plotG(vx,vy,a,b,c)

c9184b9d-280d-41a0-9d3c-ca0700e1da1d 81 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

plotG(vx,vy,a,b,c)

data char size clr plotG k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

n 1167.0521452767 724213.16703206 - 17.073846940092 - 12020.82470247 3232555.0322333 - 14.91510861353 4823.2657361591 - 405113.40542057 0.23855557567849 - 650.17534844798 101 mat :

K 273.15 : t v t K + (n 9 el t K + (n 10 el - / + : t A t v n 1 el + (t v * n 2 el + : t B n 3 el t v * n 4 el + (t v * n 5 el + : t C n 6 el t v * n 7 el + (t v * n 8 el + : t bar_1 102 t C * t B - t B 2^4 t A * t C * - (0.5^+ / (4^* : u 0 x ≤ (x 373.946 ≤ (* : 71 sys

a 348.05185628969 1.1671859879975 - 0.0010192970039326 572.54459862746 13.918839778870 51 mat :

K 273.15 : t bar_2 10 a 3 el t K + (* a 2 el + (t K + (* a 1 el + (* : p °C a 4 el p 10 / a 5 el - a 3 el / (0.5^+ K - : w 350 x ≤ (x 590 ≤ (* : 41 sys

critical [t,p] °C 373.946 : bar 220.64 : °C bar + 20 black 15 mat 31 line

x bar_1 u / x bar_2 w / °C bar + 14 black 1 5 mat 3 1 sys

IAPWS 97 regions 1, 2

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critical 373.946 220.64 12 mat : pseudo_critical 350 165.292 12 mat : 21 line

critical region 350 165.292 350 220.64 373.946 220.64 373.946 165.292 350 165.292 52 mat

regions x bar_1 u / x bar_2 w / 350 165.292 350 220.64 373.946 220.64 373.946 165.292 350 165.292 52 mat 31 sys :

critical uncertain region [,]

regions

1. chemengineer.guide@about.com 2. IAPWS-97 formulas Bernhard Spang

mmbar 1 :

bar 1 :

ice sublimation pressure

water saturation pressure bar(°C)

b 6.10501 0.461255 0.0123084 8.41162 107 -^* 8.22031 106 -^* - 2.23132 107 -^* - 2.84695 109 -^* - 1.83516 1011 -^* - 4.80134 1014 -^* - 91 mat :

ice vapor tension 
'x' is °C => [mmbar] x ice b j el x j 1 -^* j 19 sum :

a 0.0062673 3.457 104 -^* 2.359425 105 -^* 4.929532 108 -^* - 8.22913 109 -^* 2.590993 1011 -^* - 3.084182 1013 -^* 9.580651 1016 -^* - 1.00556 1018 -^* 91 mat :

water saturation pressure
'x' is °C =>  bar x water a j el x j 1 -^* j 19 sum :

20 - ice 0.01 - ice 21 mat mmbar 1.04 6.1 21 mat

374 water 100 water 0.01 water 31 mat bar 220.64 1.01 0.01 31 mat

Observe => Lagrange criterium

coefficients 'a' alternate ±

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ice 90 - x ≤ (x 0 ≤ (* :

water 0.01 x ≤ (x 374 ≤ (* :

x ice ice / 90 - 2 90 - 2 - 2 2 mat 2 1 sys x water water / 374 250 374 50 - 2 2 mat 2 1 sys

ice sublimation [-90 ... 0.01 °C] t mbar 0.009316586 t * 2.168177 + 180.4903 t 31.5538 - 986.407 t 12.10429 + 62.33773 t 97.41639 + / + / + / + :

Water saturation °C(bar)

PTJ 0.01 6.97 6.97 0.05 32.88 0.00154381 0.1 45.81 64.6501606 0.25 64.96 0.01207155 0.5 81.32 58.9205637 0.75 91.76 0.04464202 1 99.61 55.8064501 2.5 127.41 0.12544148 5 151.84 85.7831459 10 179.89 0.51767979 25 223.96 218.6908193 50 263.94 0.67755242 - 100311 24.0134742 - 150 342.16 4.030032846 200 365.75 118.8151349 220 373.71 2.887421696 - 163 mat :

P PTJ 1 col : T PTJ 2 col : J PTJ 3 col : PT P T augment . 12 black plotG : 41 line

j 0.01 x ≤ (x 220 ≤ (* :

°C(p)

p °C J 1 el p 0.01 - (J 2 el p 0.05 - (J 3 el p 0.1 - (J 4 el p 0.25 - (J 5 el p 0.5 - (J 6 el p 0.75 - (J 7 el p 1 - (J 8 el p 2.5 - (J 9 el p 5 - (J 10 el p 10 - (J 11 el p 25 - (J 12 el p 50 - (J 13 el p 100 - (J 14 el p 150 - (J 15 el p 200 - (J 16 el / + / + / + / + / + / + / + / + / + / + / + / + / + / + / + :

