Equilibrium Thermodynamics and Statistical Physics

Equilibrium thermodynamics

Thermodynamics overview. [tln2]
Preliminary list of state variables. [tln1]
Physical constants. [tsl47]
Primitive concepts and axiomatic structure of thermodynamics.
Equation of state.
Equations of state for ideal gas and real fluid. [tsl12]
Quasi-static process.
Classification of thermodynamic systems. Laws of thermodynamics. [tln10]
Exact differentials. Applications to internal energy and entropy. [tln14]
Exact and inexact differentials. [tex5]
Carnot engine. [tln11]
Maximum efficiency. [tln12]
Absolute temperature. [tln13]
Entropy change caused by expanding ideal gas. [tex1]
Carnot cycle of the classical ideal gas. [tex3]
Carnot cycle of an ideal paramagnet. [tex4]
Carnot cycle of thermal radiation. [tex24]
Reversible processes in fluid systems [tln15]
Adiabates of the classical ideal gas [tex7]
Roads from 1 to 2: isothermal, isentropic, isochoric, isobaric [tex25]
Room heater: electric radiator versus heat pump [tex13]
Mayer's relation for the heat capacities of the classical ideal gas [tex12]
Positive and negative heat capacities [tex26]
Gasoline engine [tln65]
Idealized gasoline engine(Otto cycle) [tex8]
Ideal-gas engine with two-step cycle I [tex106]
Ideal-gas engine with two-step cycle II [tex107]
Joule cycle [tex108]
Rubber band heat engine [tex39]
Retrievable and irretrievable energy put in heat reservoir [tex6]
Fundamental equation of thermodynamics [tln16]
Free energy [tln3]
Legendre transform
Thermodynamic potentials [tln4]
Alternative set of thermodynamic potentials [tln9]
Thermodynamic functions [tln5]
Maxwell's relations [tln17]
Free energy stored and retrieved [tln18]
Useful relations between partial derivatives [tln6]
Diesel engine [tln66]
Idealized Diesel engine [tex16]
Heating the air in a room [tex2]
Response functions (thermal, mechanical, magnetic) [tln7] (2)
Isothermal and adiabatic processes in fluid systems and magnetic systems [tln8]
Equation of state and adiabate of an elastic band [tex40]
Entropy and internal energy of the classical ideal gas [tex14]
Thermodynamic potentials of the classical ideal gas with N=const. [tex15]
Chemical potential of the classical ideal gas [tex17]
Work extracted from finite heat reservoir in infinite environment [tex9]
Work extracted from finite heat reservoir in finite environment [tex10]
How not to modify the ideal gas equation of state [tex11]
Conditions for thermal equilibrium [tln19]
Stability of thermal equilibrium [tln20]
Jacobi transformations [tln21]
Determining CV of condensed matter [tex28]
Thermodynamics of an ideal paramagnet I [tex19]
Thermodynamics of an ideal paramagnet II [tex20]
Van der Waals equation of state [tln22]
Heat capacities of the van der Waals gas [tex27]
Internal energy and entropy of the van der Waals gas [tex38]
Cooling gases: Joule effect (free expansion) and Joule-Thomson effect (throttling) [tln23]
Joule coefficient of the van der Waals gas [tex31]
Joule-Thomson coefficient of the van der Waals gas [tex32]
Joule-Thomson inversion curves [tsl1]
Effects of first virial correction on ideal gas properties [tex33]
Thermodynamics of an ideal paramagnet III [tex21]
Entropy due to electronic spins in iron ammonium alum [tsl2]
Adiabatic demagnetization [tln24]
Thermodynamics of a real paramagnet [tex36]
Thermodynamics of a paramagnetic gas [tex22]
Thermodynamics of blackbody radiation [tex23]
Entropy of mixing [tln25]
Osmotic pressure [tln26]
Assembling thermodynamic information [tex29]
Reconstructing the equation of state of a fluid system [tex42]
Reconstructing the equation of state of a gas [tex43]
Ideal gas heat capacity by design [tex35]
Sound velocity in the classical ideal gas I [tex18]
Sound velocity in the classical ideal gas II [tex99]
 

