Construct Thiele on the length of 'K'

ecd0d2c4-fa77-44e6-859a-d9524e1c2faa 52 4 5 decimal

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

user length j 16 :

SS 6179 supports latest SS versions complain

j 1 - (0 range

Thiele on length 'j' of support points K X x Cfr N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (1 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 51 line :

Expandable Thiele wrt X's, K's
Export, enable, set 'j' on length of support points K X x Cfr K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el x X 9 el - K 10 el x X 10 el - K 11 el x X 11 el - K 12 el x X 12 el - K 13 el x X 13 el - K 14 el x X 14 el - K 15 el x X 15 el - K 16 el / + / + / + / + / + / + / + / + / + / + / + / + / + / + / +

Water Saturation

Water Saturation Temperature ... bar(°C)

t0 1 time :

°C 1 :

bar 1 :

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 0.01 x ≤ (x 373.946 ≤ (* : 71 sys

373.946 bar_1 bar 220.64

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 + (* : w 350 x ≤ (x 590 ≤ (* : 31 sys

x bar_1 u / x bar_2 w / 373.95 220.64 + 40 black 1 5 mat 3 1 sys

critical °C 373.946 ≡ bar 220.64 ≡ 21 sys

X t bar_1 100 - 0 ≡ t 250350 solve :

X °C 311

sterilized units X °C * bar_1 450 °C * bar_2 21 mat bar 100 370.39 21 mat

conversion 101325 Pa * 1 atm * ≡ 100000 Pa * 1 bar * ≡ 21 sys

=========================================================================================

Water Saturation Pressure ... °C(bar)

bar u 10 :

K 273.15 : p β p 10 / (0.25^: p E p β n 3 el + (p β * n 6 el + : p F n 1 el p β * n 4 el + (p β * n 7 el + : p G n 2 el p β * n 5 el + (p β * n 8 el + : p D 2 p G * p F - p F 2^4 p E * p G * - (0.5^- / : p °C n 10 el p D + n 10 el p D + (2^(4 n 9 el n 10 el p D * + (* - (0.5^- 2 / K - : x c 1 0.006117 x ≤ (x 220.64 ≤ (& cases : 81 sys

user 4 - 322432 u u °C 32 mat :

x °C x c * user 2 1 sys

u u °C 12 mat °C 10 179.89 12 mat

sanity 1.01325 °C °C 100.0

triple point 0.006117 °C °C 0.01

X 0.01 0.05 0.1 0.25 0.5 0.75 1 2.5 5102550100150200220161 mat :

X X °C vectorize augment 0.01 6.97 0.05 32.875 0.1 45.808 0.25 64.963 0.5 81.317 0.75 91.758 1 99.606 2.5 127.414 5 151.836 10 179.886 25 223.956 50 263.943 100 310.999 150 342.158 200 365.746 220 373.707 162 mat

4 appVersion 0.98.6179.21440 ≡

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

XY 0.01 6.97 0.05 32.875 0.1 45.808 0.25 64.963 0.5 81.317 0.75 91.758 1 99.606 2.5 127.414 5 151.836 10 179.886 25 223.956 50 263.943 100 310.999 150 342.158 200 365.746 220 373.707 162 mat :

X XY 1 col : Y XY 2 col : 12 mat data XY o 5 black plot : 21 sys

clear K 0 : Table 0 : 12 mat

t0 1 time :

Thiele table of inverse differences ... Carlos i 1 Y rows range Table i 1 el Y i el : for j 2 Y rows range i j Y rows range Table i j el X j 1 - el X i el - Table j 1 - j 1 - el Table i j 1 - el - / : cont j : 21 line break try for for i 1 cont range K i el Table i i el : for 31 line

K K 6 round vectorize :

... NUMERIC ...

K 6.97 0.001544 64.665098 0.012071 58.784285 0.044128 53.788366 0.111931 73.87338 0.336136 108.536467 1.083103 152.213798 3.652783 66.257584 2.896986 - 161 mat

Expand to View/Export as required Table 11 mat

isolate 'K' K K eval :

x λ 10 x ≤ (x 220 ≤ (& cases :

isolated 'K'

