The Zeroth Law of Thermodynamics

Mechanical equilibrium occurs when no net force acts across a movable boundary, so the pressures on both sides are equal. Thermal equilibrium occurs when there is no net heat flow between systems, resulting in equal temperatures.

Temperature is a measure of the average kinetic energy of the particles in a system.

The higher the temperature, the greater the system's energy, given that other variables, such as volume and pressure, remain constant.

When two systems of any size, with different temperatures, are brought together, energy transfers until their temperatures gradually become equal, achieving thermal equilibrium. This energy transfer due to a temperature difference is known as heat.

The Zeroth Law of thermodynamics states that if each of these two systems is in thermal equilibrium with a third system, they must be in equilibrium with each other.

This validates that temperature is a state function, meaning that irrespective of initial conditions or paths taken, systems reaching the same temperature are in an identical state.