# 6a - E nergy Balance Lecture outline L ecture Closedsystem...

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Energy Balance

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Lecture outline Theoretical Background - Energy Hypothetical process paths Specific heat capacity Closed system Open system Phase change operation
Theory background Law of conservation of energy Energy input = Energy output + losses Heat capacity For Ideal gas, c p -c v = R The ratio of c p /c v = γ = 1.4 Heat capacity at constant pressure for any gas is Cp = a + bT + cT 2 + dT 3 Where a, b, c and d are constants Heat capacity of gas mixture is C pm = Σx i c pi Where x i = mole fraction of component C pi = molar heat capacity of component

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Enthalpy changes with chemical reaction ∆H R ° - standard heat of reaction at 25°C ∆H f ° - standard heat of formation at 25°C ∆H c ° - standard heat of combustion at 25°C ∆H R ° = Σ∆H f ° (products) - Σ∆H f ° (reactants) ∆H R ° - +ve – endothermic reaction; ∆H R ° - -+ve – exothermic reaction Effect of temperature on heat of reaction ∆H R = ∆H° (products) + ∆H R ° - ∆H° (reactants) ∆H R – Heat of reaction at operating conditions ∆H R ° - Standard heat of reaction at 25°C ∆H° (products) – Enthalpy of products over 25°C ∆H° (reactants) - Enthalpy of reactants over 25°C Standard heat of reaction from heats of combustion ∆H R ° = Σ∆H c ° (reactants) - Σ∆H c ° (products)
Enthalpy change in reactions q =  ∆H = Σ ∆H p + Σ ∆H R ° - Σ ∆H R Σ ∆H p – Enthalpy of products at 25 °C ∆H R - Enthalpy of reactants at 25 For adiabatic reaction q = 0 Clausius Claypeyron equation Where P and P 0 – Vapor pressure at T and T 0 T and T 0 – absolute temperature - Molar latent heat of vaporization - = T T R P P 1 1 ln 0 0 λ

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What we learnt so far… far… General energy balance equation:  Closed systems: E k   E p   =   Q  –  W Open systems: H  +  E k   E p   =   Q  –  W s When work ( W  or  W s ),  E k   E p  are neglected : Closed systems:  Q = Σ out n f Ū f  –  Σ in n Ū i Open systems:  Q  = Σ out n f   Ĥ f  –  Σ in n Ĥ i  Energy balance using tabulated  Ū  Ĥ  (e.g. steam  tables) Q: What if tabulated data are not found?
Hypothetical process path Ū  &  Ĥ  are  state properties  – their values depends on  the state of the system: Mainly on  T  & state of  aggregation (solid, liquid or gas) Rarely on pressure Ū  &  Ĥ  are calculated  based on 5 hypothetical path: P  @ constant  T  & state of aggregation (this lecture) @ constant  P  & state of aggregation (this lecture) Phase change @ constant  T  &  P  (this lecture) Mixing/separation of 2 or more substances @ constant  T  &  P   (omit) Chemical reaction @ constant  T  and  P

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T @ constant P P Sensible heat : heat that must be transferred to  raise/lower the  T
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## This note was uploaded on 06/06/2011 for the course CHEM 3040 taught by Professor Reddy during the Spring '10 term at Taylor's.

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6a - E nergy Balance Lecture outline L ecture Closedsystem...

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