Thermodynamics, Statistical Physics, and Quantum Mechanics

156 SOLUTIONS d) During adiabatic compression, the entropy is constant, so from (S.4.52.7) and we have e) The work done is given ...

THERMODYNAMICS AND STATISTICAL PHYSICS 157 Substituting the Dietrici equation into (S.4.53.1) gives Using the second criterion ( ...

158 Mixtures and Phase Separation Entropy of Mixing (Michigan, MIT) a) The energy of the mixture of ideal gases is the sum of en ...

THERMODYNAMICS AND STATISTICAL PHYSICS 159 and so In the case of identical gases, reversing the process only requires the reinse ...

where is the concentrationratio of heliummolecules in the bag to their concentration in the air. In regular units 160 SOLUTIONS ...

THERMODYNAMICS AND STATISTICAL PHYSICS Therefore The Gibbs potential of themixture 161 where are partial pressures corresponding ...

162 or SOLUTIONS where we only take intoaccount the first-orderterms in the solute. If we alsoassume, which is usually thecase, ...

THERMODYNAMICS AND STATISTICAL PHYSICS 163 b) Consider the particular case of equilibrium between liquid and vapor. The volume o ...

(^164) SOLUTIONS At the critical point, so(S.4.58.3) becomes For (S.4.58.4) tohold forarbitrary wehave See Landauand Lifshitz,St ...

THERMODYNAMICS AND STATISTICAL PHYSICS 165 be the sublimation rate. Taking the average velocityfromProblem4.13, weget where is t ...

166 SOLUTIONS Had we assumedthatoxygen iscondensing at we would get Thiscontradicts thefact thatoxygen boils at a highertemperat ...

THERMODYNAMICS AND STATISTICAL PHYSICS 167 where is thehydrostatic pressure ( is the height of the water). We disregard anyeffec ...

(^168) SOLUTIONS The coefficient 2 in front of thesecond termresultsfrom thepresence of two surfaces of thesoapfilmenclosing the ...

THERMODYNAMICS AND STATISTICAL PHYSICS is associated with the surface tension: The Gibbs free energy The entropy change where is ...

170 SOLUTIONS where the last equationrepresents theideal gas lawat constanttempera- ture. This yields the equation Solvingthis c ...

THERMODYNAMICS AND STATISTICAL PHYSICS 171 4.65 Two-Dimensional Fermi Gas (MIT, Wisconson-Madison) a) At the noninteractingfermi ...

becomes a stepfunction. All thestatesabove acertainenergy, are empty, andthe states below, are filled (seeFigure S.4.66). This e ...

THERMODYNAMICS AND STATISTICAL PHYSICS 173 and therefore To calculate thetotalenergy of thegas, we canwrite and therefore and we ...

(^174) SOLUTIONS law is linear: The number of quantum states is the same as for the nonrelativistic case considered in Problem 4 ...

THERMODYNAMICS AND STATISTICAL PHYSICS 175 where the upper sign in (S.4.68.1) andbelow correspondsto Fermistatistics and the low ...