Thermodynamics of phase transitions

Phase diagram of a pure pVT system
Phase diagram of a "normal" substance [tsl3]
Phase diagram of H2O [tsl4]
Phase diagram of carbon [tsl6]
Phase coexistence: Gibbs' phase rule [tln27]
Classification of phase transitions [tln28]
Gibbs free energy and derivatives at discontinuous transition [tsl7]
Gibbs free energy and derivatives at continuous transition [tsl8]
Clausius-Clapeyron equation [tln29]
Entropy of a supercooled liquid [tex30]
Coexistence line of continuous phase transition [tex37]
Heat capacity of vapor in equilibrium with liquid phase [tex41]
Discontinuous transition: change in internal energy [tex123]
Latent heat and response functions [tex124]
Dry ice [tex125]
Liquid-vapor coexistence region
Law of corresponding states [tln30]
Guggenheim plot [tsl9]
Van der Waals equation of state with coexistence curve [tsl10]
Dieterici equation of state [tex34]
Melting or freezing [tex51]
Triple-point phase changes [tex52]
Maxwell construction [tln31]
Gibbs and Helmholtz free energies of the van der Waals fluid at T<Tc [tsl11]
Condensation and evaporation [tln32]
Helium liquids [tln33]
Phase diagram of  4He [tsl13]
Phase diagram of  3He [tsl14]
Exotic properties of helium II [tln34]
Thermodynamics of a superconductor
Superconducting transition [tln35]
Structural transitions of iron [tex53]
Phase coexistence of ammonia [tex55]
Latent heat and heat capacities at superconducting transition [tex44]
Thermodynamics of a ferromagnet [tsl5]
Thermodynamics of the mean-field ferromagnet I [tex45]
Thermodynamics of the mean-field ferromagnet II [tex46]
What is wrong with these coexistence lines? [tex54]
 

Probability and kinetic theory

Statistical concept of uncertainty
Statistical concept of uncertainty [tex47]
Statistical uncertainty and information [tln37]
Statistical uncertainty and information [tex48]
Information of sequenced messages [tex61]
Uncertainty and entropy
Kinetic theory (on the most elementary level)
Kinetics of classical ideal gas [tsl28]
Pressure and mean square velocity in classical ideal gas [tex49]
Maxwell velocity distribution [tln38]
Maxwell velocity distribution (Maxwell's derivation) [tex50]
Maxwell distribution in D-dimensional space [tex56]
Boltzmannn equation [tln39]
Boltzmann's H-theorem [tln40]
Energy distribution for N ideal gas atoms [tex57]
Maxwell velocity distribution (Boltzmann's derivation) [mex58]
Ideal-gas entropy and Boltzmann's H-function [tex59]
H-theorem and entropy [tln41]
Boltzmann's H-function simulated [tsl27]
Maxwell distribution derived from minimizing the H-function [tex60]
Ideal gas atoms escaping from a container [tex62]
Doppler broadening of atomic spectral lines [tex63]
Toward thermal equilibrium via particle transfer [tex64]
Isotope separation via diffusion [tex65]
Kinetic pressure and interaction pressure [tln42]
Interaction pressure produced by Gaussian interparticle potential [tex66]
Rate of chemical reaction A + A -> 2A in gas phase [tex67]
Kinetic forces and mobility [tln43]
Average force of particle beam on heavy hard sphere [tex68]
Mobility of a hard sphere in a dilute gas [tex69]
Collision rate and mean free path [tln44]
Collision rate in classical ideal gas [tex70]
Mean free path of particle in classical ideal gas [tex71]
Effect of escaping particles on temperature of 1D ideal gas [tex72]

