Utilities

3e87838f-4349-4a10-b3a7-869753050035 87 6 5 decimal

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

data char size clr plot 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 :

3 appVersion 0.98.6179 ≡ Created jmG, 2018_10_17 ≡ 21 line

NBS fixed points Monograph 125

-------------------------------------

Helium NBP -268.935

Hydrogen TP -259.340

Hydrogen NBP -252.870

Neon TP -248.595

Neon NBP -246.048

Oxygen TP -218.789

Nitrogen TP -210.002

Nitrogen NBP -195.802

Oxygen NBP -182.962

Carbon Dioxide SP -78.476

Mercury FP -38.862

Ice Point 0.00

Ether TP 26.87

Water BP 100.00

Benzoic TP 122.37

Indium FP 156.634

Tin FP 231.9681

Bismuth FP 271.442

Cadmium FP 321.108

Lead FP 327.502

Mercury BP 356.66

Zinc FP 419.580

Sulfur BP 444.674

Cu-Al FP 548.23

Antimony FP 630.74

Aluminum FP 660.37

Silver FP 961.93

Gold FP 1064.43

Copper FP 1084.5

]]>

T 6.2563 - 268.935 - 6.2292 - 259.34 - 6.1977 - 252.87 - 6.1536 - 246.048 - 5.873 - 218.789 - 5.7533 - 210.002 - 5.5356 - 195.802 - 5.3147 - 182.962 - 2.7407 - 78.476 - 1.4349 - 38.862 - 00 1.0679 26.87 4.2773 100 5.3414 122.37 7.0364 156.634 11.0133 231.9681 13.2188 271.442 16.0953 321.108 16.4733 327.502 18.2179 356.66 202 mat :

J 8.0957 - 210.002 - 7.7963 - 195.802 - 7.4807 - 182.962 - 3.7187 - 78.476 - 1.9063 - 38.862 - 00 1.3739 26.87 5.2677 100 6.4886 122.37 8.3743 156.634 12.5517 231.9681 14.7427 271.442 17.4928 321.108 17.8462 327.502 19.456 356.66 22.9259 419.58 24.3123 444.674 30.1095 548.23 34.9108 630.74 36.6933 660.37 55.669 961.93 61.716 1064.43 62.880 1084.5 232 mat :

NBP NormalBoilingPoint ≡ TP TriplePoint ≡ SP SublimationPoint ≡ BP BoilingPoint ≡ FP FreezingPoint ≡ 51 line

Part 1: Popular Segments [low cryogenic omitted]

XY T 519 range 12 range el :

Popular Segments:

Both fitting functions were done Mathcad 11 [2003].

They were done from MCD GenfitMatrix Padé rational ,

then converted to J-Frac continued fractions.

]]>

X XY 1 col : Y XY 2 col : T T . 12 black plot : 31 line

x c 1 5.873 - x ≤ cases :

x T356 1579.4 42563.52 x 0.2335992 + 1757.435 x 104.3645 + 11790.76 x 69.55679 - 2.041063 x 7.885124 + / + / + / - / - :

T x T356 x c * 5.873 - 218.789 - + 30 blue 1 5 mat 3 1 sys

Mutual conformity @ NBS fixed points δ i 1 XY rows range Δ i el Y i el X i el T356 - 2 round eval : for X Y Δ augment 21 line :

δ 5.873 - 218.789 - 0.27 - 5.7533 - 210.002 - 0.02 - 5.5356 - 195.802 - 0.04 5.3147 - 182.962 - 0.03 - 2.7407 - 78.476 - 0.01 - 1.4349 - 38.862 - 0.04 00 0.04 - 1.0679 26.87 0 4.2773 100 0.02 5.3414 122.37 0 7.0364 156.634 0.02 - 11.0133 231.9681 0.01 13.2188 271.442 0 16.0953 321.108 0 16.4733 327.502 0153 mat

XY J 223 range 12 range el :

X XY 1 col : Y XY 2 col : J J . 12 black plot : 31 line

x c 1 7.4807 - x ≤ cases :

x J1064 0.04538168 x * 12.91152 + 98.28046 x 35.55858 + 96.40391 x 563.9309 + 369377.4 x 649.2875 - 6.649292 x 12.6438 + / - / + / + / + :

x J1064 x J1064 x * :

J x J1064 x c * 7.4807 - 182.962 - + 30 blue 1 5 mat 3 1 sys

Mutual conformity @ NBS fixed points δ i 1 XY rows range Δ i el Y i el X i el J1064 - 3 round eval : for X Y Δ augment 21 line :

