# What is the difference between temperature and thermodynamic temperature?

My course book says that kelvin is the unit of thermodynamic temperature, then what is the difference between temperature and thermodynamic temperature.

Temperature is more of a relative notion--heat flows from higher temperature to lower temperature, but that's about it. The zero in a temperature scale is meaningless; it is an arbitrary convention. Usually, we measure temperature in Celsius, Fahrenheit, Rankine, etc (note that Kelvin measures temperature as well--but it also measures thermodynamic temperature)

Thermodynamic temperature is such that zero temperature is absolute zero (unlike Celsius, where -273.15°C is absolute zero). It is related to the energy (specifically the kinetic energy) of the molecules of a substance-- for example, in a gas, kinetic energy per molecule is $\frac12k_BT$ (rotational energy, etc can be obtained if you know the type of molecule--but temperature is principally a measure of kinetic energy). It also has strong ties with entropy.

We generally don't use "temperature" in thermodynamics, thermodynamic temperature is more convenient. Temperature is only useful in equations involving temperature difference--whereas equations involving the absolute value of temperature (Arrhenius equation in kinetics, entropy, Maxwell distribution equation, etc) demand thermodynamic temperature.

• Whenever you use a temperature in any calculation rather than a temperature difference, you have to use Kelvin! (Or another thermodynamic temperature scale.) If you are working out chemical reaction rates, for example (Which aren't normally thought of as thermodynamics but kinetics.)
– Nick
Jul 16 '12 at 10:52
• Do these equations involve general gas equation? @ManishEarth Nov 20 '16 at 12:43

There is no difference between temperature and thermodynamic temperature. Wikipedia has a nice writeup. The book likely uses the adjective in order to differentiate from ill-defined conventional connotations. Temperature is an ensemble property, e.g., an ideal gas has an average energy of $\frac{1}{2}k_BT$. Outside of equilibrium, temperature is ill-defined.

"Thermodynamic temperature" is a misnomer. It arises from the misinterpretation of the double adjective used in English. For example, if we say "Jane is a Chinese History Professor," does this mean that "Jane is a Professor of History who happens to be Chinese" or that "Jane is Professor of Chinese History"? For the case of temperature, does "thermodynamic temperature scale" mean "thermodynamic scale of temperature" or "scale of thermodynamic temperature"? It appears that when the kelvin was introduced into the SI, the former was intended but the physical quantity was (falsely) interpreted as the latter.