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1 Table of Contents [ttc] 1. Equilibrium Thermodynamics I: Introduction Thermodynamics overview. [tln2] Preliminary list of state variables. [tln1] Physical constants. [tsl47] Equations of state. [tln78] Equation of state for ideal gas and real fluid. [tsl12] Classification of thermodynamic systems. Laws of thermodynamics. [tln10] Thermodynamic processes (irreversible, quasi-static, adiabatic). [tln79] Fast heat. [tex143] Expansion and compression of nitrogen gas. [tex144] Bathtub icebreaker. [tex145] Exact differentials. Applications to internal energy and entropy. [tln14] Exact and inexact differentials I. [tex5] Exact and inexact differentials II. [tex146] 2. Equilibrium Thermodynamics II: Engines 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] Reversible processes in fluid systems. [tln15] Adiabates of the classical ideal gas. [tex7]
2 Roads from 1 to 2: [tex25] isothermal, isentropic, isochoric, isobaric. 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] Work extracted from finite heat reservoir in infinite environment. [tex9] Work extracted from finite heat reservoir in finite environment. [tex10] Heating the air in a room. [tex2] Gasoline engine. [tln65] Idealized gasoline engine(otto cycle). [tex8] Diesel engine. [tln66] Idealized Diesel engine. [tex16] Escher-Wyss gas turbine. [tln75] Joule cycle. [tex108] Stirling engine. [tln76] Idealized Stirling cycle. [tex131] Ideal-gas engine with two-step cycle I. [tex106] Ideal-gas engine with two-step cycle II. [tex107] Circular heat engine I. [tex147] Circular heat engine II. [tex148] Square heat engine. [tex149] 3. Equilibrium Thermodynamics III: Free Energies Fundamental equation of thermodynamics. [tln16] Free energy. [tln3] Retrievable and irretrievable energy put in heat reservoir. [tex6] Legendre transform. [tln77]
3 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] Response functions (thermal, mechanical, magnetic). [tln7] (2) Isothermal and adiabatic processes in fluid systems and magnetic systems. [tln8] Conditions for thermal equilibrium. [tln19] Stability of thermal equilibrium. [tln20] Jacobi transformation. [tln21] Entropy of mixing. [tln25] Osmotic pressure. [tln26] 4. Equilibrium Thermodynamics IV: Applications Entropy and internal energy of the classical ideal gas. [tex14] Thermodynamic potentials of the classical ideal gas. [tex15] Chemical potential of the classical ideal gas. [tex17] 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] Absolute temperature from measurements. [tex134] Polytropic process of classical ideal gas. [tex138] Heavy piston. [tex141] Isothermal atmosphere. [tex150] Adiabatic atmosphere. [tex151] Homogeneous atmosphere. [tex152] Van der Waals equation of state. [tln22]
4 Cooling gases: Joule effect (free expansion) and Joule-Thomson effect (throttling). [tln23] Joule-Thomson inversion curves. [tsl1] Heat capacities of the van der Waals gas. [tex27] Internal energy and entropy of the van der Waals gas. [tex38] Joule coefficient of the van der Waals gas. [tex31] Joule-Thomson coefficient of the van der Waals gas. [tex32] Assembling thermodynamic information. [tex29] How not to modify the ideal gas equation of state. [tex11] Reconstructing the equation of state of a fluid system. [tex42] Reconstructing the equation of state of a gas. [tex43] Effects of first virial correction on ideal gas properties. [tex33] Entropy due to electronic spins in iron ammonium alum. [tsl2] Adiabatic demagnetization. [tln24] Thermodynamics of an ideal paramagnet I. [tex19] Thermodynamics of an ideal paramagnet II. [tex20] Thermodynamics of an ideal paramagnet III. [tex21] Thermodynamics of a real paramagnet. [tex36] Thermodynamics of a classical ideal paramagnetic gas I. [tex22] Thermodynamics of a classical ideal paramagnetic gas II. [tex133] Hydrostatic pressure. [tex132] Rubber band heat engine. [tex39] Equation of state and adiabate of an elastic band. [tex40] Determining C V of condensed matter. [tex28] Thermodynamics of blackbody radiation. [tex23] Carnot cycle of thermal radiation. [tex24] 5. Thermodynamics of Phase Transitions I Phase diagram of a normal substance. [tsl3]
