Chapter 8 Balances on Nonreactive Processes 8.1 Elements of Energy Balances Calculations 8.1a Reference States A Review

Transcription

1 Chater 8 Balances on Nonreactve Processes 8.1 Elements of Energy Balances Calculatons 8.1a Reference States A Revew We can never know the absolute values of U and H for a seces at a gven state. t Fortunately, t we never need dto know the absolute values of U and H at secfed states; we only need to know du and dh for secfed changes of state, and we can determne these quanttes exermentally. We may therefore arbtrarly choose a reference state for a seces and determne du = U U ref for the transton from the reference state to a seres of other states. If we set U ref equal to zero, then U=dU for a secfed state s the secfc nternal energy at that state relatve to the reference state. The secfc enthales at each state can then be calculated from the defnton, H=U+PV U+PV, rovdedthat the secfcvolume ( V )of the seces at the gven temerature and ressure s known. The values of U and H n the steam tables were generated usng ths rocedure. The reference state was chosen to be lqud water at the trle ont [H 2 O(l, 0.01 C, bar)], at whch ont was defned to be zero. 1

2 Ths does not mean that the absolute value of for water vaor at 400 C and 10.0 bar s 2958 kj/kg. It means that of water vaor at 400 C and 10.0 bar s 2958 kj/kg relatve to water at the reference state, or 2

3 8.1b Hyothetcal Process Paths and are state roertes of a seces; that s, ther values deend only on the state of the seces rmarly on ts temerature, state of aggregaton (sold, lqud d or gas), and, to a lesser extent, on ts ressure (and for mxture of some seces, on ts mole fracton n the mxture). A state roerty does not deend on how the seces reached ts state. Consequently, when a seces asses from one state to another, both and for the rocess are ndeendent of the ath taken from the frst state to the second one. 3

4 In most of ths chater and n chater 9, we wll learn how to calculate nternal energy and enthaly changes assocated wth certan rocesses; secfcally, 1.Changes n P at constant T and state of aggregaton (Secton 8.2). 2.Changes n T at constant P and state of aggregaton (Secton 8.3). 3.Phase changes at constant T and P meltng, soldfyng, vaorzng, condensng, sublmatng (Secton 8.4). 4.Mxng of two lquds or dssolvng of a gas or a sold n a lqud at constant T and P (Secton 8.5). 5.Chemcal reacton at constant T and P (Chater 9). For examle, we wsh to calculate for a rocess n whch sold henol at 25 C and 1 atm s converted to henol vaor at 300 C and 3 atm. ΔĤ = Ĥ(vaor, 300 C, 3atm ) Ĥ(sold, 25 C, 1atm ) However, we do not have such a table. น า นา (l,25c,1atm) ---- > ไอน า( ไอนา(v,200C,1atm) ΔH ˆ = Hˆ ( l,25 C,1atm ) Hˆ ( v,200 C,1 atm ) น า (l,25c,1atm) ---> น า (l,100c,1atm) --->ไอน า(v,100C,1atm) --->ไอน า(v,200C,1atm) 4

5 From Aendx B Table B.1 Selected Physcal Proerty Data Tm = meltng ont (จ ดหลอมเหลว) เปล ยนสถานะจากของแข ง ---> ของเหลว Tb = bolng ont (จ ดเด อด) เปล ยนสถานะจากของเหลว ---> ไอ Ste 1,3, 5 Tye 2 (change n T at constant P) (Sec 8.2) Ste 2,4 Tye 3 (change n hase at constant T and P) (Table B.1) Ste 6 Tye 1 (change n P at constant T) (Sec 8.2) ΔĤ = ΔĤ 1 + ΔĤ2 + ΔĤ3 + ΔĤ4 + ΔĤ5 + ΔĤ6 5

6 8.1c Procedure for Energy Balance Calculatons The rocedure to follow for the energy balance calculaton. 1.Perform all requred materal balance calculatons. 2.Wrte the arorate form of the energy balance (closed or oen system) and delete any of the terms that are ether zero or neglgble for the gven rocess system. 3.Choose a reference state hase, temerature, and ressure for each seces nvolved n the rocess. 4.For a closed system, construct a table wth columns for ntal and fnal amounts of each seces (m or n )andsecfc nternal energes relatve to the chosen reference state ( Û ). For an oen system, construct a table wth columns for nlet and outlet stream comonent flow rates ( m& & or & ) and secfc enthales relatve lt to the chosen reference n& states. 5.Calculate all requred values of ( Û or Ĥ ) and nsert the values n the arorate laces n the table. 6.Calculate ΔU = fnal n Û ntal n Û or fnal m Û ntal m Û Closed System Δ H = out n& Ĥ n n& Ĥ or out m& Ĥ n m& Ĥ Oen System 7.Calculate any work, knetc energy, or otental energy terms that you have not droed from the energy balance. 8.Solve the energy balance for whchever varable s unknown (often Q or Q & ). Closed System Oen System Q W = ΔU + ΔE k + ΔE Q & W& = ΔH& + ΔE& + ΔE& s k 6

7 Examle Acetone (denoted as Ac) s artally condensed out of a gas stream contanng 66.9 mole% acetone vaor and the balance ntrogen. Process secfcatons and materal balance calculatons lead to the flowchart shown below. The rocess oerates at steady state. Calculate the requred coolng rate. Soluton 0. Bass: 100 mole/s of mxed gas (Ac & N 2 ) 1.Perform requred materal balance calculatons. None are requred n ths examle. 2.Wrte and smlfy the energy balance. Q & W& = ΔH& + ΔE& + ΔE& s k 3.Choose reference states for acetone and ntrogen. N 2 (g, 25 C, 1 atm) From Table B.8 Ac (l, 20 C, 5 atm) No enthaly data s avalable Q& = ΔH& = n& Ĥ n& Ĥ out n 7

8 4.Construct an nlet-outlet enthaly table. Note the followng onts about the table Ntrogen has only one state for nlet and outlet Acetone has one nlet state but two outlet state Snce the lqud acetone leavng the system s at the reference state, so ts secfc enthaly s zero. 5.Calculate all unknown secfc enthales. ΔĤ1a ΔĤ1b Ac(l, 20 C, 5atm ) Ac(l, 20 C,1atm ) Ac(l, 56 C,1atm ΔĤ1c ΔĤ1d Ac(v (v, 56 C,1atm ) Ac(v, 65 C,1atm ) ) 8

9 9

10 Table B.1 Table B.1 Ĥ = ΔĤ 1 = Vˆ Ac(l) : C Ac(v) : C 1a Ac(l) + ΔĤ 1b + ΔĤ 1c (1atm 5atm) + + ΔĤ 56 C 20 C 1d (C ) Ac(l) kj = mol C dt + ( ΔĤ ) L/mol 30.2 kj/mol kj mol 5 T = C 5 v Ac + 65 C 56 C T (C ) Ac(v) dt Table B.1 2 T T 3 Ĥ 1 = ( )kJ / mol = 35.7kJ / mol 6.Calculate ΔH & ΔH& = out n& Ĥ = [(3.35)(32.0) + (63.55)(0) + (33.1)( 0.10) (66.9)(35.7) (33.1)(1.16)]kJ / s = 2320kJ n / s n& Ĥ 7.Calculate nonzero work, knetc energy, and otental energy terms. Nothng to do n ths ste. 8.Solve the energy balance for Q & Q & = ΔH & = 2320kJ / s = 2320kW Heat must be transferred from the condenser at a rate of 2320 kw to acheve the requred coolng and condensaton. 10

11 การบ าน จากตารางให หาค า H2, H3, H4 ส งเป น fle มาท หร อ 11