Where the Gibbs Thomson Coefficient k _ { GT } assumes different values for different liquids and different interfacial geometries ( spherical / cylindrical / planar ).
12.
At high temperature, Z and PV decrease as the gas expands; if the decrease is large enough, the Joule-Thomson coefficient will be negative.
13.
Since this is true at all temperatures for ideal gases ( see expansion in gases ), the Joule Thomson coefficient of an ideal gas is zero at all temperatures.
14.
If the Thomson coefficient of a material is measured over a wide temperature range, it can be integrated using the Thomson relations to determine the absolute values for the Peltier and Seebeck coefficients.
15.
Where \ scriptstyle T is the absolute temperature, \ scriptstyle \ mathcal K is the Thomson coefficient, \ scriptstyle \ Pi is the Peltier coefficient, and \ scriptstyle S is the Seebeck coefficient.
16.
The first step in obtaining these results is to note that the Joule Thomson coefficient involves the three variables " T ", " P ", and " H ".
17.
By proxy, these measurements led to the determination of absolute Seebeck coefficients for " all materials ", even up to higher temperatures, by a combination of Thomson coefficient integrations and thermocouple circuits.
18.
In particular, the 1932 measurements may have incorrectly measured the Thomson coefficient over the range 20 K to 50 K . Since nearly all subsequent publications relied on those measurements, this would mean that all of the commonly used values of absolute Seebeck coefficient ( including those shown in the figures ) are too low by about 0.3 ?V / K, for all temperatures above 50 K.
