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Lecture_5_090908 - Lecture 5 September 9 2008 Virial...

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Page 1 of 8 Lecture 5 – September 9, 2008 Virial Expansions Empirical Treatment of Real Gasses Consider the Compression Factor, Z RT V p Z = For the case of a perfect gas, Z = 1 For the case where finite size effects matter, V p is larger than expected for an ideal gas so Z > 1 For the case where attractive interactions are important, V p is smaller than expected for an ideal gas so Z < 1 Quantifying these Effects, the van der Waals Equation of State (1) Molecular Volume correction to the perfect gas law: b V RT p = where b = molar volume = m 3 /mol (accounts for repulsions) (2) Attractive Interactions 2 ideal V a p p = , where a = attractive interactions which reduce pressure units = pressure x volume 2 (3) Putting the two together yields the van der Waals Equation of State 2 V a b V RT p = valid for b V >> or ( ) RT b V V a p 2 = + 2 V a V b 1 V RT p =
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