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105A_synthesis

# 105A_synthesis - 105 A synthesis Conservation of Energy The...

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105 A synthesis

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Conservation of Energy: The 1 st Law of Thermodynamics KE PE U Q W + ∆ + ∆ = Change in amount of energy contained within the system during some time interval = Net amount of energy transferred in across the system boundary by heat transfer during the time interval - Net amount of energy transferred out across the system boundary by work during the time interval
Alternative Forms of the Energy Balance Differential Form: dE Q W δ δ = Time Rate Form: dE Q W dt =

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Simple compressible systems H U pV h u pv = + = + Due to the frequent occurrence of the above combination of properties we construct a new property called enthalpy. dU Q pdV δ = 0 0 W pdV dKE dPE δ = = = Simple Compressible Systems
Cycle Analysis Power Cycles Refrigeration & Heat Pump Cycles cycle cycle Q W = cycle in W Q η = in cycle Q W β = out cycle Q W γ = 0 cycle E = hence

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Quality For Saturated Mixture (Liquid-Vapor) Region Quality; x; an intensive property x gives fraction that is vapor (gas) (1-x) gives Moisture Content g f g m x m m + 0 x 1; x = 0 Saturated Liquid (subscript ‘f’) x = 1 Saturated Vapor (subscript ‘g’) ‘fg’ ‘g’-’f’ LET b = ANY INTENSIVE PROPERTY (b = v, u, h, s, etc.) (1 ) f f g f fg f fg fg g f g f b b b b x b b b b b x b b b b b x b x b = = = + = = +
Using Saturated Liquid Data (‘Compressed Liquid Rule’) Using ‘Incompressible Substance Model’ ( , ) ( ) ( , ) ( ) ( , ) ( ) ( , ) ( ) f f f f v T p v T h T p h T u T p u T s T p s T 2 1 2 1 2 1 2 1 2 1 2 1 2 1 ( ) ( ) ( ) ( ) p v c c c u u c T T h h c T T v P P h h c T T = = = = + Specific Heats (Heat Capacities ) v v u c T = p p h c T = p v c k c =

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Properties for Ideal Gases Pv nRT Pv RT PV mRT = = = The Ideal Gas Model: ( ) ( ) ( ) u u T h h T u T RT = = = + ( ) ( ) v p du c T dT dh c T dT = = Tables A-22(E) and A-23 (E) When specific heats are assumed constant Table A-20(E): 2 1 2 1 2 1 2 1 ( ) ( ) v p u u c T T h h c T T = = Requirements: 1 c c Z P P T T ± ² R R M =
Polytropic Process of an Ideal Gas For a closed system: 2 1 1 2 constant P V P V n n PV = = Expansion/Compression (Moving Boundary) Work (Ideal Gas OR liquid): 2 2 2 1 1 1 2 2 1 1 1 1 , ( 1) 1 ln , ( 1) P V P V P d V n n V P d V P V n V = = = Ideal Gases ONLY: ( 1)/ ( 1) 2 2 1 1 1 2 2 2 1 1 2 2 1 1 ( ) ,( 1) 1 ln n n n T P V T P V mR T T P dV n n V P dV mRT V = = = =

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