Heat Bal Calc

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    Str-name Nat Gas Burnr Air CmbstGas StackGas Leak Air

    Streams 1 2 3 4 5

    Flow 1,308 14,739 16,067 16,391 325Al, (c) 0 0 0 0 0

    CH4, (g) 1,243 0 0 0 0

    C2H6, (g) 39.2 0 0 0 0

    CO2, (g) 0 0 1,321 1,321 0

    H2O, (g) 0 0 2,603 2,603 0

    N2, (g) 26.2 11,644 11,670 11,926 256.4

    O2, (g) 0 3,095 472.7 540.9 68.2

    Hot combustion gas(16.07 kg-mol, 1800oC)

    Heated aluminum(800 kg/min, 550oC)

    1Nat Gas(1.31 kg-mol, 25oC) Burner

    Heat loss

    Ingot Heating Fur2

    7

    3

    Heat loss

    Burner air(14.74 kg-mol, 25oC)

    Material Balance for the Process (from work

    Table 1. Stream amounts in g-mol/min

    A Heat Balance Calculator for an Alu

    Figure 1. Flowsheet with gas stream amounts i

    Constructing a Heat Balance

    Note: before starting, you may want to collect all 4 previous workbooks i

    series as worksheets in one workbook. It'll help you keep track of some

    necessary calculations.1. Look at workbook MatBalCalc to obtain the stream flowrates for the specified pro

    heating 800 kg of Al/min. Label the flowsheet with these flows, using g-mol for gas st

    See Table 1 and Fig. 1.

    2. Use workbook HeatCalc to obtain the heat of combustion (LHV) for the specified n

    gas. Table 1 has units of g-mol; see Table 2, with more useful units of kJ/kg-mol.

    3. Obtain heat content equation parameters for each stream substance from FREED

    instructed in datafiles worksheets. See Table 3; note units.

    4. Write the overall heat balance for the burnerdevice. Streams entering at the refe

    temperature of 25 C have zero heat content. Burn the NatGas at 25 C and heat the

    combustion products from 25 C to 1800 C. Sum the heat effect factors for each stre

    and the heat loss, and set the sum to zero. The only unknown is the heat loss. See T

    The burner loss is 13 ,400 kJ/min (cell T44).

    5. Repeat the overall heat balance arithmetic around the aluminum heating furnace.

    all instreams to 25 C, and heat all outstreams to their outstream temperature. See T

    The furnace heat loss is 186,550 kJ/min (cell T56).

    HeatBalCalc is aThermart Softwareprogram. 2012

    by Arthur E. Morris.

    www.thermart.net

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    References1. Wikipedia contributors, Enthalpy, Thermodynamic Databases for Pure Substances.

    2. Fact-W Wikipedia, the Free Encyclopedia, July 2012. http://en.wikipedia.org/wiki/Main_P

    3. NIST Chemistry WebBook, http://webbook.nist.gov/chemistry/

    4. NIST-JANAF Tables, http://kinetics.nist.gov/janaf/

    5. Thermart Software, http://www.thermart.net/

    6. Overall, the process heat loss is 199,950 kJ/min, or 200 MJ/min.

    7. Summarize the results. See Table 6.

    8. Use Goal Seek to explore the effect of stack gas temperature (stream 4) on the ma

    of aluminum (stream 6/7). Read instructions near Table 7.

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    DHcomb, kJ/g-mol NG -805.04

    Heat Content Data, kJ/mol = A

    N2, 600 - 2200 C

    A B C

    -2077 31.40 1.317E-03

    Cold Al Hot Al H2O(g), 600 - 2200 C

    6 7 A B C

    29,650 29,650 -2563 36.04 4.323E-03

    29,650 29,650

    0 0

    0 0 Air, 5 - 550 C

    0 0 A B C

    0 0 -713 28.43 3.390E-03

    0 0

    0 0

    1. Heat content of incoming natural gas (stream

    2. Heat content of incoming combustion air (stre

    3. Heat of combustion of natural gas (stream #1

    4a. Heat burner gas CO2 to 1800 C (stream #3

    4b. Heat combustion gas H2O to 1800 C (strea

    4c. Heat combustion gas N2 to 1800 C (stream4d. Heat combustion gas O2 to 1800 C (stream

    5. Heat loss from burner, kJ/min

    1. Cool incoming burner gas to 25 C (stream #

    2. Heat content of incoming aluminum (stream

    3. Heat content of incoming leak air (stream #5)

    4. Heat product aluminum to 550 C (stream #7)

    Stack gas(16.39 kg-mol, 800oC)

    Aluminum ingots(800 kg/min, 25oC)

    Leak air(0.33 kg-mol, 25oC)

    ace

    4

    6

    5

    ook MatBalCalc.xlsx)

    inum Heating Process

    Table 3. Heat Content Tables (

    n kg-mol/min

    in this

    cess for

    reams.

    atural

    s

    ence

    am,

    able 4.

