HW10_solution - : (see example 6.7 in the textbook) I only...

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Homework 10 solution (1) Verify/show that Zc always equals 3/8 in the van der Waals equation. (Zc is the value of Z at the critical point.) Method 1 : As we know, at critical point, 0 ) ( ; 0 ) ( 2 2 = = T T P P ρ Combined with van der Waals equation, 2 1 1 1 a b RT P RT a b RT P Z = = = a b bRT P a b RT P T T 2 ) 1 ( 2 ) ( ; 2 ) 1 ( ) ( 3 2 2 2 = = Therefore, at critical point (Tc, Pc), we have the following three equations: = = = 0 2 ) 1 ( 2 0 2 ) 1 ( 1 1 3 2 a b bRT a b RT RT a b RT P C C C C C C C C C C Solve for a, b and ρ C , C C C C C C C RT P P T R b P T R a 3 8 ; 125 . 0 ; 64 27 2 2 8 3 = C Z C C P T R a 64 27 2 2 and C C P T R b 125 . 0 were solved simultaneously with 8 3 = C Z , therefore, they can not be considered as known formula here. Method 2
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Unformatted text preview: : (see example 6.7 in the textbook) I only will show how to rearrange the van der Waals equation in terms of Ac and Bc. Van der Waals equation: ) ( ) ( ) ( 2 3 2 2 = + + = = = ab aV V RT bP PV b V a RT V b V PV VRT a b V V RT PV Z Multiply by P 2 /R 3 T 3 , ) 1 ( 2 2 2 2 2 3 = + + T R aP RT bP Z T R aP Z RT bP Z Let RT bP B C = and 2 2 T R aP A C = ) 1 ( 2 3 = + + C C C C B A Z A Z B Z 6.10...
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HW10_solution - : (see example 6.7 in the textbook) I only...

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