Exercises for Statistical Physics I

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Equilibrium Thermodynamics

Entropy change caused by expanding ideal gas [tex1] gif pdf ps
Heating the air in a room [tex2]   gif pdf   ps
Carnot cycle of the classical ideal gas [tex3] gif pdf ps
Carnot cycle of an ideal paramagnet [tex4] gif pdf ps
Exact and inexact differentials [tex5]   gif pdf   ps
Retrievable and irretrievable energy put in heat reservoir [tex6]   gif pdf ps
Adiabates of the classical ideal gas [tex7] gif pdf ps
Idealized gasoline engine (Otto cycle) [tex8] gif pdf ps
Idealized Diesel engine [tex16]   gif pdf   ps
Work extracted from finite heat reservoir in infinite environment [tex9]   gif pdf ps
Work extracted from finite heat reservoir in finite environment [tex10]   gif pdf ps
How not to modify the ideal gas equation of state [tex11] gif pdf ps
Mayer's relation for the heat capacities of the classical ideal gas [tex12]   gif pdf ps
Room heater: electric radiator versus heat pump [tex13] gif pdf ps
Entropy and internal energy of the classical ideal gas [tex14]   gif pdf ps
Thermodynamic potenials of the classical ideal gas with N=const [tex15]   gif pdf ps
Chemical potential of the classical ideal gas [tex17] gif pdf ps
Sound velocity of the classical ideal gas I [tex18] gif pdf ps
Sound velocity in the classical ideal gas II [tex 99] gif pdf ps
Thermodynamics of an ideal paramagnet I [tex19] gif pdf ps
Thermodynamics of an ideal paramagnet II [tex20] gif pdf ps
Thermodynamics of an ideal paramagnet III [tex21] gif pdf ps
Thermodynamics of a paramagnetic gas [tex22] gif pdf ps
Thermodynamics of black-body radiation [tex23] gif pdf ps
Carnot cycle of thermal radiation [tex24] gif pdf ps
Roads from 1 to 2: isothermal, isentropic, isochoric, isobaric [tex25]   gif pdf ps
Positive and negative heat capacities [tex26] gif pdf ps
Heat capacities of the van der Waals gas [tex27] gif pdf ps
Determining C_V of condensed matter [tex28] gif pdf ps
Assembling thermodynamic information [tex29] gif pdf ps
Joule coefficient of van der Waals gas [tex31] gif pdf ps
Joule-Thompson coefficient of van der Waals gas [tex32] gif pdf ps
Effects of first virial correction on ideal gas properties [tex33]   gif pdf ps
Dieterici equation of state [tex34]   gif pdf   ps
Ideal gas heat capacity by design [tex35] gif pdf ps
Thermodynamics of a real paramagnet [tex36] gif pdf ps
Internal energy and entropy of van der Waals gas [tex38] gif pdf ps
Rubber band heat engine [tex39]   gif pdf   ps
Equation of state and adiabate of an elastic band [tex40] gif pdf ps
Reconstructing the equation of state of a fluid system [tex42]   gif pdf ps
Reconstructing the equation of state of a gas [tex43] gif pdf ps

Thermodynamics of phase transitions

Entropy of supercooled liquid [tex30]   gif pdf   ps
Coexistence line of continuous phase transition [tex37] gif pdf ps
Heat capacity of vapor in equilibrium with liquid phase [tex41]   gif pdf ps
Latent heat and heat capacities at superconducting transition [tex44]   gif   pdf ps
Thermodynamics of the mean-field ferromagnet I [tex45] gif   pdf ps
Thermodynamics of the mean-field ferromagnet II [tex46] gif   pdf ps
Melting or freezing? [tex51]   gif pdf   ps
Triple point phase changes [tex52]   gif pdf   ps
Structural transitions of iron [tex53]   gif pdf   ps
What is wrong with these coexistence lines? [tex54] gif   pdf ps
Phase coexistence of ammonia [tex55]   gif pdf   ps

