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Thermodynamics filled in class notes_Part_131

Thermodynamics filled in class notes_Part_131 - 7.2...

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Unformatted text preview: 7.2. ADIABATIC, ISOCHORIC KINETICS 269 Now at the initial state, we have T = T o , so U o = V parenleftBig hatwide ρ A u o T o ,A + hatwide ρ B u o T o ,B parenrightBig . (7.287) So, we can say our caloric equation of state is U − U o = V parenleftBig ( ρ A + ρ B ) c v ( T − T o ) + ( ρ A − hatwide ρ A ) u o T o ,A + ( ρ B − hatwide ρ B ) u o T o ,B parenrightBig , (7.288) = V parenleftBig ( hatwide ρ A + hatwide ρ B ) c v ( T − T o ) + ( ρ A − hatwide ρ A ) u o T o ,A + ( ρ B − hatwide ρ B ) u o T o ,B parenrightBig . (7.289) As an aside, on a molar basis, we scale Eq. (7.289) to get u − u o = c v ( T − T o ) + ( y A − y Ao ) u o T o ,A + ( y B − y Bo ) u o T o ,B . (7.290) And because we have assumed the molecular masses are the same, M A = M B , the mole fractions are the mass fractions, and we can write on a mass basis u − u o = c v ( T − T o ) + ( c A − c Ao ) u o T o ,A + ( c B − c Bo ) u o T o ,B . (7.291) Returning to Eq. (7.289), our energy conservation relation, Eq. (7.274), becomesReturning to Eq....
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