ThermodynamicsThermal Equilibrium
Riya's mother stands a steel tumbler of hot milk in a bowl of cold water. A few minutes later the milk is cooler and the water warmer, and after that nothing changes any more, however long they wait. The milk and the water have settled into a state that no longer changes with time.
In mechanics, a body is in equilibrium when the net external force and torque on it are zero. In thermodynamics the word has a different meaning: a system is in an equilibrium state when the macroscopic variables that describe it (pressure, volume, temperature, mass and composition) do not change with time. A gas in a closed, rigid container that is fully insulated from its surroundings, with all those values fixed, is in thermodynamic equilibrium.
Whether two systems settle down together depends on the wall between them. An adiabatic wall is an insulating wall, which may even be movable, that lets no heat through. A diathermic wall is a conducting wall that lets heat flow. Below, gas A starts at 80 °C and gas B at 20 °C, both insulated from everything else. Try each wall, and start the clock each time.
With the adiabatic wall the dashed lines stay flat. Any state of A can sit beside any state of B for ever, because no energy crosses. With the diathermic wall the two curves close in and meet at the purple dot: A cools, B warms, and then both stop changing. A is now in thermal equilibrium with B, and no more energy flows between them.
The pressure and volume of each gas may change on the way, or, if the containers are rigid, only the pressure. Either way, what the two systems end up sharing is a common temperature. To say exactly what temperature is, we need the next law.