cea881c4-a2ea-4c77-a0b7-76b99383e4af 7 4 5 decimal

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

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

Data PT 0.01 6.97 0.05 32.88 0.1 45.81 0.25 64.96 0.5 81.32 0.75 91.76 1 99.61 2.5 127.41 5 151.84 10 179.98 25 223.96 50 263.94 100311150 342.16 200 365.75 220 373.71 162 mat :

Xk PT 1 col : Yk PT 2 col : XY Xk Yk . 10 black plotG : 31 line

Thiele table of inverse differences i 1 Yk rows range φ i 1 el Yk i el : for j 2 Yk rows range i j Yk rows range φ i j el Xk j 1 - el Xk i el - φ j 1 - j 1 - el φ i j 1 - el - / : cont j : 21 line break try for for 21 line

With the Try / on error function, division by zero is avoided when the inverse differences of a column are all the same, and the loop is exited.

φ 11 mat Extend Thiele table ≡

cont 16

φ 6.97 0000000 32.88 0.0015 000000 45.81 0.0023 64.6502 00000 64.96 0.0041 77.0761 0.0121 0000 81.32 0.0066 89.1681 0.0163 58.9206 000 91.76 0.0087 97.4437 0.0198 64.5207 0.0446 00 99.61 0.0107 103.9078 0.0229 69.0993 0.0491 55.8065 0 127.41 0.0207 128.0685 0.0378 87.3027 0.0705 67.7642 0.1254 151.84 0.0344 150.452 0.0571 105.4693 0.0967 81.6822 0.1546 179.98 0.0577 177.0509 0.0881 128.2791 0.137 100.1869 0.2028 223.96 0.1152 219.5862 0.1607 166.5098 0.2277 132.4587 0.3131 263.94 0.1945 258.8183 0.257 203.1257 0.3433 164.9259 0.449 311 0.3289 305.3417 0.4151 247.5293 0.5275 205.527 0.6612 342.16 0.4475 336.2607 0.5519 277.4065 0.6843 233.3444 0.8393 365.75 0.5574 359.7045 0.6775 300.1815 0.8269 254.7095 1.0005 373.71 0.5999 367.6194 0.7258 307.8832 0.8817 261.9423 1.0624 168 mat

cont 16

Assign the diagonal of the Matrix of the inverse differences i 1 cont range Yφ i el φ i i el 4 round : for

Rounding the values of the inverse differences for the purpose of presenting the equation to make it shorter

Thiele Continued Fraction s P p size T i size 2 range i size ≡ T s i 1 - el eval p P i 1 - el eval - s i el eval / (+ : T T : 21 line T s i 1 - el eval p P i 1 - el eval - T / (+ : T T : 21 line if for s P p size T T : 21 line :

Thiele table above is constructed on the overal data set 'PT'. For shorter user range, reduce the range of the Thiele continued fraction by "size"

Thiele Size size 10 :

recast °C(bar) over p=bar p Tbar Yφ Xk p size T :

Xk 0.01 0.05 0.1 0.25 0.5 0.75 1 2.5 5102550100150200220161 mat

Yφ 6.97 0.0015 64.6502 0.0121 58.9206 0.0446 55.8065 0.1254 85.7831 0.4473 107.9361 0.8389 113.5761 2.8153 92.5928 3.0301 - 161 mat

Data [Xk,Yφ] represent the overall Thiele. @ 'size 10', the last Thiele interpolant is shown on this overall data. At this point, the expansion Tbar(p)can be exported to Mathcad up to MCD 11. Smath and Mathcad native kernel do take the contunied fraction. Other softwares [OriginLab 7.5, Kalculator, Excel ...] will have to be scripted bottom to top.

size 10 ≡

The size 10 continued fraction. p Tbar 6.97 p 0.01 - 0.0015 p 0.05 - 64.6502 p 0.1 - 0.0121 p 0.25 - 58.9206 p 0.5 - 0.0446 p 0.75 - 55.8065 p 1 - 0.1254 p 2.5 - 85.7831 p 5 - 0.4473 / + / + / + / + / + / + / + / + / +

Optimiz => numeric Tbar p 0.01 size 0.025 range : i 1 p rows range u i el p i el : ρ i el p i el Tbar eval : 21 line for u ρ augment 31 line :

Domestic pressure cooker 1.333 Tbar 1.667 Tbar 2 Tbar 31 mat 108.2 114.8 120.5 31 mat

Tbar 1 99.6 + 20 red 1 5 mat XY 3 1 sys

p 0.01 10100 logpts :

low high N logpts linear-log populate step high low / log10 N / : i 1 N range x i el low 10 step i *^* : for x 41 line :

Optimiz => numeric Tlogpts i 1 p rows range u i el p i el : ρ i el p i el Tbar eval : 21 line for u ρ augment 21 line :

Water saturation temperature °C <= p[bar]

1 99.6 + 40 green 1 5 mat Tlogpts XY 3 1 sys