    Cool

    able 5.

    Table 2. Heat of Combustion (LHV) of N

    Heat Balance for the Process (data fro

    Table 4. Heat Balance Around the Burner (kJ/mi

    Table 5. Heat Balance Around the Furnace (kJ/

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    5a. Heat stack gas CO2 to 800 C (stream #4)

    5b. Heat stack gas H2O to 800 C (stream #4)

    5c. Heat stack gas N2 to 800 C (stream #4)

    5d. Heat stack gas O2 to 800 C (stream #4)

    6. Heat loss from furnace, kJ/min

    age.

    Factor

    Heat available from combustion of NatGas

    Heat carried out by stack gas

    Heat carried out by aluminum ingots

    Heat loss

    ss flow

    Table 6. Heat Balance Summary, MJ/mi

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    kJ/kg-mol -805,040 use this value

    BT + CT2. T = C

    O2, 600 - 2200 C

    A B C

    -2265 33.41 1.255E-03

    CO2, 600 - 2200 C

    A B C

    -6014 52.48 2.257E-03

    (note Al heat units)

    Solid aluminum, kJ/kgA B C

    -21.1 0.875 2.54E-04

    1. Cool incoming burne

    2. Heat content of inco

    3. Heat content of inco

    4. Heat product alumin

    5a. Heat stack gas CO

    #1) 0 5b. Heat stack gas H2

    am #2) 0 5c. Heat stack gas N2 t

    ) -1,052,963 5d. Heat stack gas O2 t

    126,507 6. Heat loss from furna

    m #3) 198,638 7. Sum of heat effects f

    #3) 685,150#3) 29,282

    13,387

    ) -1,039,576

    6) 0

    0

    429,484

    rom FREED data)

    G (from workbook HeatCalc)

    m Tables 2 and 3)

    in) to calculate heat loss

    Table 7. Using Goal Se

    Calculatethe Effec

    The sum of values in

    cells T39:T44 must

    in) to calculate heat loss

    Using Goal Seek to Exami

    Gas Temperature on the1. Look at your Excel Help text t

    2. Enter a value for the altered

    3. Go to Data/What-If analysis/

    4. Tell Goal Seek to change cell

    5. Click OK twice.

    6. Goal Seek will respond with t

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    49,426

    75,576

    284,875

    13,667

    186,549

    Value % of available

    1053 100%

    424 40%

    429 41%

    200 19%

    cells T51:T56 must

    equal zero.

    in of Operation

    . opy e va ues o ce s

    8. Repeat the above process for

    9. Chart the results.

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    Goal Seek Operation. Enter/edit

    r gas to 25 C (stream #3) -1,039,576 Sum of furnace heat effects 0

    ing aluminum (stream #6) 0 Stack gas temperature 788 775

    ing leak air (stream #5) 0 kg of Aluminum 814 828

    m to 550 C (stream #7) 436,736

    to 800 C (stream #4) 48,537

    to 800 C (stream #4) 74,235

    o 800 C (stream #4) 280,082

    o 800 C (stream #4) 13,437

    e, kJ/min 186,549

    or furnace 0

    k with the Furnace Heat Balance to

    t of Stack Gas T on Al Flowrate

    800

    820

    840

    860

    880

    900

    760770780790800

    kgAl/m

    in

    stack as tem

    Aluminum Flow vs. Stac

    ne the Effect of Changing the Stack

    Aluminum Heating Rate.o refresh your understanding of Goal Seek.

    stack gas temperature in cell AI33.

    Goal Seek, and enter a value of zero for AI32.

    AI34.

    he updated flowrate of aluminum in cell AI34.

    Goal Seek dialog

    box with correctly-

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    an o a near y array o ce s.

    other stack gas temperatures as desired.

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    value in cell AI33 only.

    750 725

    856 884

    720730740750

    erature, C

    Gas Temperature

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    Using the FREED Thermodynamic Database--AlumPlease read

    GRAPH:

    Al, (c,l,g) Tmax(K): 5000

    (Aluminum) Atomic mass of Al: 26.982

    Table 1. Heat content of Aluminum in SI units.T (K) T, C HT-H25 (Cal/g-mol)

    300.0 26.9 11

    363.4 90.2 387 Figure 1. Heat content of Alumi426.7 153.6 774

    490.1 216.9 1170

    553.4 280.3 1577

    616.8 343.7 1996

    680.2 407.0 2428

    743.5 470.4 2874

    806.9 533.7 3336

    870.2 597.1 3815933.6 660.5 4310

    933.6 660.5 6890

    983.5 710.4 7269

    1016.8 743.7 7521

    1100.0 826.9 8153

    1150.0 876.9 8532

    Table 3. Heat content for solid aluminum = A+ BT +A B C

    cal/g-mol; T = C -136 5.64 1.64E-03

    kJ/kg; T = C -21.1 8.75E-01 2.54E-04 We'll useBtu/lb-mol; T = F -424 5.58 9.09E-04

