Explain and write the Zeroth Law of Thermodynamics.

Explanation

To know whether a system is in thermal equilibrium with its surrounding, third system (body) can be used.

(a) Systems A and B are separated by a adiabatic wall and they are in contact with third system C through a diathermic wall.
(b) The adiabatic wall between A and B is replaced by a conducting wall and C is insulated (separated) from A and B by an adiabatic wall.
In figure (a) systems A and B separated by an adiabatic wall (can displace) and both of them are in contact with a third system C separated by conducting wall (diathermic wall). This whole device is covered by an insulating wall.
The states of system (means macroscopic variable quantity) not being changed until the system A and B attained thermal equilibrium with C.
After doing this, suppose system adiabatic wall between A and B is replaced by a conducting wall, while C is insulated from A and B by an adiabatic wall which is shown in figure (b), then the states of system of A and B being not changed.
Means they are in thermal equilibrium to each other. This is the base of zeroth law of thermodynamics. Hence, this law is written as under: "The system in thermal equilibrium with a third system separately are in thermal equilibrium with each other." This is the zeroth law of thermodynamics.
R. H. Fowler formulated zeroth law of thermodynamics in 1931 long after the first and second laws of thermodynamics were stated and so numbered.
The zeroth law clearly suggested that when two systems A and B are in thermal equilibrium there must be a physical quantity that has the same value for both.
This variable whose value is equal for two systems in thermal equilibrium is called temperature (T).
Thus, if A and B are separately in equilibrium with C, `T_A = T_C` and `T_B = T_C`. This implies that `T_A = T_B`. That means, the system A and B are also in thermal equilibrium.
Thus the following conclusion can be drawn from this law, "there exists an important physical quantity called temperature".