Equilibrium statistical mechanics

Classical Hamiltonian system [tln45]
Classical Liouville operator [tln46]
Quantum Liouville operator [tln47]
Gibbs entropy [tln48]
Microcanonical ensemble [tln49]
Classical ideal gas (microcanonical ensemble) [tex73]
Array of classical harmonic oscillators (microcanonical ensemble) [tex74]
Quantum harmonic oscillators (microcanocal ensemble) [tex75]
Quantum harmonic oscillators (microcanocal ensemble) [tex126]
Entropy of mixing revisited [tln50]
Canonical ensemble [tln51]
Classical ideal gas (canonical ensemble) [tex76]
Ultrarelativistic classical ideal gas (canonical idela gas) [tex77]
Array of classical harmonic oscillators (canonical ensemble) [tex78]
Ensemble averages [tln52]
Fluctuations in a magnetic system [tln53]
Fluctuations in a magnetic system [tex109]
Systems of noninteracting particles [tln54]
Further ensemble averages [tln55]
Classical ideal gas in a uniform gravitational field [tex79]
Relative momentum of two ideal gas particles [tex80]
Distribution of distances between two particles
Partition function and density of states [tln56]
Ideal gas partition function and density of states [tex81]
Vibrational heat capacities of solids [tln57]
Array of quantum harmonic oscillators (canonical ensemble) [tex82]
Vibrational heat capacities of solids (Debye theory) [tsl29]
Vibrational heat capacity of a solid [tex83]
Anharmonic oscillator and thermal expansion [tex104]
Paramagnetism [tln58]
Paramagnetic salts [tsl30]
Classical paramagnet (canonical ensemble) [tex84]
Quantum paramagnet (two-level system) [tex85]
Quantum paramagnet (microcanonical ensemble) [tex127]
Quantum paramagnet (Brillouin function) [tex86]
Negative temperatures [tsl31]
Gases with internal degrees of freedom [tln59]
Classical rotational free energy of NH3 gas [tex87]
Classical rotational entropy of HCl and N2 gas [tex88]
Quantum rotational heat capacity of a gas at low temperature [tex89]
Quantum rotational heat capacity of a gas at high temperature [tex90]
Rotational and vibrational heat capacities [tsl32]
Relativistic classical ideal gas
Relativistic classical ideal gas (canonical partition function) [tex91]
Relativistic classical ideal gas (entropy and internal energy) [tex92]
Relativistic classical ideal gas (heat capacity) [tex93]
Relativistic classical ideal gas (heat capacity) [tsl34]
Grandcanonical ensemble [tln60]
Classical ideal gas (grandcanonical ensemble) [tex94]
Density fluctuations and compressibility [tln61]
Density fluctuations in the grand canonical ensemble [tex95]
Density fluctuations and compressibility in the classical ideal gas [tex96]
Energy fluctuations and thermal response functions [tex103]

Ideal quantum gases (with graphs designed and prepared by Geoffrey Potter) 

Microscopic states of quantum ideal gases [tln62]
Partition function of quantum ideal gases [tln63]
Ideal quantum gases: grand potential and thermal averages [tln64]
Ideal quantum gases: average level occupancies [tsl35]
Occupation number fluctuations [tex110]
Density of energy levels for ideal quantum gas [tex111]
Maxwell-Boltzmann gas in D dimensions [tex112]
Bose-Einstein functions [tsl36]
Ideal Bose-Einstein gas: equation of state and internal energy [tln67]
BE gas in D dimensions I: fundamental relations [tex113]
Reference values for T, V/N, and p [tln71]
Bose-Einstein condensation [tsl38]
Ideal Bose-Einstein gas: isochores [tsl39]
BE gas in D dimensions II: isochore [tex114]
BE gas in D dimensions III: isotherm and isobar [tex115]
Bose-Einstein gas: isotherms [tsl40]
Bose-Einstein gas: isobars [tsl48]
Bose-Einstein gas: phase diagram [tln72]
Bose-Einstein heat capacity [tsl41]
BE gas in D dimensions IV: heat capacity at high temperature [tex97]
BE gas in D dimensions V: heat capacity at low temperature [tex116]
BE gas in D dimensions VI: isothermal compressibility [tex128]
BE gas in D dimensions VII: isobaric expansivity [tex129]
BE gas in D dimensions VIII: speed of sound [tex130]
Ultrarelativistic Bose-Einstein gas [tex98]
Blackbody radiation [tln68]
Statistical mechanics of blackbody radiation [tex105]
Fermi-Dirac functions [tsl42]
Ideal Fermi-Dirac gas: equation of state and internal energy [tln69]
Ideal Fermi-Dirac gas: chemical potential [tsl43]
FD gas in D dimensions: chemical potential I [tex117]
FD gas in D dimensions: chemical potential II [tex118]
Ideal Fermi-dirac gas: average level occupancy [tsl44]
Ideal Fermi-Dirac gas: isochores I [tsl46]
FD gas in D dimensions: statistical interaction pressure [tex119]
Ideal Fermi-Dirac gas: isotherms [tln70]
FD gas in D dimensions: isotherm and adiabate [tex120]
FD gas in D dimensions: ground-state energy [tex102]
Ideal Fermi-Dirac gas: heat capacity [tsl45]
FDgas in D dimensions: heat capacity at high temperature [tex100]
FD gas in D dimensions: heat capacity at low temperature [tex101]
Ideal Fermi-Dirac gas: isochores II [tln73]
Ideal Fermi-Dirac gas: phase diagram in infinite dimensions [tln74]
Stable white dwarf [tex121]
Unstable white dwarf [tex122]
Thermionic emission (Richardson effect)
Schottky effect
Photoelectric effect (Hallwachs effect)
Pauli paramagnetism

Textbooks


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Last updated 11/19/07