    Btu/lb; T = F -15.7 2.07E-01 3.37E-05

    Melting point of Al

    H = 1.64E-03T2 + 5.64T - 136

    H = 7.58

    0

    2000

    4000

    6000

    8000

    10000

    0 100 200 300 400 500 60

    HT-H25

    (Cal/g-mol)

    T, C

    Molar Heat Content of Al

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    inum

    Table 2. Heat content of Aluminum in AES unitsT, F HT-H77 (Btu/lb-mol)

    80.3 20

    um in SI units 194.4 696 Figure 2. Heat content of Aluminum in AES units308.4 1393

    422.5 2106

    536.5 2839

    650.6 3593

    764.6 4371

    878.7 5174

    992.7 6005

    1106.8 68661220.8 7758

    1220.8 12402

    1310.7 13084

    1370.6 13539

    1520.3 14675

    1610.3 15358

    CT2

    this data

    T + 1878

    700 800 900

    s. T

    H = 9.09E-04T2 + 5.58T - 424

    H = 7.589x + 3138

    0

    4000

    8000

    12000

    16000

    0 200 400 600 800 1000 1200 1400 1600

    HT-H77(Btu/lb-mol)

    T, F

    Molar Heat Content of Al vs. T

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    Datafiles an

    AirT (C) HT-H298 (J)

    25 0

    77.5 1528

    130 3059182.5 4603

    235 6166

    287.5 7749

    340 9353

    392.5 10977

    445 12621

    497.5 14283

    550 15963

    H2O, (g)

    (Hydrogen Oxide)

    T (C) HT-H298 (J)

    700 24894

    850 31175

    1000 37719

    1150 44514

    1300 51541

    1450 587841600 66223

    1750 73839

    1900 81612

    2200 97549

    H = 4.323E-03T2 + 36.04x -

    R = 9.9999E-01

    0.00E+00

    2.00E+04

    4.00E+04

    6.00E+04

    8.00E+04

    1.00E+05

    1.20E+05

    700 900 1100 1300 1500 1700

    HT-H298

    (J)

    T (C)

    Plot: HT-H298 vs. T for H2O

    H = 0.00339T2 + 28.43T - 713

    R = 1.00000

    0.00E+00

    2.00E+03

    4.00E+03

    6.00E+03

    8.00E+03

    1.00E+04

    1.20E+04

    1.40E+04

    1.60E+04

    1.80E+04

    25 125 225 325 4

    HT-H

    298

    (J)

    T (C)

    Plot: HT-H298 vs. T for N1.58O.42

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    Charts from FREED

    N2, (g)

    (Nitrogen dimer)

    T (C) HT-H298 (J)700 20607

    850 25549

    1000 30595

    1150 35730

    1300 40944

    1450 46224

    1600 51563

    1750 56950

    1900 62379

    2200 73328

    O2, (g)

    (Oxygen dimer)

    T (C) HT-H298 (J)

    700 21770

    850 27025

    1000 32371

    1150 37792

    1300 432781450 48821

    1600 54416

    1750 60062

    1900 65755

    2200 77284

    2563

    1900 2100

    0.00E+00

    1.00E+04

    2.00E+04

    3.00E+04

    4.00E+04

    5.00E+04

    6.00E+04

    7.00E+048.00E+04

    700 900 1100 13

    HT-H

    298

    (J)

    Plot: HT-H29

    H =

    0.00E+00

    1.00E+04

    2.00E+04

    3.00E+04

    4.00E+04

    5.00E+04

    6.00E+04

    7.00E+04

    8.00E+04

    9.00E+04

    700 900 1100 13

    HT-H

    298

    (J)

    Plot: HT-H2

    25 525

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    CO2, (g)

    (Carbon Dioxide)

    T (C) HT-H298 (J)

    700 31,961

    850 40,184

    1000 48,624

    1150 57,234

    1300 65,982

    1450 74,842

    1600 83,795

    1750 92,825

    1900 101,921

    2200 120,268

    H = 1.317E-03T2 + 31.40T - 2077

    R = 9.9999E-01

    0 1500 1700 1900 2100

    T (C)

    vs. T for N2

    1.255E-03T2 + 33.41T - 2265

    R = 1.0000E+00

    00 1500 1700 1900 2100

    T (C)

    8 vs. T for O2

    H =

    2.00E+04

    4.00E+04

    6.00E+04

    8.00E+04

    1.00E+05

    1.20E+05

    1.40E+05

    700

    HT-H

    298

    (J)

    Plot:

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    .257E-03T2 + 52.48T - 6014

    R = 9.9999E-01

    1200 1700 2200T (C)

    T-H298 vs. T for CO2

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    Using the NIST Chemistry WebBook On-Line Thermodynamic Datab

    Please read Heat content, heat capacity, and entropy equations for reference state

    Data compilation copyright by the U.S. Secretary of Commerce on behalf of the U.S.A.

