# Why the thermoelectric figure of merit is denoted “ZT”?

Why the thermoelectric figure of merit is denoted ZT? Does ZT come from the abbreviation of words in some language?

Update: So far T has been figured out --- it is the temperature to make the whole quantity dimensionless. So the question is left only for Z.

## migrated from physics.stackexchange.comOct 27 '16 at 6:12

This question came from our site for active researchers, academics and students of physics.

• Possibly German? – Farcher Oct 26 '16 at 6:29
• @Farcher I do not think so. According to Google translation, thermoelektrischen Gütefaktor is corresponding to thermoelectric figure of merit --- the letter "Z" does not even appear in the German word. – Alexander Zeng Oct 26 '16 at 7:11
• I guess because German Physicists were very much involved in the foundations of Thermodynamics.. – Farcher Oct 26 '16 at 7:50

## 2 Answers

My guess for the Z

From THIS Germain-English dictionary, we see that "Figure of merit" in German could be

Gütezahl $\qquad$ or $\qquad$ Leistungskennzahl

in electrical engineering. So probably the letter Z is for Zahl, the German word for "number".

[moral: use Google translate with a grain of salt]

• This seems plausible. Just wanted to add that the Z might also come from the word Ziffer (as in thermoelektrische Kennziffer which translates to thermoelectric indicator). Ziffer is a synonym for Zahl that is perhaps more frequently used in the sciences and engineering. (Disclaimer: I'm German.) – Casimir Jan 21 at 14:06

The concept of the thermoelectric figure of merit and the abbreviation ZT were introduced by the Russian physicist Abram Fedorovich Ioffe in 1949, so I assume the acronym originates from Russian. However all the references I can find are behind paywalls so frustratingly I cannot tell you how ZT is derived.

If your university has access to it, Ioffe's book where all this is described is Ioffe AF (1957) Semiconductor thermoelements, and Thermoelectric cooling.

• In that book, it is just denoted as a lowercase "z", rather than the uppercase "ZT". – Alexander Zeng Oct 27 '16 at 6:06
• While according to Goldsmid, H. J. Introduction to Thermoelectricity, Springer-Verlag Berlin Heidelberg, 2016, "ZT" is dimensionless, and "T" there means temperature. – Αλέξανδρος Ζεγγ Oct 27 '16 at 6:16
• @AlexanderZeng: I've seen it as both zT and ZT. I don't know how Ioffe used it because I don't have access to his papers. – John Rennie Oct 27 '16 at 6:23
• So the point is, you take the original figure of merit $Z$ and multiply by tempurature $T$ to make it dimensionless. The result is $ZT$. So half the answer is "$T$ stands for tempurature". Now we just need to know where $Z$ comes from. – Gerald Edgar Oct 27 '16 at 15:03
• It cannot be a Russian acronym. In Russian a "thermoelectric figure of merit" is "термоэлектрическая добротность". Nothing resembles Z or З, neither graphically nor phonetically. – user58697 Oct 28 '16 at 3:10