Cf(x) Export Thiele [X, K]... plug in any sytem compatibele

x Cf K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el x X 9 el - K 10 el x X 10 el - K 11 el x X 11 el - K 12 el x X 12 el - K 13 el x X 13 el - K 14 el x X 14 el - K 15 el x X 15 el - K 16 el / + / + / + / + / + / + / + / + / + / + / + / + / + / + / + :

bar u 75 :

user 001120 u u Cf 32 mat :

u u °C 12 mat °C 75 290.54 12 mat

t0 1 time :

user x Cf x λ * data u u Cf + 20 blue 1 5 mat 4 1 sys

1 time t0 - 1.2 s *

OBSERVE ... The canvas evaluates on pixels In this plot, it evaluates 648 times Thiele Cf(x) ... 1.3 s

u u Cf 12 mat °C 75 290.54 12 mat

Water saturation bar(°C )... IAPWS-97 ± 0.000 mutual conformity

c 7.45405359891067 103 -^* 1.325012145171 104 -^* 2.55178597883334 105 -^* 1.3180616369901 107 -^* - 5.04814989587821 109 -^* 1.20800120409375 1011 -^* - 6.56045886848592 103 -^* - 2.14781927781255 105 -^* 4.15864048208323 108 -^* - 3.73870830454988 1011 -^* 1.01734440690023 1014 -^* - 111 mat :

data Y Y bar_1 vectorize augment (: 6.97 0.01 32.875 0.05 45.808 0.1 64.963 0.25 81.317 0.5 91.758 0.75 99.606 1 127.414 2.5 151.836 5 179.886 10.0001 223.956 24.9998 263.943 50.0001 310.999 99.9993 342.158 150.0002 365.746 200.0002 373.707 220.0012 162 mat

data data :

x Genfit c 1 el c 2 el x * + c 3 el x 2^* + c 4 el x 3^* + c 5 el x 4^* + c 6 el x 5^* + 1 c 7 el x * + c 8 el x 2^* + c 9 el x 3^* + c 10 el x 4^* + c 11 el x 5^* + / :

x G 1 0.01 x ≤ (x 374 ≤ (& cases :

°C 200 :

X data 1 col : Y data 2 col : 12 mat ΔGenfit X Y X Genfit - vectorize (augment : support data o 5 black plot : 31 sys

track 32 - 192256192 °C °C Genfit 32 mat :

bar 1 :

ΔGenfit 6.970 0.000 32.875 0.000 45.808 0.000 64.963 0.000 81.317 0.000 91.758 0.000 99.606 0.000 127.414 0.000 151.836 0.000 179.886 0.000 223.956 0.000 263.943 0.000 310.999 0.000 342.158 0.000 365.746 0.000 373.707 0.000 162 mat

Water saturat'n temperature bar(°C) mutual conformity ± 0.0001

track x Genfit x G * support 3 1 sys

°C °C Genfit 12 mat bar 200 15.55 12 mat

275 bar_1 275 Genfit 21 mat bar 59.46 59.46 21 mat

Tetens formulae ... ≤ 300 °C

Tetens formulae ... some details

x p 1 0.01 x ≤ (x 373.946 ≤ (* cases :

above 0 °C T P 0.0061078 17.27 T * T 237.3 + / exp * :

0.61078 0.01 * 0.0061078

below 0 °C T sublimation 0.0061078 21.875 T * T 265.5 + / exp * :

U 373.946 :

bar deviation 1 U P * U bar_1 21 mat 236.79 220.64 21 mat

1 x P * 1 * x bar_1 x p * 35 0.125 35 0.0625 - 2 2 mat 3 1 sys 1 x P * x bar_1 -

U 45 :

bar deviation 1 U P * U bar_1 21 mat 0.096 0.096 21 mat

U 200 :

bar deviation 1 U P * U bar_1 21 mat 16.45 15.55 21 mat

X 458012016018051 mat :

X bar_1 vectorize 0.096 0.474 1.987 6.181 10.026 51 mat

XY X X bar_1 vectorize augment : 45 0.0959 80 0.4741 120 1.9867 160 6.1814 180 10.0263 52 mat

16.808 228.649 21 mat

X 180230300350 373.707 51 mat :

X bar_1 vectorize 10.026 27.968 85.877 165.292 220.001 51 mat

XY X X bar_1 vectorize augment : 180 10.0263 230 27.9679 300 85.8771 350 165.2916 373.707 220.0012 52 mat

17.451 248.083 21 mat

x Tetens 0.0061078 21.875 x * x 265.5 + / exp * 90 - x ≤ (x 0 ≤ (& 0.0061078 17.27 x * x 237.3 + / exp * 0 x ≤ (x 45 ≤ (& 0.0061078 16.808 x * x 228.649 + / exp * 45 x ≤ (x 180 ≤ (& 0.0061078 17.451 x * x 248.083 + / exp * cases :