    Hgas -393.51 0.13 kJ/mol. Review Cox, Wagman, et al., 1984 CODATA Review

    Hgas -393.52 kJ/mol. Review Chase, 1998. Data last reviewed in September, 196

    Sgas,1 bar 213.785 0.010 J/mol*K. Review Cox, Wagman, et al., 1984 CODATA R

    Sgas,1 bar 213.79 J/mol*K. Review Chase, 1998. Data last reviewed in September,

    Gas Phase Heat Capacity (Shomate Equation)

    Cp = A + B*t + C*t2 + D*t3 + E/t2

    H - H298.15= A*t + B*t2/2 + C*t3/3 + D*t4/4 - E/t + F - H

    S = A*ln(t) + B*t + C*t2/2 + D*t3/3 - E/(2*t2) + GCp = heat capacity (J/mol*K)

    H = standard enthalpy (kJ/mol)

    S = standard entropy (J/mol*K)

    t = temperature (K) / 1000.

    Table 1. Equation parameters for the thermodynamic properties of CO2

    Temp, (K) 298. - 1200. 1200. - 6000.

    A 24.99735 58.16639

    B 55.18696 2.720074

    C -33.69137 -0.492289

    D 7.948387 0.038844

    E -0.136638 -6.447293

    F -403.6075 -425.9186

    G 228.2431 263.6125

    H -393.5224 -393.5224

    Reference Chase, 1998 Chase, 1998

    Comment: Data last reviewed in September, 1965.

    Figure 1. Heat content of CO2 in SI units

    H = 58.91T - 10312

    R = 0.9998

    50,000

    60,000

    70,000

    80,000

    90,000

    100,000110,000

    HT-H25,

    J/g-m

    ol

    Molar Heat Content of CO2 above 800 C

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    Table 3. Heat content for CO2 = A + BT

    A BkJ/kg-mol; T = C -10312 58.91

    kJ/m3; T = C -460 2.628

    Btu/lb-mol; T = F -4887 14.08

    Btu/ft3; T = F -13.6 0.0392

    (Volumes are STP)

    30,000

    ,

    800 1000 1200 1400 1600 1800T, C

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    ase--Carbon Dioxide Carbon dioxideMolecular weight: 44.0095

    O2 Table 2. Values for the thermodynamic properties of CO2 in SI units

    Temp, Temp, Cp S -(G -H298.15)/TH - H298.15 H - H298.15

    alue (K) (C) (J/mol*K) (J/mol*K) (J/mol*K) (kJ/mol) (J/mol)

    298 37.12 213.8 213.8 -0.01

    300 37.22 214 213.8 0.07

    eview value 400 41.34 225.3 215.3 4.00

    1965 500 44.61 234.9 218.3 8.31

    600 47.32 243.3 221.8 12.91

    700 49.57 250.8 225.4 17.75

    800 51.44 257.5 229 22.81

    900 53 263.6 232.5 28.03

    1000 54.3 269.3 235.9 33.401100 826.85 55.4 274.5 239.2 38.89 38,890

    1200 926.85 56.31 279.4 242.3 44.47 44,470

    1300 1026.85 57.14 283.9 245.4 50.15 50,150

    1400 1126.85 57.83 288.2 248.3 55.89 55,890

    1500 1226.85 58.4 292.2 251.1 61.71 61,710

    1600 1326.85 58.9 296 253.8 67.57 67,570

    1700 1426.85 59.33 299.6 256.3 73.48 73,480

    1800 1526.85 59.7 303 258.8 79.44 79,440

    1900 1626.85 60.04 306.2 261.2 85.42 85,420

    2000 1726.85 60.34 309.3 263.6 91.44 91,440

    2100 1826.85 60.61 312.2 265.8 97.49 97,490

    2200 1926.85 60.85 315.1 268 103.6 103,600

    2300 61.07 317.8 270.1 109.7

    2400 61.28 320.4 272.1 115.8

    2500 61.47 322.9 274.1 121.9

    2600 61.64 325.3 276 128.1

    2700 61.8 327.6 277.9 134.2

    2800 61.95 329.9 279.7 140.4

    2900 62.1 332.1 281.5 146.6

    3000 62.23 334.2 283.2 152.8

    3100 62.35 336.2 284.9 159.1

    3200 62.47 338.2 286.5 165.3

    3300 62.59 340.1 288.1 171.63400 62.69 342 289.7 177.8

    3500 62.8 343.8 291.2 184.1

    3600 62.89 345.6 292.7 190.4

    3700 62.99 347.3 294.1 196.7

    3800 63.08 349 295.6 203

    3900 63.17 350.6 297 209.3

    4000 63.25 352.2 298.3 215.6

    4100 63.34 353.8 299.6 222

    4200 63.42 355.3 301 228.3

    4300 63.5 356.8 302.2 234.6

    Figure 2. Heat content of CO2 in AES units

    H = 14.08T - 4887

    R = 0.9998

    25,000

    30,000

    35,000

    40,000

    45,000

    HT-H77,

    Btu

    /lb

    -mo

    l

    Molar Heat Content of CO2 above 1500 F

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    4400 63.58 358.3 303.5 241