°C 1 :

PT x °C j / 2 1 sys PT x °C j / 2 1 sys

0.01 °C 1 °C 220 °C 31 mat °C 6.97 99.61 373.71 31 mat

Enthalpy saturation

Enthalpy Water ke 599.3 2.06612 87.70865 0.28073 444.5461 0.29356 - 849.96936 - 2.0626 - 74.12943 2.66168 33.49078 1.58508 - 23.12122 0.87324 - 141 mat :

EnthalpySteam kv 5.02 0.99602 5025.02 0.00624 16324.23113 - 0.01094 12803.75677 0.10107 5186.36809 0.0063 3795.17033 - 0.05921 9707.2127 - 0.00044 141 mat :

Hev 5 5.02 599.3 10 10.04 601.72 25 25.04 608.24 50 50.00 618.93 100 100.10 639.06 150 151.01 655.86 200 203.59 666.88 250 259.32 669.02 300 321.20 656.74 325 356.69 641.19 350 399.08 612.31 360 420.73 592.58 370 452.06 557.36 374 498.54 499.61 143 mat :

X Hev 1 col : Y Hev 3 col : EnthalWater X Y augment . 12 black plotG : 31 line

X Hev 1 col : Y Hev 2 col : EnthalpySteam X Y augment . 12 black plotG : 31 line

Enthalpy Water

t He ke 1 el t 5 - (ke 2 el t 10 - (ke 3 el t 25 - (ke 4 el t 50 - (ke 5 el t 100 - (ke 6 el t 150 - (ke 7 el t 200 - (ke 8 el t 250 - (ke 9 el t 300 - (ke 10 el t 325 - (ke 11 el t 350 - (ke 12 el t 360 - (ke 13 el t 370 - (ke 14 el / + / + / + / + / + / + / + / + / + / + / + / + / + :

EnthalpySteam

t Hs kv 1 el t 5 - (kv 2 el t 10 - (kv 3 el t 25 - (kv 4 el t 50 - (kv 5 el t 100 - (kv 6 el t 150 - (kv 7 el t 200 - (kv 8 el t 250 - (kv 9 el t 300 - (kv 10 el t 325 - (kv 11 el t 350 - (kv 12 el t 360 - (kv 13 el t 370 - (kv 14 el / + / + / + / + / + / + / + / + / + / + / + / + / + :

kcal_kg 1 :

300 Hs 300 He 21 mat kcal_kg 32165721 mat

v 5 x ≤ (x 374 ≤ (* :

EnthalWater x He v / 2 1 sys EnthalpySteam x Hs v / 2 1 sys

Entropy saturation

Entropy 10 0.03596 2.1262 50 0.1681 1.9293 100 0.3121 1.7568 150 0.4398 1.6327 200 0.5567 1.5353 250 0.6673 1.4499 300 0.7774 1.3636 370 0.9820 1.1498 83 mat :

X Entropy 1 col : Y Entropy 2 col : EntropyWaterWater X Y augment . 12 black plotG : 31 line

X Entropy 1 col : Y Entropy 3 col : EntropySteam X Y augment . 12 black plotG : 31 line

se 1.87804 104 -^* - 3.8091 103 -^* 1.76923 105 -^* - 3.3417 107 -^* 4.7508 109 -^* - 3.9818 1011 -^* 1.9778 1013 -^* - 5.7415 1016 -^* 8.998 1019 -^* - 5.8805 1022 -^* 101 mat :

kcal_kg 1 :

sv 2.18785 6.6924 103 -^* - 4.34896 105 -^* 3.62069 107 -^* - 2.4730 109 -^* 1.0247 1011 -^* - 2.2014 1014 -^* 1.8911 1017 -^* - 81 mat :

Entropy water phase x se se j el x j 1 -^* j 110 sum 11 line :

Entropy vapor phase x sv sv j el x j 1 -^* j 18 sum 11 line :

s 0.01 x ≤ (x 374 ≤ (* :

x se s / x sv s / EntropyWaterWater EntropySteam 4 1 sys

Observe => Lagrange criterium

coefficients 'se, sv' alternate ±

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kcal_kg_°C 1 :

CT 10 1.001 50 1.0013 100 1.0093 150 1.0303 200 1.0744 250 1.1619 300 1.3495 370 2.5756 82 mat :

T CT 1 col : c CT 2 col : cT CT . 12 black plotG : 31 line

c 1.001646 2.0188 104 -^* - 1.161 105 -^* 2.1897 107 -^* - 1.8655 109 -^* 6.6982 1012 -^* - 8.8248 1015 -^* 71 mat :

Heat mass water phase x c c j el x j 1 -^* j 17 sum 11 line :

250 c kcal_kg_°C 1.16

cT x c s / 2 1 sys

x c x 030 int kcal_kg 30.027

x so 1 0.01 x ≤ (x 374 ≤ (* cases :