δ 7.7963 - 195.802 - 0.263 - 7.4807 - 182.962 - 0.036 3.7187 - 78.476 - 0 1.9063 - 38.862 - 0000 1.3739 26.87 0 5.2677 100 0.001 6.4886 122.37 0.002 8.3743 156.634 0.002 12.5517 231.9681 0.003 - 14.7427 271.442 0.003 - 17.4928 321.108 0.001 - 17.8462 327.502 0.001 - 19.456 356.66 0.004 22.9259 419.58 0.013 24.3123 444.674 0.012 30.1095 548.23 0.022 - 34.9108 630.74 0.004 - 36.6933 660.37 0.024 55.669 961.93 0.032 - 61.716 1064.43 0.146 62.88 1084.5 0.116 - 223 mat

Note: Both fixed points [Gold, Copper] are undetermined

NBS Monograph 125 wrt to 'J' . They are just reference.

'J' fit was done Mathcad 11 [2003]. => GenfitMatrix.

This rational fraction passes very closely to the fixed points.

]]>

Part 2:

Hyperfit type 'T' thermocouple

Utilities

data char size clr plot 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 :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

T 6.25629 - 268.935 - 6.22919 - 259.34 - 6.19773 - 252.87 - 6.17138 - 248.595 - 6.15358 - 246.048 - 5.87302 - 218.789 - 5.75328 - 210.002 - 5.53559 - 195.802 - 5.31472 - 182.962 - 2.7407 - 78.476 - 1.43494 - 38.862 - 1.0679 26.87 4.2773 100 5.3414 122.37 7.0364 156.634 11.0133 231.9681 13.2188 271.442 16.0953 321.108 16.4733 327.502 18.2179 356.66 202 mat :

X T 1 col : Y T 2 col : n T rows : 31 line

The 'T' hyperfit is reduction technique. The point [0,0] is removed from the fixed. Immaterial for the suite of x*Tr(x,β) [plot, conformity, on-line calculations]

Treduced X Y X / vectorize augment :

jmG Mathcad DAEP [2003] β 25.8149913045858 12.7668104944864 - 1.25727409574702 3.04185012250532 0.611123673599964 0.040154623061311 0.0006438455716873 0.46562548019054 - 0.030977484107051 0.119835340769071 0.027040212533505 0.002100716189884 0.0000488329299122 131 mat :

Treduced o 4 black plot

roundOFF β β 13 round vectorize :

fit to the reduced data set.
Normalized Padé rational 6/6.
RoundOFF wisely ... rational
are sensitive to true decimals x β Tr β 1 el β 2 el x * + β 3 el x 2^* + β 4 el x 3^* + β 5 el x 4^* + β 6 el x 5^* + β 7 el x 6^* + 1 β 8 el x * + β 9 el x 2^* + β 10 el x 3^* + β 11 el x 4^* + β 12 el x 5^* + β 13 el x 6^* + / :

reverse the fit to the original data set x β f x x β Tr * :

Mutual conformity @ NBS fixed points δ i 1 T rows range Δ i el Y i el X i el β f - 3 round eval : for X Y Δ augment 21 line :

x c 1 6.25629 - x ≤ cases :

0 β f 0

Rational fraction to Type 'T' T/C, NBS Monograph 125

T . 12 black plot x β f x c * 2 1 sys

sanity cryogenic X 1 el β f 268.936 -

Δelta X δ 3 col augment : stem Δelta Error : bar Δelta 0.075 BarSize : datum X 0 Y * . 12 black plotG : 41 line

0 stem datum 3 1 sys

β 15 D 0 0.001 0.003 - 0.001 0.003 0.001 - 0.005 - 0.001 0.004 0.004 - 0.002 0 0.003 - 0 0.004 0.004 0.004 - 0.003 0.002 0.007 - 201 mat

δ 6.2563 - 268.935 - 0.001 6.2292 - 259.34 - 0.001 6.1977 - 252.87 - 0.003 - 6.1714 - 248.595 - 0.001 6.1536 - 246.048 - 0.003 5.873 - 218.789 - 0.001 - 5.7533 - 210.002 - 0.005 - 5.5356 - 195.802 - 0.001 5.3147 - 182.962 - 0.004 2.7407 - 78.476 - 0.004 - 1.4349 - 38.862 - 0.002 1.0679 26.87 0 4.2773 100 0.003 - 5.3414 122.37 0 7.0364 156.634 0.004 11.0133 231.9681 0.004 13.2188 271.442 0.004 - 16.0953 321.108 0.003 16.4733 327.502 0.002 18.2179 356.66 0.007 - 203 mat