    4500 63.66 359.7 304.7 247.4

    4600 63.74 361.1 305.9 253.7

    4700 63.82 362.5 307.1 260.1

    4800 63.9 363.8 308.3 266.5

    4900 63.98 365.1 309.4 272.9

    5000 64.06 366.4 310.6 279.3

    5100 64.14 367.7 311.7 285.75200 64.22 368.9 312.8 292.1

    5300 64.31 370.2 313.8 298.5

    5400 64.39 371.4 314.9 305

    5500 64.48 372.5 315.9 311.4

    5600 64.58 373.7 316.9 317.9

    5700 64.67 374.9 318 324.3

    5800 64.77 376 318.9 330.8

    5900 64.87 377.1 319.9 337.3

    6000 64.98 378.2 320.9 343.8

    2000 15,000

    20,000

    1500 2000 2500 3000 35T, F

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    CO2 in AES units

    Temp, H - H77

    (F) (Btu/lb-mol)

    1520.3 16,731

    1700.3 19,131

    1880.3 21,575

    2060.3 24,044

    2240.3 26,548

    2420.3 29,069

    2600.3 31,612

    2780.3 34,176

    2960.3 36,749

    3140.3 39,338

    3320.3 41,941

    3500.3 44,570

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    00

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    Please read

    Using the NIST JANAF On-line Thermochemical

    Water (H2O, gas)

    WaterMolecular wt: 18.0153

    Table 1. Thermodynamic properties of H2O(g)

    Enthalpy Ref, Temperature = Tr= 298.15 K Standard State Pressu

    JK-1

    mol-1

    kJmol-1

    T/K C p

    S -[G

    -H

    (T r)]/T H -H

    (T r) fH

    0 0 0 INFINITE -9.90 -238.921

    100 33.299 152.388 218.534 -6.62 -240.083

    200 33.349 175.485 191.896 -3.28 -240.9

    Reference temperature ==> 298.15 33.59 188.834 188.834 0.00 -241.826

    300 33.596 189.042 188.835 0.06 -241.844400 34.262 198.788 190.159 3.45 -242.846

    500 35.226 206.534 192.685 6.93 -243.826

    600 36.325 213.052 195.55 10.50 -244.758

    700 37.495 218.739 198.465 14.19 -245.632

    800 38.721 223.825 201.322 18.00 -246.443

    900 39.987 228.459 204.084 21.94 -247.185

    1000 41.268 232.738 206.738 26.00 -247.857

    1100 42.536 236.731 209.285 30.19 -248.46

    1200 43.768 240.485 211.73 34.51 -248.997

    1300 44.945 244.035 214.08 38.94 -249.473

    1400 46.054 247.407 216.341 43.49 -249.894

    1500 47.09 250.62 218.52 48.15 -250.265

    1600 48.05 253.69 220.623 52.91 -250.592

    1700 48.935 256.63 222.655 57.76 -250.881

    1800 49.749 259.451 224.621 62.69 -251.138

    1900 50.496 262.161 226.526 67.71 -251.368

    2000 51.18 264.769 228.374 72.79 -251.575

    2100 51.823 267.282 230.167 77.94 -251.762

    2200 52.408 269.706 231.909 83.15 -251.934

    2300 52.947 272.048 233.604 88.42 -252.092

    2400 53.444 274.312 235.253 93.74 -252.239

    2500 53.904 276.503 236.86 99.11 -252.379

    2600 54.329 278.625 238.425 104.52 -252.513

    2700 54.723 280.683 239.952 109.97 -252.6432800 55.089 282.68 241.443 115.46 -252.771

    2900 55.43 284.619 242.899 120.99 -252.897

    3000 55.748 286.504 244.321 126.55 -253.024

    3100 56.044 288.337 245.711 132.14 -253.152

    3200 56.323 290.12 247.071 137.76 -253.282

    3300 56.583 291.858 248.402 143.40 -253.416

    3400 56.828 293.55 249.705 149.07 -253.553

    3500 57.058 295.201 250.982 154.77 -253.696

    3600 57.276 296.812 252.233 160.49 -253.844

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    3700 57.48 298.384 253.459 166.22 -253.997

