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Unformatted text preview: 3.3. IDEAL MIXTURES OF IDEAL GASES 81 For the ideal gas, one has PV = RT N summationdisplay k =1 n k , (3.70) V = RT ∑ N k =1 n k P , (3.71) ∂V ∂n i vextendsingle vextendsingle vextendsingle vextendsingle T,P,n j ,i negationslash = j = RT ∑ N k =1 ∂n k ∂n i P , (3.72) = RT ∑ N k =1 δ ki P , (3.73) = RT =0 bracehtipdownleftbracehtipuprightbracehtipupleftbracehtipdownright δ 1 i + =0 bracehtipdownleftbracehtipuprightbracehtipupleftbracehtipdownright δ 2 i + ··· + =1 bracehtipdownleftbracehtipuprightbracehtipupleftbracehtipdownright δ ii + ··· + =0 bracehtipdownleftbracehtipuprightbracehtipupleftbracehtipdownright δ Ni P , (3.74) v i = RT P , (3.75) = V ∑ N k =1 n k , (3.76) = V n . (3.77) Here the so-called Kronecker delta function has been employed, which is much the same as the identity matrix: δ ki = , k negationslash = i, (3.78) δ ki = 1 , k = i. (3.79) Contrast this with the earlier adopted definition of molar specific volume v i = V n i .....
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This note was uploaded on 11/26/2011 for the course EGN 3381 taught by Professor Park-sou during the Fall '11 term at FSU.
- Fall '11