Thermocouple emf reference functions
Project description
Python module containing calibration data and lookup functions for standard thermocouples of types B, C, D, E, G, J, K, M, N, P, R, S, T, and some less standard types too.
Usage and examples
Below, the first computation shows that the type K thermocouple emf at 42 °C, with reference junction at 0 °C, is 1.694 mV (compare to NIST table); the second calculation shows how passing in an array applies the function for each element, in the style of numpy:
>>> from thermocouples_reference import thermocouples >>> typeK = thermocouples['K'] >>> typeK <Type K thermocouple reference (270.0 to 1372.0 degC)> >>> typeK.emf_mVC(42, Tref=0) 1.6938477049901346 >>> typeK.emf_mVC([3.14159, 42, 54], Tref=0) array([0.12369326, 1.6938477 , 2.18822176])
An inverse lookup function is provided that you can use to get a temperature out of a measured voltage, including cold junction compensation effects. If we put our type K thermocouple into a piece of spam and we read 1.1 mV, using our voltmeter at room temperature (23 °C), then the spam is at 50 °C. [1]
>>> typeK.inverse_CmV(1.1, Tref=23.0) 49.907928030075773 >>> typeK.emf_mVC(49.907928030075773, Tref=23.0) # check result 1.1000000000000001
The functions are called emf_mVC and inverse_CmV just to remind you about the units of voltage and temperature. Other temperature units are supported as well:
Temperature unit  EMF lookup  Inverse lookup 

degrees Celsius  .emf_mVC  .inverse_CmV 
degrees Fahrenheit  .emf_mVF  .inverse_FmV 
kelvins  .emf_mVK  .inverse_KmV 
degrees Rankine  .emf_mVR  .inverse_RmV 
You can also compute derivatives of the emf function. These are functional derivatives, not finite differences. The Seebeck coefficients of chromel and alumel differ by 42.00 μV/°C, at 687 °C:
>>> typeK.emf_mVC(687,derivative=1) 0.041998175982382979
Data sources
Readers may be familiar with thermocouple lookup tables (example table). Such tables are computed from standard reference functions, generally piecewise polynomials. [2] This module contains the source polynomials directly, and so in principle it is more accurate than any lookup table. Lookup tables also often also include approximate polynomials for temperature lookup based on a given compensated emf value. Such inverse polynomials are not included in this module; rather, the inverse lookup is based on numerically searching for a solution on the exact emf function.
For any thermocouple object, information about calibration and source is available in the repr() of the .func attribute:
>>> typeK.func <piecewise polynomial+gaussian, domain 270.0 to 1372.0 in degC, output in mV; ITS90 calibrated, from NIST SRD 60, type K>
The data sources are:
 Types B, E, J, K, N, R, S, T use coefficients from NIST’s website, and are calibrations to the ITS90 scale. [3]
 Types G, M, P, and nonlettered types Au/Pt, Au/Pd, AuFe 0.07, IrRh 40/0, PtMo 5/0.1, PtRh 40/20 use coefficients from ASTM E 175100 and are calibrations to ITS90.
 Types C, D [4] use coefficients found from a publication of OMEGA Engineering Inc., and are calibrations to IPTS68 scale. [5]
Graphs of functions (if you don’t see anything, see low temperature types here, intermediate temperature types here, and high temperature types here):
Requirements
 numpy
 scipy (optional, only needed for inverse lookup)
 python2 or python3 languages
Installation
Recommended installation is via pip. First, install pip. Then:
pip install thermocouples_reference user
(Remove the user option if you are superuser and want to install systemwide.)
Disclaimer
This module is provided for educational purposes. For any realworld process, I strongly recommend that you check the output of this module against a known good standard.
I make no warranties as to the accuracy of this module, and shall not be liable for any damage that may result from errors or omissions.
[1]  This is the optimal temperature for spam. Always make sure your spam reads around 1.1 millivolt and you’ll have a tasty treat. 
[2]  A notable exception is NIST’s type K curve which uses a polynomial plus gaussian. The gaussian conveniently captures a wiggle in the Seebeck coefficient of alumel, that happens around 130 °C. 
[3]  The ITS90 value T_{90} is believed to track the true thermodynamic temperature T very closely. The error T − T_{90} is quite small, of order 0.01 K for everyday conditions (up to about 200 °C), rising to around 0.05 K up at 1000 °C, and increasing even further after that. See Supplementary Information for the ITS90. Generally your thermocouple accuracy will be more limited by manufacturing variations and by degradation of the metals in the thermal gradient region. 
[4]  An extra type G IPTS68 curve from the same source is available in thermocouples_reference.source_OMEGA.thermocouples. The type G in the main thermocouples_reference.thermocouples contains the ASTM curve which is ITS90 calibrated. 
[5]  IPTS68 reads higher than ITS90 by about 1 °C at high temperatures around 2000 °C. See Supplementary Information for the ITS90 (specifically Fig. 5 in the Introduction) for more information about the difference. 
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