscopic interactions. Instead, it proposes several general principles,
the most difficult aspects of thermodynamics are its conceptual underpinnings. reinforced many times over by empirical observation, with which any problem
Students often struggle with the seemingly simple task of how to begin thinking can be analyzed. That is, the postulatory approach begins a priori with the laws
about a problem, for example: what constitutes the system? What is constant or of thermodynamics. Although they may be phrased in different ways, the
constrained? What thermodynamic variables are equal across a boundary? What
following gives some usual possibilities for the laws:
assumptions and models are reasonable? All of these questions precede the
analytical analysis and are concerned with how to transform the physical 1. No process can operate so as to create or destroy energy.
problem into a mathematical one. When this is done, the solutions often present
The total energy of an isolated system is constant. If the internal
themselves in a rather straightforward manner, at least for an introductory
energy of a closed system changes, the difference must exactly equal
treatment.
the sum of the heat added and work done on it: (cid:1856)(cid:1831)=(cid:2012)(cid:1843)+(cid:2012)(cid:1849).
It is exactly these conceptual ideations on which this book is focused.
2. No process can operate so as to completely convert the heat
This text presents an advanced undergraduate or early graduate-level overview
absorbed by a system into usable work.
of thermodynamics aimed at students in chemical science and engineering. It is
designed to provide a fundamental understanding of thermodynamic principles Systems have a quantity called the entropy that is a function of state
that emphasizes general concepts and approaches, rather than notations, and that can be measured using reversible heat transfers: (cid:1856)(cid:1845)=
mathematical frameworks, or solution strategies for specific kinds of (cid:2012)(cid:1843) ⁄(cid:1846). In an isolated system, the entropy of spontaneous
rev
applications. It adopts a philosophy that the most important step a student can processes can only increase with time.
take in this area is to gain basic physical intuition and confidence in problem
3. No process can operate so as to bring a system to absolute zero in a
analysis and model-development. To some extent, this book is designed to “fill
finite number of steps and in finite time.
in the gaps” from earlier, introductory exposure to the subject and to help
students see and become comfortable with the “big picture.” That being said, it The entropy of all perfect, pure, monatomic crystalline substances at
is assumed that the reader is equipped with some prior exposure and training in absolute zero is zero.
the following areas:
The brilliance of these statements is that, despite their simplicity, they have
 multivariate differential and integral calculus: familiarity with total profound implications that can be studied in great mathematical detail for every
differentials, partial derivatives, single- and multiple-variable physical process. Furthermore, they require no understanding of molecular
integrations, and solutions to very simple differential equations. interactions or the fundamental theory thereof.
1-1 1-2
Unfortunately, while the postulatory formulation is often greatly problems than others, and this is because they are natural synthesis
esteemed by experienced scientists, it can be a challenging starting point for the points for incorporating earlier material.
early learner. The main problem is that it requires students to merely accept
 Think in terms of functions and variables, not values. Oftentimes,
these statements, without explanation as to how they connect to molecular
principles that they surely have seen in other courses. What really is the entropy students become complacent with plugging numbers into off-the-shelf
and why does it exist? The gap between the atomic world and thermodynamics equations. This is a value-focused way to solve problems, and it is
entirely the wrong way to understand thermodynamics. Instead, much
often leaves students feeling unsatisfied, confused, absent intuition, and missing
of the beauty of this subject is that properties are interrelated through a
the big picture.
systematic calculus of functions. Indeed, any equilibrium property is a
This book therefore takes a different, integrated approach to teaching function of state and thus also a mathematical function. This means
thermodynamics that blends molecular and statistical-mechanical concepts that such properties have multiple independent variables and partial
with the exposition of the classical laws. It attempts to be bottom-up rather than derivatives. At first it may seem unsettling to consider temperature as a
top-down by first presenting and then rationalizing ideas on the basis of atomic- function, for example (cid:1846)(cid:4666)(cid:1831),(cid:1848),(cid:1840)(cid:4667), but keep in mind that its behavior is
scale interactions. In this sense, it aims to give the reader some feeling for the no different than the generic (cid:1858)(cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667).
