Equilibrium of a Particle

Introduction

In classical mechanics, the equilibrium of a particle is achieved if its net force is zero. Mechanical equilibrium exists when the net force on each physical system’s component constituents is zero. In addition to defining mechanical equilibrium in terms of force, there are various theoretically similar definitions. A system is said to be in momentum equilibrium if the momentum of all of its members is constant. If the system’s velocity remains constant, it is in equilibrium. The item’s angular momentum is preserved in rotational mechanical equilibrium and zero net torque. In general, equilibrium is obtained in conservative systems at a location in configuration space where the gradient of the potential energy concerning the generalised coordinates is zero.

Thermal Equilibrium

To be able to understand these things, we need to know certain measurable things, like size (volume), mass, temperature, and more.

No macroscopic change occurs when a system is in internal thermodynamic equilibrium.
Mutual thermodynamic equilibrium is achieved when systems simultaneously are in thermal, mechanical, chemical, and radiative equilibrium. A system may have one kind of mutual equilibrium but not another. Unless a thermodynamic action intervenes, all stable states exist continuously and indefinitely. The scientific underpinning for the idea of macroscopic equilibrium is that in a macroscopic equilibrium, tiny exchanges are completely or almost perfectly balanced.

Internal thermodynamic equilibrium occurs when a thermodynamic system’s temperature is spatially homogeneous. Apart from temperature, a continuous long-range force field applied by its surroundings may result in spatial inhomogeneity and the intensity characteristics of the force field.

In contrast, non-equilibrium systems exhibit net matter or energy flows. A system is considered to be in a meta-stable equilibrium if future alterations are possible.

The thermodynamic state of internal equilibrium of a system

A material’s body may be fully separated from its environment. According to classical thermodynamics, no changes or fluxes occur if an unchanged system is held indefinitely long. This is an illustration of a thermodynamic internal equilibrium state (In some fields, this is referred to as the thermodynamic ‘minus first’ rule; in others, it is not). One textbook refers to it as the ‘zeroth rule,’ which the authors say is a more accurate title than the Fowler interpretation that is more often used.

These states are critical in what is known as classical or equilibrium thermodynamics, since they are the only well-defined states for the system in that region. A thermodynamic operation may isolate a system that is in equilibrium with another system while maintaining its equilibrium state. As a result, a system in contact with another system is considered to be in internal thermodynamic equilibrium.

Typically, a thermodynamic system’s surroundings is another thermodynamic system. In this perspective, the system and its surroundings may be seen as two interdependent systems linked by long-range forces. A system’s enclosure is defined as the surface of contiguousness or the border between two systems.

According to thermodynamics, the surface has specific permeability qualities. Consider the case when the surface of contiguity is totally permeable to heat, enabling energy to be transmitted solely by heat. When the long-range forces remain constant throughout time, thermal equilibrium prevails between the two systems. Energy transfer between them in the form of heat has reduced and finally halted; this is an example of contact equilibrium.

Permeability gradations correspond to various types of contact equilibrium. When two systems are in equilibrium with respect to a particular type of permeability, they share the intensity variable associated with that type of permeability. Temperature, pressure, and chemical potential are just a few of the variables that affect the reaction.

A contact equilibrium may also be referred to as an exchange equilibrium. When two systems are in equilibrium, the rate at which a quantity is transmitted between them is zero. For instance, the diffusion rates of internal energy in the form of heat between the two systems are equal and opposite for a wall permeable to only heat.

If the adiabatic wall is more sophisticated, with leverage and an area ratio, the pressures in exchange equilibrium between the two systems are proportional to the volume exchange ratio; this maintains the zero balance of work transfer rates.

Two otherwise autonomous systems may share radiation. When the temperatures in both systems are identical, radiative equilibrium occurs.

Understanding the distinction between global and local thermodynamic equilibrium is beneficial. In thermodynamics, intensity factors have an effect on the interactions inside the system as well as the interactions between the system and its external environment. For instance, temperature regulates heat transmission. Global thermodynamic equilibrium (GTE) denotes the homogeneity of the system-wide intense parameters. In contrast, local thermodynamic equilibrium (LTE) suggests that these intensive parameters change in space and time, but at a modest rate the thermodynamic equilibrium may be assumed in some areas around that place.

Assume that the description of the system necessitates numerous adjustments in the intensity parameters. In this case, the assumptions underlying their definitions are violated, and the system is neither global nor local in equilibrium. For instance, a particle must collide with its surroundings a certain amount of times before it may equilibrate with it.

Conclusion

When a system comes into contact with its surroundings, the most general kind of thermodynamic equilibrium occurs, enabling all chemical components and all types of energy to flow simultaneously. A thermodynamically balanced system may travel through space with uniform acceleration but cannot change shape or size; as a result, it is represented as a hard volume in space. 

It may be positioned inside exterior fields of force regulated by external factors far more robust than the system itself. Events within the system have no meaningful influence on the outside force fields. Only if the external force fields are uniform and regulate the system’s uniform acceleration, or if the system lives in a non-uniform force field but is kept stationary by local forces on its surface, such as mechanical pressures, can the system be regarded in thermodynamic equilibrium.