More statistical insight

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 n sum : 0.000208

χ X Mean : μ Y Mean : n T rows : 31 line

χ μ n 31 mat 1.754059 14.306345 - 2031 mat

Pearson’s correlation coefficient corr X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / / : 0.9999999

correlation between [X,Y data]

correlation between [X,fitted model]

X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / 21 mat 0.986337977 0.98633812 21 mat

Part 3:

Ultimate 'J' fit

'c' normalised coefficients

c 19.8518394369938 3.39708430077966 0.052276519294839 8.91649190043396 103 -^* - 9.92828185332406 105 -^* 8.38053206800752 106 -^* 3.1464248690302 107 -^* - 4.25243756863902 109 -^* 2.07174891774966 1011 -^* - 0.183112912617708 3.87083881009766 103 -^* 5.08713285834413 104 -^* - 2.26745307368593 106 -^* 6.6275111583499 107 -^* 2.21691344604783 108 -^* - 2.87497042511128 1010 -^* 1.36525976453514 1012 -^* - 171 mat :

x J1084 x 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^* + c 7 el x 6^* + c 8 el x 7^* + c 9 el x 8^* + 1 c 10 el x * + c 11 el x 2^* + c 12 el x 3^* + c 13 el x 4^* + c 14 el x 5^* + c 15 el x 6^* + c 16 el x 7^* + c 17 el x 8^* + / * :

X J 1 col : Y J 2 col : J J . 12 black plot : 31 line

Mutual conformity @ NBS fixed points ΔJ1084 X Y Y X J1084 - (vectorize 3 round vectorize augment :

ΔJ1084 8.0957 - 210.002 - 0 7.7963 - 195.802 - 0 7.4807 - 182.962 - 0 3.7187 - 78.476 - 0 1.9063 - 38.862 - 0000 1.3739 26.87 0 5.2677 1000 6.4886 122.37 0 8.3743 156.634 0 12.5517 231.9681 0 14.7427 271.442 0.001 17.4928 321.108 0 17.8462 327.502 0 19.456 356.66 0 22.9259 419.58 0 24.3123 444.674 0 30.1095 548.23 0 34.9108 630.74 0 36.6933 660.37 0 55.669 961.93 0 61.716 1064.43 0 62.88 1084.5 0233 mat

x c 1 8.0957 - x ≤ (x 62.88 ≤ (& cases :

J x J1084 x c * 2 1 sys

Calibrate the mV/I converter

XmV 100 - :

XmV °C ≡

mV 1 :

mV J1084 XmV - mV 5 - 4 - solve mV 4.6322 -

Low range: -100°C => -4.6322 mV

4.6309 - J1084 99.97 -

XmV 200 :

XmV °C ≡

mV 1 :

mV J1084 XmV - mV 020 solve mV 10.7765

High range: 200°C => 10.7765 mV

10.7768 J1084 200

'J'cryogenic [-210.002...26.87] 'T'cryogenic [-268.935...26.87

Part 4: =>

x Jcryo 2319.64 286005.3 x 123.8632 + 5.737392 x 10.21686 + / - / - :

J J 17 range 12 range el :

J 8.0957 - 210.002 - 7.7963 - 195.802 - 7.4807 - 182.962 - 3.7187 - 78.476 - 1.9063 - 38.862 - 00 1.3739 26.87 72 mat

X J 1 col : Y J 2 col : 21 line

Jcryo J . 12 black plot :

x c 1 8.0957 - x ≤ cases :

Jcryo x Jcryo x c * 2 1 sys

Mutual conformity @ NBS fixed points ΔJcryo X Y Y X Jcryo - (vectorize 2 round vectorize augment :

ΔJcryo 8.0957 - 210.002 - 0.02 - 7.7963 - 195.802 - 0.07 7.4807 - 182.962 - 0.05 - 3.7187 - 78.476 - 0.02 1.9063 - 38.862 - 0.02 - 00 0.08 - 1.3739 26.87 073 mat

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

T T 112 range 12 range el :

x Tcryo 18.41415 x * 76.66062 + 791.578 x 10.35533 + 0.1977402 x 6.656865 + 0.005441432 x 6.30942 + / - / - / - :