why of thermodynamics. Of course, this approach itself is not devoid of
postulates. To begin, one must accept some level of atomic theory, whether  Always solve problems from general principles, not specialized
quantum or classical or other. Moreover, ultimately the second law requires the equations. One of the attractive features of thermodynamics is that
equal a priori assumption that is the foundation of statistical mechanics, as there are just a small handful of fundamental equations from which
discussed in Chapter 4. In this sense the approach taken by this text is motivated essentially all other results can be derived. Therefore, you should not
on pedagogical grounds, not scientific ones. After understanding the material, try to memorize every equation, but instead strive to be able to quickly
therefore, the reader is highly encouraged to revisit the postulatory presentation pinpoint the underlying assumptions so that you would be able to re-
to appreciate the generality of thermodynamics as an empirical natural science derive the key ones in isolation. Throughout this book, the most
that is independent of the microscopic world. important equations are numbered in bold.
The reader should be cautioned that a deep understanding of Finally, the reader is encouraged to explore other texts as a means to broaden
thermodynamics does not simply evolve from the page, but rather requires a understanding and clarify confusing points. Some especially useful texts are
concerted effort to explore the material outside of the main narrative. Some referenced at the end of this chapter. In particular, many parts of the present
recommendations for working through this text are the following: book follow closely and were inspired by the brilliant texts of Denbigh, Hill, and
McQuarrie. While these seminal works have a less modern tone, they present
 Pay particular attention to general, broad concepts. The most
the material with great care and in significantly greater depth. In addition, the
important ones are highlighted for you in gray call-out boxes. Ask
text by Dill gives a terrific introduction to thermodynamics suited to a more
yourself: does this make sense intuitively? Does this make sense
general audience, and it addresses many background concepts that are not
mathematically? Challenge yourself to understand and apply the ideas,
covered in detail by the present work.
initially in very simple examples. Make sure that you feel comfortable
with the concepts before proceeding too far ahead, as it is easy to
become lost. Check yourself with questions in the Conceptual and

thought problems section at the end of each chapter.
 Work end-of-chapter problems. One simply cannot appreciate
thermodynamics without tackling actual problems. If you are reading
this text outside of class, a suggested course of study is the end-of-
chapter problems that are indicated with boxed numbers. You will
likely struggle through them, and it is important that you do so! It is
through this process of struggle that subtleties bubble to the surface.
This book has been written so that many important results and
implications are explicitly left for you to discover in this engaged,
problem-driven manner. Note that some chapters have many more
1-3 1-4
References
Highly recommended supplemental reading for early graduate-level students
in the chemical sciences and engineering
K. Denbigh, The Principles of Chemical Equilibrium (4th Edition). New York:
Cambridge University Press, 1981.
K. Dill and S. Bromberg , Molecular Driving Forces: Statistical Thermodynamics
in Biology, Chemistry, Physics, and Nanoscience (2nd Edition). New York: Garland
Science (2010).
T. L. Hill, An Introduction to Statistical Thermodynamics. Reading, MA: Addison-
Wesley (1960); New York: Dover (1986).
D. A. McQuarrie, Statistical Mechanics. Sausalito, CA: University Science Books
(2000).
D. A. McQuarrie, Quantum Chemistry. Mill Valley, CA: University Science Books
(1983).
Also recommended
H. Callen, Thermodynamics and an Introduction to Thermostatistics (3rd Edition).
New York: Wiley (1985).
D. Chandler, Introduction to Modern Statistical Mechanics, New York: Oxford
University Press (1987).
J. R. Elliot and C. T. Lira, Introductory Chemical Engineering Thermodynamics
(2nd Edition). Upper Saddle River, NJ: Prentice Hall (2012).
J. Israelachvili, Intermolecular and Surface Forces (3rd Edition). Burlington, MA:
Academic Press (2011).
C. Kittel and H. Kroemer, Thermal Physics. New York: W. H. Freeman (1980).
A. Z. Panagiotopoulos, Essential Thermodynamics. Princeton, NJ: Drios Press
(2011).
J. M. Smith, H. V. Ness, and M. Abbott, Introduction to Chemical Engineering
Thermodynamics (7th Edition). New York: McGraw-Hill (2005).
J. W. Tester and M. Modell, Thermodynamics and Its Applications (3rd Edition).
Upper Saddle River, NJ: Prentice Hall (1997).
For this chapter
A. Einstein, “Autobiographical Notes” in Albert Einstein: Philosopher-Scientist, P.
A. Schlipp, ed. Evanston, IL: Library of Living Philosophers, 1949.

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