“When two systems A and B have thermal equilibrium (equality of temperature) with a third system C, then they (A and B) in turn have thermal equilibrium (equality of temperature) with each other”.
To explain the above statement let us consider three systems A, B and C as shown in Fig. 2.1 (a), enclosed in a rigid adiabatic wall (r). Let systems A, B and C coupled to system C via diathermal wall (e). A is separated from B by an adiabatic wall (d). Then it is natural that A and B will be separately in thermal equilibrium with C. Practically it is seen that A will be in thermal equilibrium with B though it is separa ted by an adiabatic wall (d). It is thus equivalent to systems A and B being coupled to each other via diathermal wall (j), and decoupled from C by adiabatic wall (g) as shown in Fig. 2.1 (b).
It is to be noted that the zeroth law was introduced when first and second laws already existed at that time. So it was stated as the zeroth law so that it precedes the first and second laws to form a logical sequence.