X T 1 col : Y T 2 col : 21 line

Tcryo T . 12 black plot :

Mutual conformity @ NBS fixed points ΔTcryo X Y Y X Tcryo - (vectorize 2 round vectorize augment :

x c 1 6.2563 - x ≤ cases :

ΔTcryo 6.2563 - 268.935 - 0 6.2292 - 259.34 - 0.02 6.1977 - 252.87 - 0.06 - 6.1714 - 248.595 - 0 6.1536 - 246.048 - 0.04 5.873 - 218.789 - 0.01 5.7533 - 210.002 - 0.03 - 5.5356 - 195.802 - 0.01 - 5.3147 - 182.962 - 0.03 2.7407 - 78.476 - 0.02 - 1.4349 - 38.862 - 0.02 1.0679 26.87 0123 mat

Tcryo x Tcryo x c * 2 1 sys

About this document . . .

1. You will read all sorts of empirical jargon from literature [outdated, repeated, not CAS].

This document is a project guide . Many more types T/C exist, not explored.

All in all, T, J cover most industrial processes. If you need down to absolute '0', you may

consider cryogenic sensors in that particular short low range, eventually RTD Pt100.

2. This document exemplifies fitting the NBS fixed points. For an accurate measurement

from T/C suppliers, you would need to simulate fixed points from thermal bath and run the

Mathcad GenfitMatrix of which the core algorithm is the built-in genfit(X,Y,guesses,F)

where X,Y are the data set, and F the model function. Unfortunately and up todate, such

an algorithm is not available yet in Smath. If not from public, will have to be user coded.

]]>

Part 5: => Prefered 'J' [-210.002 ... 500 °C]

Genfit Utilities

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

data char size clr plot 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 :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

Applicable parts are: Optimiz "numeric" XY f φ β Minimize X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line :

Vector gradient ... Optimiz Symbolic x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

XY 8.0957 - 210.002 - 7.7963 - 195.802 - 7.4807 - 182.962 - 3.7187 - 78.476 - 1.9063 - 38.862 - 00 1.3739 26.87 5.2677 100 6.4886 122.37 8.3743 156.634 12.5517 231.9681 14.7427 271.442 17.4928 321.108 17.8462 327.502 19.456 356.66 22.9259 419.58 24.3123 444.674 172 mat :

Padé rational fraction
..... NORMALIZED .....
leading 1 in denom x β f β 1 el β 2 el x * + β 3 el x 2^* + β 4 el x 3^* + β 5 el x 4^* + 1 β 6 el x * + β 7 el x 2^* + β 8 el x 3^* + / :

t0 1 time :

conjugate gradient x β φ x β f 8 φ :

0.5 - 20 1.5 - 0.05 0.01 00081 mat

X XY 1 col : Y XY 2 col : n XY rows : 31 line

3 appVersion 0.98.6179 ≡ Timing 17 sec ≡ 21 line

β β 1 el 0.5 - 20 1.5 - 0.05 0.01 00081 mat : iter 13 : i 1 : i iter ≤ β i 1 + el XY f φ β i el Minimize : i i 1 + : 21 line while β β iter el : 51 line :

β β :

β 0.022892692 19.863847509 2.921904294 0.154170228 0.005263643 0.159363729 0.00876669 0.000280425 81 mat

1 time t0 - 20 s *

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 n sum : 0.02

Normalized rational Padé converted to continued J_Fraction [Maple]. x J 18.770251 x * 37.025038 - 910.027136 x 3.85542 + 317.453992 x 17.936706 + 24.686096 x 9.470053 + / - / + / + :

FIT U 8.1 - 308 - range : i 1 U rows range vy i el U i el J eval : for U vy augment 31 line :

Mutual conformity @ NBS fixed points δ i 1 XY rows range Δ i el Y i el X i el J - 2 round eval : for X Y Δ augment 21 line :

Δelta X δ 3 col 2000 * augment : bar Δelta 0.075 BarSize : data XY . 12 black plot : 31 line

δ 8.0957 - 210.002 - 0.02 - 7.7963 - 195.802 - 0.06 7.4807 - 182.962 - 0.05 - 3.7187 - 78.476 - 0.02 1.9063 - 38.862 - 0.01 00 0.02 - 1.3739 26.87 0.02 - 5.2677 100 0.02 6.4886 122.37 0.03 8.3743 156.634 0.02 12.5517 231.9681 0.04 - 14.7427 271.442 0.05 - 17.4928 321.108 0 17.8462 327.502 0.01 19.456 356.66 0.05 22.9259 419.58 0.05 24.3123 444.674 0.06 - 173 mat

