Lecture 2 - Equations of State How far can we push it?...

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Lecture 2 1 Equations of State – How far can we push it? (16.3,16.4) Consider the vdW equation of state: () 2 a P Vb R T V ⎛⎞ +− = ⎜⎟ ⎝⎠ ( ) 22 P Va V bR T V = 32 0 RT a ab V V PP P −+ + = ( ) Cubic equation in V 3 roots 0 PV RT bP V aV ab + = Fig. 16.7 Figure shows that below the critical point, liquid and gaseous phase of CO 2 can coexist. c So, at a given T<T , as you compress the gas, (G A) you reach a point where V will change with essentially no increase in P (A D), until all of the gas liquifies. Then, further compression requires a hug e increase in P (D L).
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Lecture 2 2 P vs. V for vdW equation Fig. 16.8a 2 2 At : 0 Inflection point in curve c c c T T PP T VV ∂∂ == c For T<T undulating curve reflects 3 roots of our cubic equation in V. But at the critical point, T c , the three roots become degenerate: () 3 32 2 3 03 3 0 cc c c V V V V −= + = Equate with 0 RT a ab Vb V V P ⎛⎞ −+ + = ⎜⎟ ⎝⎠
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Lecture 2 3 Equating the two equations gives the following three relations: 23 33 c cc c c RT aa b Vb V V P PP
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This note was uploaded on 04/01/2012 for the course CHEM 444 taught by Professor Gruebele,m during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lecture 2 - Equations of State How far can we push it?...

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