    3800 57.675 299.919 254.661 171.98 -254.158

    3900 57.859 301.42 255.841 177.76 -254.326

    4000 58.033 302.887 256.999 183.55 -254.501

    4100 58.199 304.322 258.136 189.36 -254.684

    4200 58.357 305.726 259.252 195.19 -254.876

    4300 58.507 307.101 260.349 201.03 -255.078

    4400 58.65 308.448 261.427 206.89 -255.288

    4500 58.787 309.767 262.486 212.76 -255.508

    4600 58.918 311.061 263.528 218.65 -255.738

    4700 59.044 312.329 264.553 224.55 -255.978

    4800 59.164 313.574 265.562 230.46 -256.229

    4900 59.275 314.795 266.554 236.38 -256.491

    5000 59.39 315.993 267.531 242.31 -256.763

    5100 59.509 317.171 268.493 248.26 -257.046

    5200 59.628 318.327 269.44 254.22 -257.338

    5300 59.746 319.464 270.373 260.18 -257.639

    5400 59.864 320.582 271.293 266.16 -257.95

    5500 59.982 321.682 272.199 272.16 -258.268

    5600 60.1 322.764 273.092 278.16 -258.595

    5700 60.218 323.828 273.973 284.18 -258.935800 60.335 324.877 274.841 290.20 -259.272

    5900 60.453 325.909 275.698 296.24 -259.621

    6000 60.571 326.926 276.544 302.30 -259.977

    PREVIOUS: March 1961 (1 atm) CURRENT: March 197

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    Database--Water Vapor

    Figure 1. Heat content of H2O in SI units

    re = p = 0.1 MPa

    fG log Kf

    -238.921 INFINITE

    -236.584 123.579

    -232.766 60.792

    -228.582 40.047

    -228.5 39.785-223.901 29.238

    -219.051 22.884

    -214.007 18.631

    -208.812 15.582 Table 2. Heat content of water vapor in different units.

    -203.496 13.287 Jmol-1 Btulb-mol

    -1

    -198.083 11.496 T, C H -H(T r) T, F H -H

    (T r)

    -192.59 10.06

    -187.033 8.881 826.85 30,191 1520.3 12,988

    -181.425 7.897 926.85 34,506 1700.3 14,845

    -175.774 7.063 1026.85 38,942 1880.3 16,753

    -170.089 6.346 1126.85 43,493 2060.3 18,711

    -164.376 5.724 1226.85 48,151 2240.3 20,715

    -158.639 5.179 1326.85 52,908 2420.3 22,762

    -152.883 4.698 1426.85 57,758 2600.3 24,848

    -147.111 4.269 1526.85 62,693 2780.3 26,971

    -141.325 3.885 1626.85 67,706 2960.3 29,128

    -135.528 3.54 1726.85 72,790 3140.3 31,315

    -129.721 3.227 1826.85 77,941 3320.3 33,531

    -123.905 2.942 1926.85 83,153 3500.3 35,773

    -118.082 2.682

    -112.252 2.443

    -106.416 2.223

    -100.575 2.021

    -94.729 1.833-88.878 1.658

    -83.023 1.495

    -77.163 1.344

    -71.298 1.201

    -65.43 1.068

    -59.558 0.943

    -53.681 0.825

    -47.801 0.713

    -41.916 0.608

    H = 4.462E-03T2 + 35.96T - 2655

    R = 1.000E+00

    30,000

    40,000

    50,000

    60,000

    70,000

    80,000

    90,000

    800 1000 1200 1400 1600 1800

    HT-H25,

    J/g-m

    ol

    T, C

    Heat Content of H2

    O above 800 C

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    -36.027 0.509

    -30.133 0.414

    -24.236 0.325

    -18.334 0.239

    -12.427 0.158

    -6.516 0.081

    -0.6 0.007

    5.32 -0.063

    11.245 -0.131

    17.175 -0.195

    23.111 -0.257

    29.052 -0.316

    34.998 -0.373

    40.949 -0.428

    46.906 -0.48

    52.869 -0.531

    58.838 -0.58

    64.811 -0.627

    70.791 -0.672

    76.777 -0.716

    82.769 -0.75888.767 -0.799

    94.77 -0.839

    100.78 -0.877

    9 (1 bar)

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    Figure 2. Heat content of H2O in AES units

    Table 3. Heat content equation parameters for water vapor = A + BT + CT2

    A B C

    kJ/kg-mol; T = C -2655 35.96 4.462E-03

    kJ/m3; T = C -118 1.604 1.991E-04

    Btu/lb-mol; T = F -1416 8.558 5.925E-04

    Btu/ft3; T = F -3.944 0.02384 1.650E-06

    (Volumes are STP)

    2000

    H = 5.925E-04T2 + 8.558T - 1416

    R = 1.000E+00

    12,000

    16,000

    20,000

    24,000

    28,000

    32,000

    36,000

    1500 2000 2500 3000 3500

    HT-H77,

    Btu

    /lb

    -mo

    l

    T, F

    Heat Content of H2

    O above 1500 F

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    Using the Fact-Web On-line Thermochemical Database--Oxygen