Type 'J' Thermocouple fit to NBS Monograph 125

bar FIT data 3 1 sys Convert Continued fraction

Define Symbolic ... Optimiz = NONE x collect x β f confrac x convert evalf maple :

Construct the J_Fraction

Optimiz NONE x collect 469256269 x * 25000000 / 2314064876250000 / - 18200542712000000 x 38554202831000000000 / + 126981597400000 x 1793670581100000000 / + 123430479750000000 x 2367513327250000000 / + (* / - (* / + (* / +

The procedure => 'J' [-210.002 ... 500 °C]

. . . suggests that if you have bath tested the fixed points,

it might be possible to evaluate the β's ... thus, personalized

the concerned 'J' T/C for high accuracy.

]]>

At the triple point [0.01 °C], all three phases can coexist.

Water critical point : However, the liquid-vapor boundary

terminates in an endpoint at some critical temperature Tc and

critical pressure pc. This is the critical point.

In water, the critical point occurs at around

647 K (374 °C ) and 22.064 MPa (3200 psia or 218 atm)

]]>

Sub-Cryogenic sensor CY7

]]> plot(data,char,size,clr) ... CY7

Universal version  [Smath 6179]. It supports "data" sets from 
source ... data sets subject to be decimated from auxilliary
module Decimate(data,n)... reasonably fast on primitive PC. data char size clr plot 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 :

CY7 1.6981 1.4 1.5978 5 1.4201 10 1.3042 15 1.2144 20 1.1246 25 1.0705 50 0.9956 90 0.9338 120 0.8687 150 0.7555 200 0.6384 250 0.5189 300 0.3978 350 0.2746 400 0.1498 450162 mat :

Suggested renovation CY7 ============================

x cry_1 20.36985 x * - 31.19133 + 3.890508 x 0.935192 - 0.001116245 x 1.099057 - / + / + :

break 1.1246 ≡

support CY7 o 5 black plot :

x cry_2 380 x * - 546.8 + 57 x 1.5 - 0.2 x 2 - 0.04 x 1 - 5 x 1 - / + / - / + / + :

x c1 1 1.1246 x ≤ (x 1.75 ≤ (& cases :

x c2 10 x ≤ (x 1.1246 ≤ (& cases :

x cry_1 x c1 * x cry_2 x c2 * 1.1246 100 1.1246 100 - 2 2 mat support 1.1246 25 o 25 black 1 5 mat 5 1 sys

1.1246 cry_1 1.1246 cry_2 21 mat 25.0 25.0 21 mat

Comment . . .

The phenomenon behaves like discontinuous.

As published, high order Chebychev Omega aren't

much inspiring ... [handling, computation load].

Rational fraction is a good candidate for interpolating

each segment. In this proposal, we consider the break

point as an Act of God . More information might help

to conclude/renovate this type of low cryogenic sensor.

]]>

XY 1.3042 15 1.2144 20 1.1246 25 1.0705 50 0.9956 9052 mat :

β 11.94 13.831 1.155 0.089 41 mat :

model to smooth
the break region x β f β 1 el β 2 el x β 3 el - (β 4 el / - exp * + :

XY XY o 5 black plot : x m 1 0.975 x ≤ (x 1.5 ≤ (& cases : 21 line

x cry_1 x c1 * x cry_2 x c2 * x β f 1.1246 100 1.1246 100 - 2 2 mat support 1.1246 25 o 25 black 1 5 mat 6 1 sys x cry_1 x c1 * x cry_2 x c2 * x β f 1.1246 100 1.1246 100 - 2 2 mat support 1.1246 25 o 25 black 1 5 mat 6 1 sys

jct x cry_2 x β f - 0 ≡ x 1.0625 1.125 solve : 1.097816

jct x cry_1 x β f - 0 ≡ x 1.125 1.25 solve : 1.183984

possible CY7 0 °K extrapolation x cry_1 0 ≡ x 1.7 1.85 solve 1.7618

x CY7 x cry_2 0 x ≤ (x 1.097816 ≤ (& x β f 1.097816 x ≤ (x 1 ≤ (& x cry_1 cases :

jct 1.097816 1.183984 21 mat :

CY7 1.6981 1.4 1.5978 5 1.4201 10 1.3042 15 1.2144 20 1.1246 25 1.0705 50 0.9956 90 0.9338 120 0.8687 150 0.7555 200 0.6384 250 0.5189 300 0.3978 350 0.2746 400 0.1498 450162 mat

x m 10 x ≤ (x 1.7 ≤ (& cases :

1.7618 CY7 0

1.098 100 1.098 100 - 2 2 mat x CY7 x m * 1.191 100 1.191 100 - 2 2 mat support 4 1 sys

Read more . . .

