problem-solution-10 - * 2 * 1 P P is greater than one....

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PROBLEM McQ 24-5 Apply Euler’s Theorem to A = A(S, V, n). Do you recognize the resulting equation? , , , ( , , ) V n T n V T A A A A T V n T V n TS VP G U TS T V n = + + = - - + = - ÷ ÷ ÷ The resulting equation is the Helmholtz free energy. PROBLEM McQ 24-18 Prove that y 2 > x 2 if * 2 P > * 1 P and that y 2 < x 2 if * 2 P < * 1 P . Interpret this result physically. Note: * * * * * * * 1 1 2 2 2 1 2 2 1 2 2 1 (1 ) ( ) total P x P x P x P x P P x P P = + = - + = + - * * 2 2 1 1 2 1 ; total total x P x P y y P P = = ÷ ÷ * * * 2 2 2 2 2 2 2 2 2 * * * * * 1 1 2 2 1 2 2 1 ( ) total x P x P x P y y y P x P x P P x P P = = = ÷ ÷ ÷ + + - If * 2 P > * 1 P then * 2 * * 2 1 * * * * 1 2 2 1 2 2 * 1 ( ) 1 ( 1) P P P P x P P P x P + - + - as both pressures are greater than zero this implies that the ratio
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Unformatted text preview: * 2 * 1 P P is greater than one. Moreover since 2 1 x &lt; &lt; the denominator of * 2 * 1 * 2 2 * 1 1 ( 1) P P P x P +-can only take on a value in between the values given by 2 0, 1 x = that is * 2 2 2 2 * 1 P x y x P &lt; &lt; . Since * 2 * 1 P P &gt; 1 and 2 1 x &lt; &lt; , 2 2 y x . Conversely, if * 2 P &lt; * 1 P then * 2 * * * * * 1 2 2 1 1 1 2 * * 2 2 1 ( ) (1 ) P P x P P P P x P P +-+-by inspection it follows that this term is always less than one which means 2 2 y x &lt; ....
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This note was uploaded on 02/08/2012 for the course CHEM 444 taught by Professor Gruebele,m during the Fall '08 term at University of Illinois, Urbana Champaign.

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problem-solution-10 - * 2 * 1 P P is greater than one....

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