thermo.temperature module

thermo.temperature.T_converter(T, current, desired)[source]

Converts the a temperature reading made in any of the scales ‘ITS-90’, ‘ITS-68’,’ITS-48’, ‘ITS-76’, or ‘ITS-27’ to any of the other scales. Not all temperature ranges can be converted to other ranges; for instance, ‘ITS-76’ is purely for low temperatures, and 5 K on it has no conversion to ‘ITS-90’ or any other scale. Both a conversion to ITS-90 and to the desired scale must be possible for the conversion to occur. The conversion uses cubic spline interpolation.

ITS-68 conversion is valid from 14 K to 4300 K. ITS-48 conversion is valid from 93.15 K to 4273.15 K ITS-76 conversion is valid from 5 K to 27 K. ITS-27 is valid from 903.15 K to 4273.15 k.

Parameters:

T : float

Temperature, on current scale [K]

current : str

String representing the scale T is in, ‘ITS-90’, ‘ITS-68’, ‘ITS-48’, ‘ITS-76’, or ‘ITS-27’.

desired : str

String representing the scale T will be returned in, ‘ITS-90’, ‘ITS-68’, ‘ITS-48’, ‘ITS-76’, or ‘ITS-27’.

Returns:

T : float

Temperature, on scale desired [K]

Notes

Because the conversion is performed by spline functions, a re-conversion of a value will not yield exactly the original value. However, it is quite close.

The use of splines is quite quick (20 micro seconds/calculation). While just a spline for one-way conversion could be used, a numerical solver would have to be used to obtain an exact result for the reverse conversion. This was found to take approximately 1 ms/calculation, depending on the region.

References

[R11181123]Wier, Ron D., and Robert N. Goldberg. “On the Conversion of Thermodynamic Properties to the Basis of the International Temperature Scale of 1990.” The Journal of Chemical Thermodynamics 28, no. 3 (March 1996): 261-76. doi:10.1006/jcht.1996.0026.
[R11191123]Goldberg, Robert N., and R. D. Weir. “Conversion of Temperatures and Thermodynamic Properties to the Basis of the International Temperature Scale of 1990 (Technical Report).” Pure and Applied Chemistry 64, no. 10 (1992): 1545-1562. doi:10.1351/pac199264101545.

Examples

>>> T_converter(500, 'ITS-68', 'ITS-48')
499.9470092992346
thermo.temperature.ITS90_68_difference(T)[source]

Calculates the difference between ITS-90 and ITS-68 scales using a series of models listed in [R11201125], [R11211125], and [R11221125].

The temperature difference is given by the following equations:

From 13.8 K to 73.15 K:

\[T_{90} - T_{68} = a_0 + \sum_{i=1}^{12} a_i[(T_{90}/K-40)/40]^i\]

From 83.8 K to 903.75 K:

\[T_{90} - T_{68} = \sum_{i=1}^8 b_i[(T_{90}/K - 273.15)/630]^i\]

From 903.75 K to 1337.33 K:

\[T_{90} - T_{68} = \sum_{i=0}^5 c_i[T_{90}/^\circ C]^i\]

Above 1337.33 K:

\[T_{90} - T_{68} = -1.398\cdot 10^{-7}\left(\frac{T_{90}}{K}\right)^2\]
Parameters:

T : float

Temperature, ITS-90, or approximately ITS-68 [K]

Returns:

dT : float

Temperature, difference between ITS-90 and ITS-68 at T [K]

Notes

The conversion is straightforward when T90 is known. Theoretically, the model should be solved numerically to convert the reverse way. However, according to [R11231125], the difference is under 0.05 mK from 73.15 K to 903.15 K, and under 0.26 mK up to 1337.33 K.

For temperatures under 13.8 K, no conversion is performed.

The first set of coefficients are: -0.005903, 0.008174, -0.061924, -0.193388, 1.490793, 1.252347, -9.835868, 1.411912, 25.277595, -19.183815, -18.437089, 27.000895, -8.716324.

The second set of coefficients are: 0, -0.148759, -0.267408, 1.08076, 1.269056, -4.089591, -1.871251, 7.438081, -3.536296.

The third set of coefficients are: 7.8687209E1, -4.7135991E-1, 1.0954715E-3, -1.2357884E-6, 6.7736583E-10, -1.4458081E-13. These last coefficients use the temperature in degrees Celcius. A slightly older model used the following coefficients but a different equation over the same range: -0.00317, -0.97737, 1.2559, 2.03295, -5.91887, -3.23561, 7.23364, 5.04151. The model for these coefficients was:

\[T_{90} - T_{68} = c_0 + \sum_{i=1}^7 c_i[(T_{90}/K - 1173.15)/300]^i\]

For temperatures larger than several thousand K, the differences have no meaning and grows quadratically.

References

[R11201125](1, 2) Bedford, R. E., G. Bonnier, H. Maas, and F. Pavese. “Techniques for Approximating the International Temperature Scale of 1990.” Bureau International Des Poids et Mesures, Sfievres, 1990.
[R11211125](1, 2) Wier, Ron D., and Robert N. Goldberg. “On the Conversion of Thermodynamic Properties to the Basis of the International Temperature Scale of 1990.” The Journal of Chemical Thermodynamics 28, no. 3 (March 1996): 261-76. doi:10.1006/jcht.1996.0026.
[R11221125](1, 2) Goldberg, Robert N., and R. D. Weir. “Conversion of Temperatures and Thermodynamic Properties to the Basis of the International Temperature Scale of 1990 (Technical Report).” Pure and Applied Chemistry 64, no. 10 (1992): 1545-1562. doi:10.1351/pac199264101545.
[R11231125](1, 2) Code10.info. “Conversions among International Temperature Scales.” Accessed May 22, 2016. http://www.code10.info/index.php%3Foption%3Dcom_content%26view%3Darticle%26id%3D83:conversions-among-international-temperature-scales%26catid%3D60:temperature%26Itemid%3D83.

Examples

>>> ITS90_68_difference(1000.)
0.01231818956580355