Sonic velocity [m/s] ... given °C

sonic vapor phase sonicS 15 420.5 50 443.96 100 472.97 150 494.04 200 504.88 250 503.11 300 482.97 350 429.97 370 391.06 92 mat :

sonic water phase sonicW 101447501545100154515014662001332250114930091035057882 mat :

σe 1406.1281 4.53204 0.040837 - 0.00010935 1.4023 107 -^* - 51 mat :

σv 406.64 0.93143 0.0037462 - 0.00001323 2.7532 108 -^* - 51 mat :

Tsw sonicW 1 col : σW sonicW 2 col : soW sonicW . 12 black plotG : 31 line

Tsv sonicS 1 col : σS sonicS 2 col : soS sonicS . 12 black plotG : 31 line

x sonicW σe j el x j 1 -^* j 15 sum 11 line :

x sonicS σv j el x j 1 -^* j 15 sum 11 line :

x sonicW x so * x sonicS x so * soW soS 4 1 sys

°C ... Vapor phase Isentropic .... bar

isentropic_°C 10 1.3275 50 1.3276 100 1.337 150 1.368 200 1.446 250 1.627 300 2.094 325 2.684 350 4.467 360 6.882 370 21.071 373 86.89 122 mat :

χ.t 1.3275 400000 0.00012803 - 402748.412 - 0.1686548 8407.8399 0.0128743 - 7559.6214 - 0.1079548 - 863.11255 - 0.0011947 - 703.6825 121 mat :

isentropic_bar 5 1.37 10 1.4 25 1.514 50 1.713 75 1.961 100 2.297 125 2.791 150 3.624 175 5.298 200 10.817 210 20.237 215 37.82 122 mat :

χ.p 1.3280 128.08 2.3893 1.2349 3.6434 - 461.032 0.3511 235.242 0.1815 - 284.33 - 101 mat :

t χ°C χ.t 1 el t 10 - (χ.t 2 el t 50 - (χ.t 3 el t 100 - (χ.t 4 el t 150 - (χ.t 5 el t 200 - (χ.t 6 el t 250 - (χ.t 7 el t 300 - (χ.t 8 el t 325 - (χ.t 9 el t 350 - (χ.t 10 el t 360 - (χ.t 11 el t 370 - (χ.t 12 el / + / + / + / + / + / + / + / + / + / + / + :

p χbar χ.p 1 el p 0.01 - (χ.p 2 el p 10 - (χ.p 3 el p 25 - (χ.p 4 el p 50 - (χ.p 5 el p 100 - (χ.p 6 el p 150 - (χ.p 7 el p 175 - (χ.p 8 el p 200 - (χ.p 9 el p 210 - (χ.p 10 el / + / + / + / + / + / + / + / + / + :

Xt isentropic_°C 1 col : Yt isentropic_°C 2 col : χ°C isentropic_°C . 12 black plotG : 31 line

Xp isentropic_bar 1 col : Yp isentropic_bar 2 col : χbar isentropic_bar . 12 black plotG : 31 line

χt 0.01 x ≤ (x 370 ≤ (* :

χp 5 x ≤ (x 215 ≤ (* :

χ°C x χ°C χt / 2 1 sys χbar x χbar χp / 2 1 sys

Latent heat of vaporisation "Latent heat of vaporization is a physical property of a substance. ... When a material in liquid state is given energy, it changes its phase from liquid to vapor; the energy absorbed in this process is called heat of vaporization. The heat of vaporization of water is about 2,260 kJ/kg, which is equal to 40.8 kJ/mol"

Latent Heat of Vaporation Data

Latent 0.0075 597.34 5 594.51 10 591.68 25 583.20 50 568.93 100 538.96 150 504.85 200 463.29 250 409.71 300 335.54 325 284.50 350 213.23 360 171.85 370 105.30 373.946 1.07 152 mat :

r 0.353357 28.3 - 0.3532526 - 84963.446 - 0.002913 - 28223.818 - 0.0104773 - 20059.1873 0.00408109 19897.0525 - 0.0043650 312195.22 - 0.000043493 622979.5218 141 mat :

X Latent 1 col : Y Latent 2 col : Latent Latent . 12 black plotG : 31 line

Latent

t Latent r 1 el t 5 - (r 2 el t 10 - (r 3 el t 25 - (r 4 el t 50 - (r 5 el t 100 - (r 6 el t 150 - (r 7 el t 200 - (r 8 el t 250 - (r 9 el t 300 - (r 10 el t 325 - (r 11 el t 350 - (r 12 el t 360 - (r 13 el t 370 - (r 14 el / + / + / + / + / + / + / + / + / + / + / + / + / + :

t LatentHeat 597.34 1 t Latent / - :

λ 0.01 x ≤ (x 374 ≤ (* :

kcal_kg 1 :

325 LatentHeat kcal_kg 284.51

Latent x LatentHeat λ / 2 1 sys