How to get thermal equilibrium in the system ?

Explanation

Consider two gases A and B occupying two different containers. The pressure and volume of a given mass of gas can be chosen to be its two independent variables.

(a) Two system A and B (two gases) are separated by an insulating wall that does not allow flow of heat.
(b) The system are insulated from the rest of the surrounding also by similar an insulating wall. In this case thermal equilibrium can be obtained after some time.
Suppose, pressure and volume of gas A and B are (`P_A,V_A`) and (`P_B, V_B`) respectively.
First that the two systems are put in proximity but are separated by an adiabatic wall that does not allow flow of heat energy from one to another.
It is found that any possible pair of values `(P_A, V_A)` will be in equilibrium with any other possible pair of values `(P_B, V_B)`. This is shown in figure (a).
Now suppose, that the adiabatic wall separating the gases A and B is replaced by a diathermic wall (conducting wall) which allows heat energy to flow from one gas to another.
It is then found that the macroscopic variables of the system A and B change spontaneously until both the system attain equilibrium states. After that there is no change in their states. This is shown in figure (b).
The pressure and volume variables of the two gases change to `(P._B, V._B)` and `(P._A,V._A)` such that the new states of A and B are in equilibrium with each other. There is no more energy flow from one to another. It is called that system A is in thermal equilibrium with system B.
No need to change the pressure and volume for attaining equilibrium for both the system. It depend on the control factors. For example, if gases are in container with contact of volume then attaining thermal equilibrium any pressure will be changed.
In thermal equilibrium the temperature of two systems are equal.