Lord Kelvin devised the thermodynamic scale based on the efficiency of heat engines as shown below:
The efficiency of an engine is the work divided by the heat introduced to the system or
where w is the work done per cycle. Thus, the efficiency depends only on q/q.
Because of Carnot theorem, any reversible heat engine operating between temperatures T and T must have the same efficiency, meaning, the efficiency is the function of the temperatures only:
In addition, a reversible heat engine operating between temperatures T and T must have the same efficiency as one consisting of two cycles, one between T and another (intermediate) temperature T, and the second between T and T. This can only be the case if
Specializing to the case that  is a fixed reference temperature: the temperature of the triple point of water. Then for any T and T,
Therefore, if thermodynamic temperature is defined by
then the function f, viewed as a function of thermodynamic temperature, is
and the reference temperature T has the value 273.16. (Of course any reference temperature and any positive numerical value could be used—the choice here corresponds to the Kelvin scale.)