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lecture_31_for_web - Energy Balances – Chapters 7 & 8...

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Unformatted text preview: Energy Balances – Chapters 7 & 8 • Closed Systems • Open Systems • Mechanical Energy balances • Terms in the equations • Balances on non-reactive systems • Sensible heat – heat capacities – change in temperature • Latent heat – heat of vaporization, heat of fusion - change in phase • Mixing and solutions Still need to know Chapters 1 – 6: Mass balances, Equilibrium, etc. W Q E E U p k − = Δ + Δ + Δ s p k W Q E E H & & & & & − = Δ + Δ + Δ i i i i H V P U ˆ ˆ ˆ = + 2 2 1 ˆ j k u E j = j p gh E j = ˆ Closed system Open system Enthalpy Internal energy ( ) n compositio P T U U , , ˆ ˆ = Kinetic energy Potential energy Work terms ( ) flow work s W PV W W , , , Heat term Q Where does U result from? Some approximations Closed system: Open system: s p k W Q E E H & & & & & − = Δ + Δ + Δ W Q E E U p k − = Δ + Δ + Δ In processes involving heaters, coolers, adsorption, KE and PE terms are small compared to Q and H terms In some processes, Q or H are small, but large changes occur in KE and PE. m W h g u P s & & − = Δ + Δ + Δ 2 2 ρ 2 2 = Δ + Δ + Δ h g u P ρ Mechanical energy balance Bernoulli Equation P V V P U H Δ + Δ + Δ = Δ ( ) PV U H H H Δ + Δ = Δ = − 1 2 ( ) PV U H + = Definition of enthalpy: Change in enthalpy: ( ) 1 1 1 PV U H + = ( ) 2 2 2 PV U H + = State 1: State 2: Pressure-volume work in closed systems Flow work in open systems Q H & & = Δ Q H = Δ Sensible versus latent heat: Addition or subtraction of heat results in temperature changing or temperature remaining constant, depending on number of phases present Liquid Solid Vapor P T Liquid Solid Vapor P T Water phase diagram Q added, T ↑ Q added, T ↑ Q added, T stays constant Vapor Liquid Constant volume process: Constant pressure process: Q U m Q U = Δ = Δ ˆ Q H m Q H & & & & = Δ = Δ ˆ ∫ = Δ 2 1 ) ( ˆ T T V dT T C U Change in T at constant V ∫ = Δ 2 1 ) ( ˆ T T P dT T C H Change in T at constant P V V T U C ∂ ∂ = ˆ ∫ = Δ 2 1 ) ( ˆ T T V dT T C U P P T H C ∂ ∂ = ˆ ∫ = Δ 2 1 ) ( ˆ T T P dT T C H Heat capacity at constant volume Heat capacity at constant pressure Some simplifying assumptions: Pure substances • Liquids & solids: C P ~ C V • Ideal gases: C P = C V +R • Kopp’s Rule • Chueh-Swanson method • Otherwise: use table or correlation → Mixtures • Take weighted average of component’s heat capacities → • For dilute mixtures, neglect the contribution of the solute • Ideal gases: C P = C V +R 3 2 dT cT bT a C P + + + = ( ) ∑ = components all i ) ( y ) ( T C T C i P mix P Valid only when enthalpy of mixing can be neglected! Sensible heat – heat capacities (change in temperature) Latent heat values (change of phase – vaporization or fusion) • Look up in table (steam table, etc.) • Trouton’s rule: correlation based on normal boiling point • Standard heats of fusion • Chen’s equation: at normal boiling point, know critical constants • Watson’s equation: knowing a value at T1 find it at T2 • Clausius – Clapeyron equation •...
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This note was uploaded on 11/12/2009 for the course CHEM 2190 at Cornell.

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lecture_31_for_web - Energy Balances – Chapters 7 & 8...

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