**Thermodynamic temperature** is a measure, in kelvins (K) of temperature for thermodynamics, with a uniquely defined zero point at absolute zero.

A temperature of 0 K is called "absolute zero," and coincides with the minimum molecular activity (*i.e.*, thermal energy) of matter.

Thermodynamic temperature was formerly called "absolute temperature."

In practice, the International Temperature Scale of 1990 (ITS-90) serves as the basis for high-accuracy temperature measurements in science and technology.

## Derivation of thermodynamic temperature

There are many possible scales of temperature, derived from a variety of observations of physical phenomena. The thermodynamic temperature can be shown to have special properties, and in particular can be seen to be uniquely defined (up to some constant multiplicative factor) by considering the efficiency of idealized heat engines.

Loosely stated, temperature controls the flow of heat between two systems and the universe, as we would expect any natural system, tends to progress so as to maximize entropy. Thus, we would expect there to be some relationship between temperature and entropy. In order to find this relationship let's first consider the relationship between heat, work and temperature. A heat engine is a device for converting heat into mechanical work and analysis of the Carnot heat engine provides the necessary relationships we seek. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, q_{H} and the heat ejected at the low temperature, q_{C}. The efficiency is the work divided by the heat put into the system or:

- (1)

_{cy}is the work done per cycle. We see that the efficiency depends only on q

_{C}/q

_{H}. Because q

_{C}and q

_{H}correspond to heat transfer at the temperatures T

_{C}and T

_{H}, respectively, q

_{C}/q

_{H}should be some function of these temperatures:

- (2)

_{1}and T

_{3}must have the same efficiency as one consisting of two cycles, one between T

_{1}and T

_{2}, and the second between T

_{2}and T

_{3}. This can only be the case if:

_{2}, this temperature must cancel on the right side, meaning f(T

_{1},T

_{3}) is of the form g(T

_{1})/g(T

_{3}) (i.e. f(T

_{1},T

_{3}) = f(T

_{1},T

_{2})f(T

_{2},T

_{3}) = g(T

_{1})/g(T

_{2})×g(T

_{2})/g(T

_{3}) = g(T

_{1})/g(T

_{3})), where g is a function of a single temperature. We can now choose a temperature scale with the property that:

- (3)

- (4)

_{C}=0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact the lowest temperature so far obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 4 from the middle portion and rearranging gives:

- (5)