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Ther­mo­dy­nam­ics and Stat­ist­ic­al Mech­an­ics is both a very inter­est­ing and very import­ant sub­ject and forms part of the found­a­tion for later stud­ies for almost ever physics/engineering/chemistry stu­dent. Without thermal phys­ics one would find it extremely dif­fi­cult to ana­lyse the flow of heat (entropy), pis­tons (mech­an­ic­al work) or chem­ic­al reac­tions (Gibbs Free Energy). Stat­ist­ic­al mech­an­ics (intro­duced here using Ein­stein Solids) leads us later to the Max­well Boltzmann, Fermi Dir­ac and Bose Ein­stein occu­pancy func­tions. Con­cep­tu­ally, the sub­ject is not par­tic­u­larly dif­fi­cult; it does how­ever pose many new quant­it­ies and their of course their names. Thus stu­dents must become com­fort­able in dif­fer­en­ti­at­ing between entropy, enthalpy, Gibbs Free Energy, Helm­holtz Free Energy etc! In this regard, my advice is to begin com­pil­ing a dic­tion­ary as you study (I cer­tainly did and it was extremely use­ful). See mine : Ther­mo­dy­nam­ics Gloss­ary of Terms (docx)Ther­mo­dy­nam­ics Gloss­ary of Terms (PDF)(a col­lab­or­a­tion with A. Butler).

Return to Video Tutori­als G-Z

The Ther­mo­dy­nam­ics and Stat­ist­ic­al Mech­an­ics video tutori­als may be viewed as part of the fol­low­ing playl­ists, or as lis­ted later on.

Ein­stein Solids Playl­ist Gibbs’ and Helm­holtz’ Free Energy Play­ist Ther­mo­dy­nam­ics Iden­tit­ies Playl­ist Van der Waals Play­ist Chem­ic­al Poten­tial Playl­ist Entropy Playl­ist 

