Heat guide
Thermal Equilibrium and Why Temperatures Settle
Two systems are in thermal equilibrium when they can exchange energy but no net heat transfer occurs between them because their temperatures are equal.
What equilibrium means
When objects at different temperatures interact, energy tends to move from the hotter object toward the colder one. As their temperatures approach one another, the driving temperature difference becomes smaller. At thermal equilibrium, no net heat transfer remains between them.
The zeroth law
The zeroth law of thermodynamics states that if system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other. This principle underlies the practical meaning of temperature measurement.
Why equilibrium can take time
Equal final temperature does not mean the process is instantaneous. The time required depends on heat capacity, thermal resistance, geometry, convection, radiation and internal conduction.
Equilibrium is not the same as no energy
A system at equilibrium still contains internal energy. Equilibrium only describes the absence of a net thermal driving force between the interacting systems.
Open systems can stay out of equilibrium
A building, engine or electronic device can maintain temperature differences indefinitely when energy continuously enters and leaves. In such cases the system may reach steady state without reaching thermal equilibrium everywhere.
Equilibrium is a model state, not instantaneous mixing
When two bodies are brought into thermal contact, temperature differences drive energy transfer over time. Thermal equilibrium describes the eventual state in which there is no net heat transfer caused by a temperature difference between them. The approach to that state can be fast or slow depending on geometry, properties and contact resistance.
A system can also reach a steady state without being in thermal equilibrium. A wall carrying constant heat flow between warm indoor air and cold outdoor air can have a stable temperature profile while a continuing energy flux passes through it.
Equilibrium is a state concept, not a statement that nothing moves microscopically
At thermal equilibrium, microscopic molecular motion continues. The defining feature is that macroscopic properties such as temperature no longer show a net tendency to change because of thermal interaction between the systems. Energy exchanges can still occur microscopically in both directions while balancing on average.
This distinction helps connect thermodynamics with statistical mechanics. Equilibrium does not mean matter is motionless; it means the observable state is stable under the permitted exchanges and there is no net thermodynamic driving force for further heat transfer.
A calorimetry example shows equilibrium and energy conservation
Suppose equal masses of the same liquid at 20 °C and 60 °C are mixed in an insulated container and the liquid properties are treated as constant. With no phase change or losses, conservation of energy gives an equilibrium temperature of 40 °C. The hotter portion loses the same amount of sensible energy that the colder portion gains.
If the masses or heat capacities differ, the final temperature is weighted toward the side with the larger thermal capacitance. The final value is therefore not always the simple arithmetic mean.
Thermal equilibrium differs from steady state
A wall can have a steady temperature profile while heat continuously flows through it. Temperatures at fixed locations stop changing with time, but the two sides remain at different temperatures and energy continues to cross the wall.
Thermal equilibrium instead requires the absence of a net heat-transfer driving difference between systems that can exchange energy thermally.
Local equilibrium is an approximation
Classical thermodynamics often assigns temperature to small regions of a system even while the entire system is not at equilibrium. This local-equilibrium idea works well for many engineering problems when microscopic relaxation is fast compared with the macroscopic changes being studied.
Very rapid processes, rarefied gases and strongly nonequilibrium systems can require more detailed descriptions.