PandV_vdw - We can arrive at the expression for Z V dW (...

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Connection between molar volume and pressure expressions for the van der Waals equation of state The van der Waals equation is P = RT V 1 1 - b/ V - a V 2 RT V ± 1 + b V + ··· ² - a V 2 RT V ± 1 + ( b - a RT ) 1 V + ··· ² where we have expanded in a power series and find that β = ( b - a RT ) now the expression for P is P RT V + β RT V 2 or P V 2 - RT V - RTβ = 0 and the roots of this quadratic equation give us an expression for the molar volume V = 1 2 P n RT ± p ( RT ) 2 + 4 βPRT o = RT 2 P ( 1 ± r 1 + 4 βP RT ) only the positive root is physical, and we can now expand the square root in a Taylor series ( 1 + x 1 + x 2 - x 2 8 + ··· ) to get for the molar volume V RT 2 P ³ 1 + (1 + 2 βP RT - ··· ) ´ or V RT P ³ 1 + βP RT - ··· )
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Unformatted text preview: We can arrive at the expression for Z V dW ( P,T ) = P V RT given in the class notes Z V dW ( P,T ) = 1 + 1 V + b 2 V + in terms of P : Z V dW ( P,T ) 1 + P RT 1 + P RT -1 + b 2 ( RT ) 2 P 2 + 1 + P RT 1-P RT + + b 2 ( RT ) 2 P 2 + or Z V dW ( P,T ) 1 + 1 RT b-a RT P + b 2 ( RT ) 2-1 ( RT ) 2 ( b-a RT ) 2 P 2 + 1 + 1 RT b-a RT P + a ( RT ) 3 (2 b-a RT ) P 2 + The above is the expression given in the notes. 1...
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This note was uploaded on 04/11/2010 for the course CHEM 1101 taught by Professor Leroy during the Spring '10 term at University of Toronto- Toronto.

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