Thermal Equilibrium

The definition and measurement of temperature should be logically preceded by the idea of thermal equilibrium and the Zeroth law.
To establish operationally whether two systems are in thermal equilibrium, they are positioned altogether in contact and isolated from the surroundings. When one of them is hot and the other cold then, after a certain time period, the previous feels less hot and the later feels less cold. Concurrently, changes in their physical properties, like length, electrical resistance, and so on take place. After an adequately long time (equal to the relaxation time) no further changes occur. The two systems are then said to be in thermal equilibrium; they are said to have similar temperature.

Definition:

The two systems are equivalent in temperature when no change in any physical property takes place whenever they are brought into communication.

This definition should not be reversed. It does not entail that “whenever two systems are equivalent in temperature, no changes outcome from their communication”. For illustration, whenever an electric lamp and a battery are linked by means of an electrical conductor, then the lamp will light up; this is, obviously, a work interaction.

The temperature is at the heart of the difference among work and heat; therefore, the requirement to employ rigor in defining ideas associating to temperature. The two points are of importance with reference to the discussion on thermal equilibrium and equality of the temperature:

• When the definition of temperature equality has to be offered in such a way as to apply uniformly well whenever it is reversed, the following condition must be added : “in the absence of any work communications”.

• The procedure of “communication” in the definition is in fact “thermal” communication (exclusive of any “work communications”). Though this usage leads to circularity and therefore is not used until after temperature equality is stated.