<p> Utilities </p>

069cb92d-176a-457f-8b7a-0464826de935 80 4 5 decimal

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

<p> Utilities </p>

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 :

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

Platinum resistance thermometre Pt100

The Platinum Thermometer was left undone after Le Châtelier [1887]. Since, it was not recognised the relation Wr vs °C was simply the XFR [Transfer Function]. The reader may want to consult the BIPM [Bureau International des Poids et Mesures] and inspect the two polynomial segments from which the Wr's are calculated ±.

http://bibli.ec-lyon.fr/exl-doc/patrimoine/11944V01/11944V01.pdf On ne pourra jamais déclarer les Wr du thermomètre théorique à résistance de platine; d'une part inférant à l'incertitude des mesures, d'autre part concluant le canevas résolvant. En d'autres mots: les Wr ne pourront que refléter la coïncidence résolvante. Dans les faits, le thermomètre théorique à résistance de platine n'existe pas par privation de la nature de se reproduire elle-même exactement et infiniment au grès de la transformation de l'homme. La nature ne donne le platine que sous forme de pépite ou par extraction. Le Créateur a donné la température [état et sensation physique] mais pas le thermomètre.

Pt100: Wr [Ω] vs temperature [t °C] t Wr Z K.p 1 α β α - (/ t 259.3467 + (- α K.p * / exp * + β β α - (/ t 259.3467 + (- β K.p * / exp * - (* + :

Wr_Pt100

Maple reflexive solver. The Maple root argument will be passed  to Smath Sol(w,t).
Given  [t °C]  from lab thermal bath, will solve for 'w', providing the thermal bath 
is itself at least equivalent to a secondary standard of ITS 90.  This direction of
experiment will enable checking the reading of the control room equipment. w sol t Wr w - t root :

w sol Z β α - (* K.p β α 1 - 259346710000 t * + 10000 α * K.p * / - exp + (* + β 259346710000 t * + 10000 β * K.p * / - exp * - (* + w β α - (* - β α - / t root

eit90 259.3467 - 0.0011907 248.5939 - 0.00844974 218.7916 - 0.09171804 189.3442 - 0.21585975 38.8344 - 0.84414211 0.01 1.0000000 29.7646 1.11813889 156.5985 1.60980185 231.928 1.89279768 419.527 2.56891730 660.323 3.37600860 961.78 4.28642053 122 mat :

Z 0.0009996 : K.p 12.4435128 : α 1.7276022 : β 228.3303460 : 41 line

°Ceit90 eit90 1 col : Wr eit90 2 col : 21 line

Enter temperature (°C) => °C 200 :

Ω °C Wr : 1.7779

on-line interpolate °C Ω 12 mat 200 1.7779 12 mat

t Pt100 259.3467 - t ≤ (t 961.78 ≤ (& t Wr NOT eit90 if :

Pt100 is not the best candidate for the lower cryogenic range. Besides "specific cryogenic" TC type 'T' is a good choice for Industrial Processing Plants.

vy i 1 U rows range y i el U i el Wr : for y 21 line :

L 259.3467 - : H 961.78 : N 1221 : U L H N xd : 41 line

The elegant/convenient Smath "Plot creator" ... pretty smart ! Ωr U vy augment : data °Ceit90 Wr augment o 7 blue plotG : Title 0 3.875 Resistance Thermometre Pt100 14 black 15 mat : m°C 375 0.35 Measured °C 12 black 15 mat : ΩrXFR 42 - 2.375 Ωr(°C) 12 black 15 mat : t_Ω °C Ω + 20 green 15 mat : 61 line

Plot arguments plot data Ωr t_Ω Title m°C ΩrXFR 256 - 325632563 °C Ω 42 mat 71 sys :

plot

°C Ω 12 mat 200 1.7779 12 mat

Z 0.0009996 ≡ K.p 12.4435128 ≡ α 1.7276022 ≡ β 228.3303460 ≡ 41 line

Z K.p 1 α β α - (/ t 259.3467 + (- α K.p * / exp * + β β α - (/ t 259.3467 + (- β K.p * / exp * - (* +

User units °C 1 : Ω 1 : 21 line

User unit system: copy/paste argument <= in the empty place holder of result.