I'm not aware of industrial process in the sub-cryogenic of Pt 100 [13.8 °K, -259.3467 °C] .

To meet the demand starting ~ 1 °K, @ best accuracy on longer range, a dual installation is

recommanded ... CY7 switching around 20 °K to Pt 100. No more detail about installation.

This technical suggestion is subject to project requirements.

]]>

Forward voltage [V]
Temperature [°K] V CY7 1 col : K CY7 2 col : 21 sys

conformity i 1 V rows range cy7 i el V i el CY7 eval : for V K K cy7 1 round vectorize - augment 21 line :

conformity 1.6981 1.4 0.3 - 1.5978 5 0.5 1.4201 10 0.2 - 1.3042 150 1.2144 20 0.1 1.1246 250 1.0705 50 1.6 - 0.9956 90 2.5 0.9338 120 3.7 0.8687 150 3.8 0.7555 200 3.2 0.6384 250 2.3 0.5189 300 1.4 0.3978 350 0.8 0.2746 4000 0.1498 450 0.8 - 163 mat

0.29 - 0.5 0.23 - 0.01 - 0.08 0.03 0.18 71 mat

x L - (U x - (- U L - (/

CY7 CY7 17 range 12 range el :

Possible reconciliation CY7

That two [2] ChebyShev have to cover such a small range [2K .. 24.5 K]

is a strict indication of poorly collected data or CY7 not reflecting the

physics of this subcryogenic range. To conclude CY7, up to better

experimental CY7 data => switch CY7 to Pt100 or type 'T'

@ either 1.2144 or 1.2146 and ignore the upper CY7 [°K]

]]>

Forward [V]
... [°K]... V CY7 1 col : K CY7 2 col : 21 sys

CY7 1.6981 1.4 1.5978 5 1.4201 10 1.3042 15 1.2144 20 1.1246 25 1.0705 5072 mat

This subcryo CY7 function flies in the blue @  'x' ≤ 1.1246 x sub_CY7 20.36985 x * - 31.19133 + 3.890508 x 0.935192 - 0.001116245 x 1.099057 - / + / + :

determine the switch point ITS x sub_CY7 13.8033 - 0 ≡ x 1.3 1.4 solve : 1.330705

sub-range to sub_CY7(x)
proposed switch => Pt100
exclusive region of sub_CY7(x) sub CY7 o 5 black plot : switch 1.2144 1.2144 sub_CY7 + 100 blue 15 mat : exclusive 1.09755 37.5 o 60 green 15 mat : 31 sys

x c 1 1.1246 x ≤ (x 1.6981 ≤ (& cases :

sub-cryogenic CY7 ... switch @ 1.2144 = 20 °K [-253.15 °C]

sub x sub_CY7 x c * switch exclusive 4 1 sys

K V sub_CY7 vectorize - 0.29 - 0.5 0.23 - 0.01 - 0.08 0.03 0.18 71 mat

°Kelvin ITS sub_CY7 1.1246 sub_CY7 21 mat 13.8 24.97 21 mat

type 'T' 268.935 - (°C * 4.215 K *

248.5939 - (°C * 24.5561 K *

13.8033 K * 20 K * 21 mat °C 259.3467 - 253.15 - 21 mat

°C ITS_1990 259.3467 - 248.5939 - 218.7916 - 189.3442 - 38.8344 - 0.01 29.7646 156.5985 231.928 419.527 660.323 961.78 121 mat TP Hydrogen TP Neon TP Oxygen TP Argon TP Mercury TP Water MP Gallium FP Indium FP Tin FP Zinc FP Aluminum FP Silver 121 mat 12 mat ≡

ITS_1990 Bible points

The triple points of several substances are used to define points

in the ITS-90 international temperature scale, ranging from the

triple point of hydrogen (13.8033 K) . . . -259.3467 °C

to the triple point of water (273.16 K, 0.01 °C, or 32.018 °F)

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