Physical Chemistry Third Edition

1122 27 Equilibrium Statistical Mechanics. III. Ensembles 27.1 The Canonical Ensemble In Chapters 25 and 26 we applied statistic ...

27.1 The Canonical Ensemble 1123 state 2, and so on. Since the systems are macroscopic in size, they are distinguishable and the ...

1124 27 Equilibrium Statistical Mechanics. III. Ensembles Exercise 27.1 Choose several different functions ofEsuch as sin(E), co ...

27.1 The Canonical Ensemble 1125 and ∑ k pk ∑ k nk n  1 A ∑ k e−βEk (27.1-16) which is equivalent to 1 A  ∑ k e−βEkZ (defin ...

1126 27 Equilibrium Statistical Mechanics. III. Ensembles In order to investigate the parameterβ, we assert thatβhas the same pr ...

27.1 The Canonical Ensemble 1127 where we now denote a molecule state by the single indexk. This molecular partition function is ...

1128 27 Equilibrium Statistical Mechanics. III. Ensembles Solution ln(Z)Nln(z)−ln(N!) z ( 2 π(6. 65 × 10 −^27 kg)(1. 3807 × 10 ...

27.2 Thermodynamic Functions in the Canonical Ensemble 1129 where we have applied the chain rule (see Appendix B). We can also w ...

1130 27 Equilibrium Statistical Mechanics. III. Ensembles We have used the statistical thermodynamics definition of the chemical ...

27.3 The Dilute Gas in the Canonical Ensemble 1131 It is remarkable that the thermodynamic functions for a dilute gas are given ...

1132 27 Equilibrium Statistical Mechanics. III. Ensembles steeply and the small factor is falling so rapidly that there is a sma ...

27.4 Classical Statistical Mechanics 1133 at a pressure of 1.000 bar. Compare your result with the result of Problem 27.10. 27.1 ...

1134 27 Equilibrium Statistical Mechanics. III. Ensembles to the flow of a compressible fluid in ordinary space and is governed ...

27.4 Classical Statistical Mechanics 1135 The integral over the momentum components factors into a product of integrals, one for ...

1136 27 Equilibrium Statistical Mechanics. III. Ensembles where zcl is the molecular phase integral or theclassical molecular pa ...

27.4 Classical Statistical Mechanics 1137 The result of this example is zrot,cl 8 π^2 IekBT ( diatomic or linear polyatomic sub ...

1138 27 Equilibrium Statistical Mechanics. III. Ensembles wherehis Planck’s constant. For a dilute monatomic gas without electro ...

27.4 Classical Statistical Mechanics 1139 The quantum rotational partition function of a nonlinear polyatomic gas is related to ...

1140 27 Equilibrium Statistical Mechanics. III. Ensembles b.At 298.15 K kBT hν  (1. 3807 × 10 −^23 JK−^1 )(298.15 K) (6. 6261 × ...

27.5 Thermodynamic Functions in the Classical Canonical Ensemble 1141 plane polar coordinates. The coordinate axis in the phase ...