    Oxygen

    Molecular wt: 31.9988

    O2

    Table 1A. Thermodynamic properties of O2 in SI unitsPlease read T(K) H(J) G(J) Vol(litre) S(J/K) Cp(J/K) A, (J)

    ------O2(g)------

    298.15 0 -61,132 24.47 205.04 29.38 -63,611

    300 54 -61,511 24.62 205.22 29.39 -64,006

    400 3,025 -82,479 32.82 213.76 30.11 -85,805

    500 6,084 -104,207 41.03 220.58 31.10 -108,364

    600 9,244 -126,560 49.24 226.34 32.08 -131,549

    700 12,497 -149,450 57.44 231.35 32.97 -155,270

    800 15,834 -172,812 65.65 235.81 33.74 -179,464

    900 19,240 -196,597 73.85 239.82 34.37 -204,080

    1000 22,703 -220,764 82.06 243.47 34.86 -229,0791100 26,213 -245,280 90.26 246.81 35.32 -254,426

    1200 29,764 -270,118 98.47 249.90 35.68 -280,095

    1300 33,348 -295,253 106.68 252.77 35.99 -306,062

    1400 36,961 -320,666 114.88 255.45 36.27 -332,306

    1500 40,601 -346,337 123.09 257.96 36.53 -358,809

    1600 44,267 -372,253 131.29 260.33 36.78 -385,556

    1700 47,957 -398,398 139.50 262.56 37.03 -412,533

    1800 51,672 -424,761 147.70 264.69 37.27 -439,728

    1900 55,411 -451,332 155.91 266.71 37.51 -467,129

    2000 59,174 -478,100 164.12 268.64 37.75 -494,729

    2100 62,960 -505,056 172.32 270.48 37.98 -522,517

    2200 66,770 -532,194 180.53 272.26 38.21 -550,486

    Figure 1. Heat content of O2 and N2 in SI units

    H = 36.88T- 4522

    H = 35.15T - 4579

    20,000

    25,000

    30,000

    35,000

    40,000

    45,000

    50,000

    55,000

    60,000

    65,000

    70,000

    800 1000 1200 1400 1600 1800 2000

    HT

    -H25,

    J/mo

    l

    T, C

    Heat Content of O2 & N2 Above 800 C

    O2 N2

    Linear (O2) Linear (N2)

    l

    l

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    and Nitrogen

    Nitrogen

    Molecular wt: 28.0134

    N2

    Table 1B. Thermodynamic propT (C) T(K) H(J) G(J) Vol(litre)

    ------N2(g)-

    298.15 0 -57,096 24.47

    300 54 -57,450 24.62

    400 2,969 -77,057 32.82

    500 5,909 -97,403 41.03

    600 8,895 -118,345 49.24

    Table 2. AES units 700 11,941 -139,792 57.44

    T (F) H(Btu) H(Btu) 800 15,050 -161,679 65.65

    O2 N2 900 18,224 -183,960 73.85

    1000 21,460 -206,598 82.06826.85 1520.3 11277 10650 1100 24,755 -229,563 90.26

    926.85 1700.3 12805 12090 1200 28,104 -252,830 98.47

    1026.85 1880.3 14347 13551 1300 31,500 -276,379 106.68

    1126.85 2060.3 15901 15030 1400 34,937 -300,190 114.88

    1226.85 2240.3 17467 16524 1500 38,408 -324,249 123.09

    1326.85 2420.3 19044 18028 1600 41,906 -348,540 131.29

    1426.85 2600.3 20632 19544 1700 45,429 -373,051 139.50

    1526.85 2780.3 22230 21071 1800 48,979 -397,770 147.70

    1626.85 2960.3 23839 22607 1900 52,550 -422,686 155.91

    1726.85 3140.3 25457 24152 2000 56,140 -447,791 164.12

    1826.85 3320.3 27086 25704 2100 59,747 -473,077 172.32

    1926.85 3500.3 28725 27262 2200 63,368 -498,534 180.53

    Figure 2. Heat content of O2 and N2 in AES units

    kJ/k

    Btu/lb

    B

    Table 4.T(K)

    300

    400

    500

    600

    700

    800

    H = 8.40T - 2239

    H = 8.81T - 2228

    10000

    12000

    14000

    16000

    18000

    20000

    22000

    24000

    26000

    28000

    30000

    1500 2000 2500 3000 3500

    H-H

    .Btu

    /lb

    -mo

    l

    T, F

    Heat Content of O2 & N2 Above 1500 F

    N2 O2

    Linear (N2) Linear (O2)

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    Using th

    rties of N2 in SI unitsS(J/K) Cp(J/K) A_(J) T (C) T(K) H(J)