XY 6.97 0.01 32.875 0.05 45.808 0.1 64.963 0.25 81.317 0.5 91.758 0.75 99.606 1 127.414 2.5 151.836 5 179.886 10 223.956 25 263.943 50 310.999 100 342.158 150 365.746 200 373.707 220162 mat :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

X XY 1 col : Y XY 2 col : 12 mat data XY o 5 black plot : 21 mat

Tetens bar Δ IAPWS-97 Δ X X bar_1 X Tetens - vectorize augment :

header °C Δbar 12 mat : deviation header Δ stack : 21 sys

X bar_1 X Tetens - vectorize

deviation °C Δbar 6.97 0 32.875 0 45.808 0.001 - 64.963 0.002 - 81.317 0.002 - 91.758 0.002 - 99.606 0.002 - 127.414 0 151.836 0.001 179.886 0.001 - 223.956 0.921 263.943 0.717 310.999 0.408 - 342.158 1.111 - 365.746 0.312 - 373.707 0.759 172 mat

TETENS U 0.01 1801 range : i 1 U rows range vy i el U i el Tetens eval : for U vy augment 31 line :

data TETENS 2 1 sys

x Tetens 0.0061078 21.875 x * x 265.5 + / exp * 90 - x ≤ (x 0.01 ≤ (& 0.0061078 17.27 x * x 237.3 + / exp * 0.01 x ≤ (x 45 ≤ (& 0.0061078 16.808 x * x 228.649 + / exp * 45 x ≤ (x 180 ≤ (& 0.0061078 16.955 x * x 232.554 + / exp * cases :

sublimation region

original Tetens 35 °C

extended Tetens [jmG]

last segment ± 0.05 bar

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

XY 6.97 0.01 32.875 0.05 45.808 0.1 64.963 0.25 81.317 0.5 91.758 0.75 99.606 1 127.414 2.5 151.836 5 179.886 10 223.956 25 263.943 50 310.999 100 342.158 150 365.746 200 373.707 220162 mat :

X XY 1 col : Y XY 2 col : 12 mat data XY o 5 black plot : 21 mat

x Tet 1 0.01 x ≤ (x 300 ≤ (& cases :

data x Tetens x Tet * 2 1 sys

± 1 bar [374]
.....
.....
± 0.5 bar [350]
.....
.....
± 0.05 bar [300] 0.0061078 17.451 x * x 248.083 + / exp * 0.0061078 17.224 x * x 240.723 + / exp * 0.0061078 16.955 x * x 232.554 + / exp * 31 sys

45 Tetens 180 Tetens 180 bar_1 300 Tetens 41 mat 0.0958 10.0275 10.0263 85.8804 41 mat

Tetens mutual regions . . . solving °C . . .given bar

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x Tet 1 0.01 x ≤ (x 300 ≤ (& cases :

°C 1 :

bar 1 :

Tetens direct ... bar(°C)

x Tetens x Tet * 0 86 300 86 300 86 300 0 4 2 mat 2 1 sys

x °C 237305000000 x * 30539 / ln * 1727 - 1005000000 x * 30539 / ln * + / - 0 x ≤ (x 0.0958 ≤ (& 2286495000000 x * 30539 / ln * 82101 - 1255000000 x * 30539 / ln * + (* / - 0.0958 x ≤ (x 10 ≤ (& 2325545000000 x * 30539 / ln * 53391 - 2005000000 x * 30539 / ln * + (* / - cases :

x b 10 x ≤ (x 86 ≤ (& cases :

Tetens solvable region ... given 'bar' find °C

0 300 86 300 86 300 86 0 4 2 mat x °C x b * 40 0 bar 14 green 1 5 mat 8 192 °C 14 green 1 5 mat 4 1 sys

Mutual ▼ sanities

bar 275 Tetens : 59.6

bar °C 275.0

bar 300 Tetens : 85.880

bar °C 300.0

bar 300 bar_1 : 85.877

bar °C 300.0

t Wr 0.0061078 17.27 t * t 237.3 + / exp * :

Inversing Tetens ... i.e: solving

t Wr x - 0 ≡ t solve maple 237305000000 x * 30539 / ln * 1727 - 1005000000 x * 30539 / ln * + / -

========================================================

t Wr 0.0061078 16.808 t * t 228.649 + / exp * :

t Wr x - 0 ≡ t solve maple 2286495000000 x * 30539 / ln * 82101 - 1255000000 x * 30539 / ln * + (* / -

========================================================

t Wr 0.0061078 16.955 t * t 232.554 + / exp * :

t Wr x - 0 ≡ t solve maple 2325545000000 x * 30539 / ln * 53391 - 2005000000 x * 30539 / ln * + (* / -