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Chapter 14 (II) - 14.3 Condition of the Classical...

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14.3 Condition of the Classical Limit-- Applicability of M-B statiscs . 1 / << = = kT j j j j e Z N g N f ε . 2 ) ( , 1 ) 2 ( 3 / 1 2 / 3 2 dB mkT h N V l h mkT V N Z N λ π π >> = << = M-B stat. is valid under the dilute gas condition: Since ε j ~kT, the above inequality is equivalent to (14.12) Molecule’s de Broglie wavelength: ( ε —the average energy of molecular thermal motion). , 2 ~ 2 mkT h m h p h ε λ = =
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Thus, the right side of the inequality is approximately the de Broglie thermal wavelength of molecule λ dB , while the left term is the average distance between molecules in the gas. The classical limit condition can be expressed as l>> λ dB . This says that as the intermolecular distance is so large that the wave-mechanical interference between the de Broglie waves of molecules becomes negligible, that is, the wave nature of the molecules becomes insignificant. Under the condition, we can treat molecules as classical particles obeying Newtonian mechanics. Indeed, an ideal gas is defined as a gas of non-interacting molecules in the classical regime.
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14.4 Properties of a monatomic ideal gas . 2 3 2 3 1 2 3 ) ln ( 2 2 NkT U NkT T NkT T Z NkT U V = = × = = ). 2 ln(
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