5 Phase diagram of H 2 O. [tsl4] Ferrimagnetic phases. [tsl49] Liquid crystal phases. [tsl51] Ordering of surfactant molecules. [tsl50] 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] Latent Heat and response functions. [tex124] Heat capacity of vapor in equilibrium with liquid phase. [tex41] Discontinuous transition: change in internal energy. [tex123] Dry ice. [tex125] Abnormal phase behavior. [tex54] Melting or freezing. [tex51] Triple-point phase changes. [tex52] Cooling down? Heating up? [tex153] Phase coexistence of ammonia. [tex55] 6. Thermodynamics of Phase Transitions II Van der Waals equation of state with coexistence curve. [tsl10] Law of corresponding states. [tln30] Maxwell construction. [tln31] Gibbs and Helmholtz free energies of the van der Waals fluid at T < T c. [tsl11] Condensation and evaporation. [tln32] Dieterici equation of state. [tex34]
6 Helium liquids. [tln33] Phase diagram of 4 He. [tsl13] Phase diagram of 3 He. [tsl14] Exotic properties of helium II. [tln34] Superconducting transition. [tln35] Thermodynamics of a ferromagnet. [tsl5] Structural transitions of iron. [tex53] Latent heat and heat capacities at superconducting transition. [tex44] Thermodynamics of the mean-field ferromagnet I. [tex45] Thermodynamics of the mean-field ferromagnet II. [tex46] 7. Kinetic Theory I Statistical uncertainty and information. [tln37] Statistical concept of uncertainty. [tex47] Statistical uncertainty and information. [tln37] Statistical uncertainty and information. [tex48] Information of sequenced messages. [tex61] 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]
7 Boltzmann s H-function simulated. [tsl27] Maxwell distribution derived from minimizing the H-function. [tex60] Doppler broadening of atomic spectral lines. [tex63] 8. Kinetic Theory II Ideal gas atoms escaping from a container. [tex62] Toward thermal equilibrium via particle transfer. [tex64] Isotope separation via diffusion. [tex65] Kinematic pressure and interaction pressure. [tln42] Interaction pressure produced by Gaussian interparticle potential. [tex66] 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] Rate of chemical reaction A + A A 2 in gas phase. [tex67] Effect of escaping particles on temperature of 1D ideal gas. [tex72] 9. Microcanonical Ensemble 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 I). [tex75]
8 Quantum harmonic oscillators (microcanocal ensemble II). [tex126] Quantum paramagnet (microcanonical ensemble). [tex127] Entropy of mixing revisited. [tln50] 10. Canonical Ensemble I Canonical ensemble. [tln51] Classical ideal gas (canonical ensemble). [tex76] Ultrarelativistic classical ideal gas (canonical idela gas). [tex77] Ultrarelativistic classical ideal gas in two dimensions. [tex154] Array of classical harmonic oscillators (canonical ensemble). [tex78] Irreversible decompression. [tex136] Irreversible heat exchange. [tex137] Reversible decompression. [tex139] Reversible heat exchange. [tex140] Heavy piston. [tex141] Ensemble averages. [tln52] Classical virial theorem. [tln83] Systems of noninteracting particles. [tln54] Further ensemble averages. [tln55] Classical ideal gas in a uniform gravitational field. [tex79] Gas pressure and density inside centrifuge. [tex135] Relative momentum of two ideal gas particles. [tex80] 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] Thermodynamic perturbation expansion. [tln80] Vibrational heat capacity of a solid. [tex83]
9 Anharmonic oscillator and thermodynamic perturbation. [tex104] 11. Canonical Ensemble II Paramagnetism. [tln58] Paramagnetic salts. [tsl30] Fluctuations in a magnetic system. [tln53] Fluctuations in a magnetic system. [tex109] Classical paramagnet (canonical ensemble). [tex84] Quantum paramagnet (two-level system). [tex85] Quantum paramagnet (Brillouin function). [tex86] Ising trimer. [tex142] Negative temperatures. [tsl31] Gases with internal degrees of freedom. [tln59] Classical rotational free energy of NH 3 gas. [tex87] Classical rotational entropy of HCl and N 2 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] Orthohydrogen and parahydrogen. [tln81] 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] 12. Grandcanonical Ensemble Grandcanonical ensemble. [tln60] Classical ideal gas (grandcanonical ensemble). [tex94] Density fluctuations and compressibility. [tln61]
10 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] 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] 13. Ideal Quantum Gases I: Bosons 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]
11 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] 14. Ideal Quantum Gases II: Fermions Fermi-Dirac functions. [tsl42] Ideal Fermi-Dirac gas: equation of state and internal energy. [tln69] Ideal Fermi-Dirac gas: chemical potentia.l [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] FD gas 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]
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