Thermal equilibrium
The definition and measurement of temperature must be logically preceded by the concept of thermal equilibrium and the Zeroth law. To determine operationally whether two systems are in thermal equilibrium, they are placed together in contact and isolated from the surroundings. If one of them is hot and the other cold then, after a certain period of time, the former feels less hot and the latter feels less cold. Simultaneously, changes in their physical properties, such as length, electrical resistance, etc. occur. After a sufficiently long time (equivalent to the relaxation time) no further changes take place. The two systems are then said to be in thermal equilibrium; they are said to have the same temperature.
Definition
Two systems are equal in temperature if no change in any physical property occurs when they are brought into communication. This definition must not be reversed. It does not imply that “when two systems are equal in temperature, no changes result from their communication”. For instance, if an electric lamp and a battery are connected by means of an electrical conductor, then the lamp will light up; this is, of course, a work interaction. Temperature is at the heart of the difference between work and heat; hence, the necessity to employ rigour in defining concepts relating to temperature. Two points are of significance with reference to the discussion on thermal equilibrium and equality of temperature:
• If the definition of temperature equality has to be given in such a manner as to apply equally well when it is reversed, the following condition should be added : “in the absence of any work interactions”.
• The process of “communication” indicated in the definition is in fact “thermal” communication (excluding any “work interactions”). But this usage leads to circularity and hence is not employed until after temperature equality is defined.