Thermodynamics, Statistical Physics, and Quantum Mechanics

216 SOLUTIONS where weused Substituting and from (S.4.93.21), we obtain a more general formula for At constant volume (S.4.93.23 ...

THERMODYNAMICS AND STATISTICAL PHYSICS 217 Similarly, for a Bose gas we have b) First solution: Since a classical ideal gas is a ...

218 SOLUTIONS Using the equation for an ideal gas, in (S.4.94.12), we obtain Third solution: Use the Poisson distribution, which ...

THERMODYNAMICS AND STATISTICAL PHYSICS 219 4.95 Wiggling Wire (Princeton) First solution: Consider the midpoint of the wire P fi ...

220 SOLUTIONS Second solution: We solve the equation of motion for the wire (see deriva- tion in Problem 1.46, Part I). For the ...

THERMODYNAMICS AND STATISTICAL PHYSICS 221 where we substituted from (S.4.95.9). Note that even modes do not contribute to the f ...

222 SOLUTIONS harmonicoscillator offrequency whoseenergylevels are The average energy in the circuit is given by (with The avera ...

THERMODYNAMICS AND STATISTICAL PHYSICS 223 as found in (S.4.96.6). The mean square noise voltage is b)If then (S.4.96.6) becomes ...

224 SOLUTIONS where we set So, Note that, in this approximation, the nextterm in the potential would not have introduced any add ...

THERMODYNAMICS AND STATISTICAL PHYSICS 225 The partitionfunction of asingleoscillatorassociatedwiththis potential energy is b) S ...

226 SOLUTIONS 4.98 Schottky Defects (Michigan State, MIT) WhenNatoms are displaced to thesurface, they leave thesamenumber of va ...

THERMODYNAMICS AND STATISTICAL PHYSICS 227 be used as an approximation). The vacancies and interstices then can be distributed i ...

228 SOLUTIONS and The condition implies that andtherefore 4.100 Two-Dimensional Debye Solid (Columbia, Boston) a) The number of ...

THERMODYNAMICS AND STATISTICAL PHYSICS 229 b)The free energy (see Problem 4.77) then becomes Defining and introducing a new vari ...

230 SOLUTIONS The specific heat at low temperatures) is At low temperatures, we can extend the upperlimit ofintegration to infin ...

THERMODYNAMICS AND STATISTICAL PHYSICS 231 b) If we assume that the N atoms of the solid each have three degrees of freedom and ...

(^232) SOLUTIONS 4.102 Gas Adsorption (Princeton, MIT, Stanford) For two systems inequilibrium, thechemicalpotentials should be ...

THERMODYNAMICS AND STATISTICAL PHYSICS 233 where the possible occupational numbers of the site for a submonolayer 0,1 (site is e ...

234 SOLUTIONS The partition function is then and the average number of particles the same as (S.4.102.8). 4.103 Thermionic Emiss ...

THERMODYNAMICS AND STATISTICAL PHYSICS 235 The current where is the electron charge. Therefore, we can express P from (S.4.103.5 ...