Zeroth law of thermodynamics & Thermal Equilibrium

A body is said to be in thermal equilibrium if thermodynamical variables like Pressure (P), Volume (V), and temperature (T) associated with body do not change with time.

According to Zeroth’s law “If two systems ‘A’ and ‘B’ are separately in thermal equilibrium with a third system ‘ C’, then the two systems ‘A’ and ‘B’ are also in thermal equilibrium with each other”.

Consider two systems A and B separated from each other by an adiabatic wall(one that conducts no heat) but each being in contact with a third system ‘C’ through a diathermic wall which permits heat to pass, then the system A will be in thermal equilibrium with C.
Now If adiabatic wall between systems A and  ‘B’ is replaced by a diathermic wall, experiments show that no further changes occur in systems A and ‘B’ indicating thereby that system A was also in thermal equilibrium with system B. This important experimental fact leads us to follow general conclusion :

This statement is called Zeroth’s law of thermodynamics.

Illustration :

A simple illustration of Zeroth’s law is provided in case of two gases A and  ‘B’ enclosed in a vessel and a mercury thermometer C.

If the there is no change in length of mercury thread on placing the thermometer C either in contact of the gas vessel containing A or that of the vessel containing B is brought in thermal contact with each other. This is in accordance with Zeroth’s law.

Zeroth’s law forms the basis of the concept of temperature. All these three systems can be said to possess a property that ensures their being in thermal equilibrium with one another. This property is known as temperature.

We may, therefore, define the temperature of a system as the property that determines “whether or not the system is in thermal equilibrium with the neighboring system”.