Video # Video Tutori­al Title Remarks
1 The Mean­ing of Tem­per­at­ure and Heat Is tem­per­at­ure a fun­da­ment­al quant­ity? What’s the dif­fer­ence between temp and heat?
2 The First Law of Thermodynamics ΔU = Q + W
3 Com­pres­sion Work dW = — PdV
4 Ideal Gas Law PV = nRT
5 Adia­bat­ic Processes No heat trans­fer in or out of the sys­tem. Q = 0 & ΔU = W PV = const
6 Heat Capa­city The energy required to raise the tem­per­at­ure of a body by per units mass and temp increase
7 Enthalpy H = U + PV = intern­al energy + energy to make room for a system
8 Ein­stein Solids 1 Macro & Micro state mul­ti­pli­cit­ies of 2 state sys­tems; non inter­act­ing particles (coins) (Bosons)
9 Ein­stein Solids 2 Micro­state Mul­ti­pli­city when we dis­trib­ute energy amongst vari­ous lin­ear har­mon­ic oscillators
10 Ein­stein Solids 3 Using E.S.1 and E.S.2 to dis­cov­er the real mean­ing of heat
11 Stirling’s Approx­im­a­tion A deriv­a­tion of this approx­im­a­tion for factori­al of a nat­ur­al logarithm
12 Bino­mi­al Theorem A deriv­a­tion
13 Deriv­a­tion of Taylor and Mac­Laur­in Series Expansions Two of the most use­ful approx­im­a­tions for real world physics
14 Taylor / Mac­Laur­in Series (1+x)n See why (1+x)(1/2) ~= 1+x/2
15 Taylor / Mac­Laur­in Series for Cos(x) Without this expan­sion we can’t derive Euler’s Equa­tioneix = Cos(x) + iSin(x)
16 Taylor / Mac­Laur­in Series for Exp(x)  
17 Taylor / Mac­Laur­in Series for ln(x)  
18 Mul­ti­pli­city of an Ideal Gas (mon­atom­ic) Bring­ing us closer to an expres­sion for and defin­i­tion of Entropy
19 a Deriv­a­tion of the Gamma Func­tion 1/2 This func­tion extends the factori­al func­tion to non integers
19 b Deriv­a­tion of the Gamma Func­tion 2/2 All the integ­rals which are required IOT derive the Gamma Function
20 Ein­stein Solids 4 The mul­ti­pli­city for a large Ein­stein Sol­id (requires Taylor Series and Stirling’s Approximation)
21 Ein­stein Solids 5 The sharp­ness of the mul­ti­pli­city func­tion. N.B., for Entropy
22    
23    
24   The sharp­ness of the mul­ti­pli­city func­tion. N.B., for Entropy
25 The Second Law of Thermodynamics Entropy = S = k.ln(w)
26 Entropy What is Entropy?
27 Entropy and Temperature Deriv­ing a gen­er­al for­mula for tem­per­at­ure T = US
28 Entropy VS Energy Graphs Dis­cuss­ing the sig­ni­fic­ance of the graph’s slope
29 Pre­dict­ing Heat Capacities Cv = UT
30 Third Law of Ther­mody­anam­ics 1/2 As the tem­per­at­ure approaches zero, so does Cv and the Entropy
31 Third Law of Ther­mo­dy­nam­ics 2/2 The net increase in Entropy is the driv­ing force of heat
32 Two State Para­mag­net 1/2 Build­ing upon the work done on Ein­stein Solids (the physics)
33 Two State Para­mag­net 2/2 Cal­cu­lat­ing the heat capa­city at con­stant volume (yet again!) (math­em­at­ic­ally tedious)
34 Mech­an­ic­al Equi­lib­ri­um & the Ideal Gas Law Deriv­a­tion of the Ideal Gas Law
35 Ther­mo­dy­nam­ic Iden­tity 1/2 dU= TdS — PdV
36 Ther­mo­dy­nam­ic Iden­tity 2/2 dU= TdS — PdV +μdN
37 Gibbs’ and Helm­holtz’ Free Energy Energy avail­able for work under con­di­tions of con­stant pres­sure (Gibbs) or volume (Helm­holtz)
38 The Chem­ic­al Poten­tial μ
 The energy added to the sys­tem when you add a single particle
39 Gibbs’ and Helm­holtz Ther­mo­dy­nam­ic Identities Helm­holtz : dF= -SdT — PdV +μdN  and Gibbs : dG= -SdT + PdV +μdN
40 Free Energy and Equilibrium Max­im­ising the Entropy and minisim­ising the Gibbs’ and Helm­holtz’ Free Energies
41 Extens­ive and Intens­ive Quantities   
42 Chem­ic­al Poten­tial and Gibbs Free Energy Gibbs’ Free Energy per Particle
43 Chem­ic­al Poten­tial of an Ideal Gas μ0 + kT.ln(P/P0)
44 Phase Trans­form­a­tion for Pure Substances Liquid/gas phase bound­ary, Heli­um 3 and car­bon VS graphite
45 Clausi­us Clapeyron Relation The rela­tion between Entropy and volume dur­ing a phase changedP/dT = (Sg — Sl)/(Vg — Vl)
46 Van der Waals 1/3 An improve­ment on the ideal gas law by includ­ing a finite particle volume and inter­particle potential
47 Van der Waals 2/3 Gibbs’ Free Energy asso­ci­ated with the Van der Waals Model
48 Max­well Con­struc­tion (Van der Waals 3/3) Phase changes dis­cussed in light of the Van der Waals Model
49 Joule Thompson Throt­tling / Adia­bat­ic Cooling Cool­ing a gas by trans­fer­ring Kin­et­ic Energy to Poten­tial Energy

 

ther­mo­dy­nam­ics entropy heat tem­per­at­ure chem­ic­al poten­tial enthalpy gibbs helm­holtz ther­mo­dy­nam­ic iden­tit­ies iden­tity ein­stein solids mul­ti­pli­city mul­ti­pli­cit­ies ther­mo­dy­nam­ics entropy heat tem­per­at­ure chem­ic­al poten­tial enthalpy gibbs helm­holtz ther­mo­dy­nam­ic iden­tit­ies iden­tity ein­stein solids mul­ti­pli­city mul­ti­pli­cit­ies ther­mo­dy­nam­ics entropy heat tem­per­at­ure chem­ic­al poten­tial enthalpy gibbs helm­holtz ther­mo­dy­nam­ic iden­tit­ies iden­tity ein­stein solids mul­ti­pli­city multiplicities

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