Probability and kinetic theory

Statistical concept of uncertainty [tex47] gif pdf   ps
Statistical uncertainty and information [tex48] gif pdf   ps
Information of sequenced messages [tex61] gif pdf   ps
Pressure and mean square velocity in classical ideal gas [tex49] gif pdf   ps
Maxwell velocity distribution (Maxwell's derivation) [tex50] gif pdf   ps
Maxwell's velocity distribution (Boltzmann's derivation) [tex58] gif pdf   ps
Maxwell distribution in D-dimensional space [tex56] gif pdf   ps
Energy distribution of N ideal gas atoms [tex57] gif pdf   ps
Ideal-gas entropy and Boltzmann's H-function [tex59] gif pdf   ps
Maxwell distribution derived from minimizing the H-function [tex60] gif pdf   ps
Ideal gas atoms escaping from a container [tex62] gif pdf   ps
Doppler broadening of atomic spectral lines [tex63] gif pdf   ps
Toward thermal equilibrium via particle transfer [tex64] gif pdf   ps
Isotope separation via diffusion [tex65] gif pdf   ps
Interaction pressure produced by Gaussian interparticle potential [tex66] gif pdf   ps
Rate of chemical reaction A + A -> 2A in gas phase [tex67] gif pdf   ps
Average force of particle beam on heavy hard sphere [tex68] gif pdf   ps
Mobility of a hard sphere in a dilute gas [tex69] gif pdf   ps
Collision rate in classical ideal gas [tex70] gif pdf   ps
Mean free path of particle in classical ideal gas [tex71] gif pdf   ps
Effect of escaping particles on temperature of 1D ideal gas [tex72] gif pdf   ps

Equilibrium statistical mechanics

Classical ideal gas (microcanonical ensemble) [tex73] gif pdf   ps
Array of classical harmonic oscillators (microcanonical ensemble) [tex74] gif pdf   ps
Array of quantum harmonic oscillators (microcanonical ensemble) [tex75] gif pdf   ps
Array of quantum harmonic oscillators (canonical ensemble) [tex82] gif pdf   ps
Classical ideal gas (canonical ensemble) [tex76] gif pdf   ps
Ultrarelativistic classical ideal gas (canonical ensemble) [tex77] gif pdf   ps
Array of classical harmonic oscillators (canonical ensemble) [tex78] gif pdf   ps
Classical ideal gas in uniform gravitational field [tex79] gif pdf   ps
Relative momentum of two ideal gas particles [tex80] gif pdf   ps
Ideal gas partition function and density of states [tex81] gif pdf   ps
Vibrational heat capacity of a solid [tex83] gif pdf   ps
Classical paramagnet (canonical ensemble) [tex84] gif pdf   ps
Quantum paramagnet (two-level system) [tex85] gif pdf   ps
Quantum paramagnet (Brillouin function) [tex86] gif pdf   ps
Classical rotational free energy of NH₃ gas [tex87] gif pdf   ps
Classical rotational entropies of HCl and N₂ gases [tex88] gif pdf   ps
Quantum rotational heat capacities of a gas at low temperatures [tex89] gif pdf   ps
Quantum rotational heat capacities of a gas at high temperatures [tex90] gif pdf   ps
Relativistic ideal gas (canonical partition function) [tex91] gif pdf   ps
Relativistic ideal gas (entropy and internal energy) [tex92] gif pdf   ps
Relativistic ideal gas (heat capacity) [tex93] gif pdf   ps
Clasical ideal gas (grandcanonical ensemble) [tex94] gif pdf   ps
Density fluctuations in the grandcanonical ensemble [tex95] gif pdf   ps
Density fluctuations and compressibility in the classical ideal gas [tex96] gif pdf   ps
Heat capacity of ideal Bose-Einstein gas [tex97] gif pdf   ps
Ultrarelativistic Bose-Einstein gas [tex98] gif pdf   ps
Heat capacity of ideal Fermi-Dirac gas I [tex100] gif pdf   ps
Heat capacity of ideal Fermi-Dirac gas II [tex101] gif pdf   ps
Internal energy of ideal Fermi-Dirac gas [tex102] gif pdf   ps
Energy fluctuations and thermal response functions [tex103] gif pdf   ps
Anharmonic oscillator and thermal expansion [tex104] gif pdf   ps
Statistical mechanics of blackbody radiation [tex105] gif pdf   ps

last updated 12/11/04