    -----

    191.50 29.14 -59,575 2 98 .1 5 - 39 3, 52 2

    191.68 29.13 -59,944 300 -393,453

    200.07 29.23 -80,383 400 -389,522

    206.62 29.61 -101,560 500 -385,219

    212.07 30.15 -123,334 600 -380,615

    216.76 30.77 -145,612 700 -375,765

    220.91 31.42 -168,331 800 -370,711

    224.65 32.06 -191,443 900 -365,488

    228.06 32.66 -214,913 1 000 -3 60,12 3231.20 33.23 -238,709 826.85 1 100 -3 54,63 9

    234.11 33.73 -262,808 926.85 1 200 -3 49,05 2

    236.83 34.18 -287,188 1026.85 1 300 -3 43,37 8

    239.38 34.55 -311,831 1126.85 1 400 -3 37,62 9

    241.77 34.86 -336,721 1226.85 1 500 -3 31,81 7

    244.03 35.09 -361,843 1326.85 1 600 -3 25,95 0

    246.17 35.37 -387,185 1426.85 1 700 -3 20,03 7

    248.19 35.61 -412,736 1526.85 1 800 -3 14,08 5

    250.12 35.81 -438,484 1626.85 1 900 -3 08,09 9

    251.97 35.99 -464,420 1726.85 2 000 -3 02,08 2

    253.73 36.14 -490,537 1826.85

    255.41 36.28 -516,826 1926.85

    Table 3. Heat content for O2 and N2 = A + BT

    N2 O2

    A B A B

    -mol; T = C -4579 35.15 -4522 36.88

    J/m3; T = C -204 1.568 -202 1.645

    -mol; T = F -2239 8.40 -2228 8.81

    tu/ft3; T = F -6.236 0.02340 -6.205 0.02454

    (Volumes are STP)

    Figure 3. Heat content of air in SI units, and quadra

    eat content for air from Tables 1A & 1BH(J) H(J) H(J) T(C)

    O2 N2 Air

    54 54 54 26.85

    3,025 2,969 2,981 126.85

    6,084 5,909 5,945 226.85

    9,244 8,895 8,969 326.85

    12,497 11,941 12,058 426.85

    15,834 15,050 15,215 526.85

    12,000

    14,000

    16,000

    kg-mol

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    0

    2,000

    4,000

    6,000

    8,000

    ,

    0 50 100

    heatcontent,kJ/

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    e Fact-Web On-line Thermochemical Database--Carbon Dioxide

    Carbon Dioxide

    Molecular wt: 44.0096

    CO2

    Table 5. Thermodynamic properties of CO2 in SI unitsG(J) Vol(litre) S(J/K) Cp(J/K) A_(J) HT-H298 T (C)

    -457,265 24.47 213.80 37.14 -459,744 0 25.0

    -457,661 24.62 214.03 37.22 -460,155 69 26.9

    -479,645 32.82 225.31 41.29 -482,970 4,001 126.9

    -502,666 41.03 234.89 44.64 -506,824 8,303 226.9

    -526,584 49.24 243.28 47.36 -531,572 12,907 326.9

    -551,292 57.44 250.75 49.59 -557,112 17,758 426.9

    -576,710 65.65 257.50 51.43 -583,362 22,811 526.9

    -602,772 73.85 263.65 52.98 -610,255 28,034 626.9

    -629,423 82.06 269.30 54.28 -637,738 33,399 726.9-656,618 90.26 274.53 55.39 -665,764 38,884 826.9

    -684,317 98.47 279.39 56.33 -694,294 44,470 926.9

    -712,485 106.68 283.93 57.13 -723,294 50,144 1026.9

    -741,093 114.88 288.19 57.82 -752,733 55,893 1126.9

    -770,114 123.09 292.20 58.41 -782,586 61,705 1226.9

    -799,525 131.29 295.98 58.91 -812,828 67,572 1326.9

    -829,304 139.50 299.57 59.34 -843,439 73,485 1426.9

    -859,433 147.70 302.97 59.70 -874,399 79,438 1526.9

    -889,893 155.91 306.21 60.01 -905,691 85,423 1626.9

    -920,669 164.12 309.29 60.32 -937,298 91,440 1726.9

    tic equation obtained using trendline.

    ------ CO2(g) ------

    H = 2.945E-03T2 + 28.67T - 713

    R = 1.000E+00

    Heat Content of Air to 600 C

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    150 200 250 300 350 400 450 500 550 600

    T, C

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    y = -3.140E-06x3 + 1.390E-02x2 + 3.888E+01x - 1.072E+03

    R = 1.000E+00

    0

    10,000

    20,000

    30,000

    40,000

    50,000

    60,000

    70,000

    80,000

    90,000

    100,000

    0 300 600 900 1200 1500 1800

    HT-

    H25,

    J/g-m

    ol

    T, C

    Heat Content of CO2