Thermal equilibrium

Thermal equilibrium is a fundamental state of balance in physics. It occurs when two systems are connected by a path that allows heat to pass between them. When this happens, there is no net flow of thermal energy between the two systems. This means that while energy might still move, the amount moving in one direction equals the amount moving in the other. This concept is vital because it allows us to define and measure temperature consistently across different objects.

The process of reaching this balance depends on how the systems interact. If two bodies are at different temperatures, heat will naturally flow from the hotter body to the colder one. This transfer can happen through thermal conduction or thermal radiation. In the case of radiation, two objects can reach equilibrium even if they are far apart and have no physical contact. This radiative exchange continues until both bodies reach the exact same temperature. At that specific moment, the systems have achieved thermal equilibrium.

Scientists use specific terms to describe these connections. A connection that allows the transfer of heat but not matter or work is called a diathermal connection. This type of connection is essential for establishing thermal equilibrium between two distinct bodies. There are also different types of equilibrium to consider. One form is radiative exchange equilibrium, which involves the exchange of energy through light and heat waves. In this state, the hotter object transfers energy to the cooler one until their temperatures match. This process is governed by principles like Kirchhoff's law of equality of radiative emissivity and absorptivity.

The history of these ideas involves many important researchers. In 1791, P. Prevost documented how objects exchange heat through radiation. Later, Max Planck contributed to our understanding of these thermal processes in the early 1900s. A major pillar of this field is the zeroth law of thermodynamics. This law states that thermal equilibrium is a transitive relation. This means if system A is in equilibrium with system B, and system B is in equilibrium with system C, then A and C are also in equilibrium. This principle allows us to use thermometers to compare different temperatures.

Thermal equilibrium can also happen within a single, isolated object. This is known as internal thermal equilibrium. An isolated system is one where no heat enters or leaves from the outside. If a system starts with different temperatures in different parts, it will eventually settle. For example, an iron rod that is hot at one end and cold at the other will eventually reach a uniform temperature throughout its length. During this transition, the rod is not yet in internal thermal equilibrium. Once the temperature is spatially uniform, the system has reached its settled state.

It is important to distinguish thermal equilibrium from thermodynamic equilibrium. These two terms are not the same. Thermal equilibrium only requires that there is no net flow of heat. However, thermodynamic equilibrium is a much more complete state of balance. In thermodynamic equilibrium, all measurable properties of the system remain constant over time. Two systems might reach the same temperature and achieve thermal equilibrium, but they may still be able to perform work. If they can still exchange work, they have not yet reached thermodynamic equilibrium.

Even in complex environments, such as a tall vessel influenced by a gravitational field, thermal equilibrium still occurs. In such a system, the temperature will eventually become spatially uniform from top to bottom. Even though the pressure or density might change due to gravity, the temperature remains the same throughout. This shows that the drive toward a uniform temperature is a very strong characteristic of physical systems. This process is often irreversible, meaning it happens spontaneously but will not spontaneously reverse itself. This behavior is a core part of the second law of thermodynamics.