The reflexive solvers

RHS of sol(w) Z β α - (* K.p β α 1 - 259346710000 t * + 10000 α * K.p * / - exp + (* + β 259346710000 t * + 10000 β * K.p * / - exp * - (* + w β α - (* - β α - /

... simplified β α - (Z w - (* K.p β 1259346710000 t * + 10000 β * K.p * / - exp - (* α 1 - 259346710000 t * + 10000 α * K.p * / - exp + (* + (* + β α - /

w t argument β α - (Z w - (* K.p β 1259346710000 t * + 10000 β * K.p * / - exp - (* α 1 - 259346710000 t * + 10000 α * K.p * / - exp + (* + (* + β α - / :

Solving for (t), given (w)... Roots(range) => 0,t,-260,970
For the point -259.3467: initialise [0,t,-265,-255] 
... Σ, divide by 2 ... -259.33 w t Sol w t argument 0 ≡ t 260 - 970 solve :

260.7 - 257.96 - 21 mat 2 / sum 259.33 -

4.2864505 t Sol °C 961.78

Solving for (w), given (t)... Roots(range)  => 0,w,-1,5 w t Sol w t argument 0 ≡ w 1 - 5 solve :

w 259.3467 - Sol Ω 0.0009996

From the data matrix, the corresponding columns wrt the reflexive solver are: ..... col<1> and col<3>. ..... Sol(col<3>,t) ... w => t ..... Sol(w,col(1>) ... w <= t

°C_wr 259.3467 - 0.0011907 0.0009996 0.0001911 248.5939 - 0.0084497 0.0110234 0.0025737 - 218.7916 - 0.091718 0.0982121 0.006494 - 189.3442 - 0.2158598 0.2149336 0.0009261 38.8344 - 0.8441421 0.8424528 0.0016893 0.01 1 0.9999903 0.0000097 29.7646 1.1181389 1.1192165 0.0010776 - 156.5985 1.6098018 1.6136646 0.0038627 - 231.928 1.8927977 1.8970493 0.0042516 - 419.527 2.5689173 2.5709767 0.0020594 - 660.323 3.3760086 3.3732862 0.0027224 961.78 4.2864205 4.2864505 0.00003 - 124 mat :

Explain "sanity"

Here, 'w' are the 'Wr' calculated from formula Wr(t). In 'sanity', we re-inject those values in the solver Sol(w,t), collect those values and express the Δt vs eit90. Remember how the first cryogenic -259.33 is calculated and fetched in the sanity program module. The conformity of our formula Wr(t) is stricking of realism wrt BIPM eit90 !

Pt100 formula from which the 'wr' were calculated, re-injected in "sanity" t Wr Z K.p 1 α β α - (/ t 259.3467 + (- α K.p * / exp * + β β α - (/ t 259.3467 + (- β K.p * / exp * - (* + ≡

w t Sol w t argument 0 ≡ t 260 - 970 solve :

Sanity Δt vs eit90 Δt w °C_wr 3 col : T 1 el 259.33 - : i 212 range T i el w i el t Sol : for °C_wr 1 col T - 41 line :

Δt 0.017 - 00000000000121 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 ≡

Note to the user:

This Smath document gives the Pt100 on the total 'eit90'. No matter how much maths you may invent wrt this formulation or else formulation, on the overall eit90, two points are known to 2 decimals. Therefore, only two decimals of mutual conformity can be expected. ____________________________________________ This scientific document accounts on 3 contributions: 1. The Pt100 formulation ..... Wr(t) [jmGiraud] 2. The Maple ................. root(Wr(t)-w,t) 3. The Smath reflexive solver Sol(w,t). ____________________________________________ Observe that Sol(w,t) is simply the Maple "root" converted in Smath executable code.

jmGiraud: 20161104