THERMODYNAMIC EQUILIBRIUM: CLASSES AND APPLICATIONS - PHYSICAL - 2025

The thermodynamic equilibrium of an isolated system is defined as a state of balance in which the variables that characterize it and that can be measured or calculated do not undergo changes, given that due to its isolation there are no external forces that tend to modify that state..

Both the systems and the classes of equilibrium to be considered are very diverse. A system can be a cell, an ice cold drink, a plane full of passengers, a person or a piece of machinery, to name just a few examples. They can also be isolated, closed or open, depending on whether or not they can exchange energy and matter with their surroundings.

The components of the cocktail are in thermal equilibrium. Source: Pexels.

An isolated system does not interact with the environment, nothing enters or leaves it. A closed system can exchange energy but not matter with the surrounding environment. Finally, the open system is free to make exchanges with the environment.

Well, an isolated system that is allowed to evolve long enough, tends spontaneously to thermodynamic equilibrium in which its variables will retain their value indefinitely. And when it is an open system, its values ​​must be the same as those of the environment.

This will be achieved as long as all the equilibrium conditions imposed by each particular type are satisfied.

Balance classes

Thermal equilibrium

One kind of fundamental equilibrium is thermal equilibrium, which is present in many everyday situations, such as a hot cup of coffee and the spoon with which the sugar is stirred.

Such a system spontaneously tends to acquire the same temperature after a certain time, after which equilibrium arrives as all parts are at the same temperature.

As that happens, there is a temperature difference that drives heat exchange throughout the system. Each system has a time to achieve thermal equilibrium and reach the same temperature at all points, called the relaxation time.

Mechanical balance

When the pressure at all points in a system is constant, it is in mechanical equilibrium.

Chemical balance

Chemical equilibrium, also sometimes called material equilibrium, is reached when the chemical composition of a system remains unchanged over time.

In general, a system is considered in thermodynamic equilibrium when it is in thermal and mechanical equilibrium simultaneously.

Thermodynamic variables and equation of state

The variables that are studied to analyze the thermodynamic equilibrium of a system are diverse, the most commonly used being pressure, volume, mass and temperature. Other variables include position, speed and others whose selection depends on the system under study.

Thus, as indicating the coordinates of a point makes it possible to know its exact location, knowing the thermodynamic variables unequivocally determines the state of a system. Once the system is in equilibrium, these variables satisfy a relationship known as the equation of state.

The equation of state is a function of the thermodynamic variables whose general form is:

Where P is pressure, V is volume, and T is temperature. Naturally the equation of state could be expressed in terms of other variables, but as said before, these are the variables most used to characterize thermodynamic systems.

One of the best known equations of state is that of the ideal gases PV = nRT. Here n is the number of moles, atoms, or molecules and R is Boltzmann's constant: 1.30 x 10 ^-23 J / K (Joule / Kelvin).

Thermodynamic equilibrium and the zero law of Thermodynamics

Suppose we have two thermodynamic systems A and B with a thermometer that we will call T, which is put in contact with system A long enough for A and T to reach the same temperature. In such a case it can be ensured that A and T are in thermal equilibrium.

With the help of a thermometer the zero law of thermodynamics is verified. Source: Pexels.

The same procedure is then repeated with system B and T. If the temperature of B turns out to be the same as that of A, then A and B are in thermal equilibrium. This result is known as the zero law or zero principle of Thermodynamics, which is formally stated as follows:

And from this principle the following is concluded:

Therefore, two bodies in thermal contact that are not at the same temperature cannot be considered in thermodynamic equilibrium.

Entropy and thermodynamic equilibrium

What drives a system to achieve thermal equilibrium is entropy, a magnitude that indicates how close the system is to equilibrium, indicating its state of disorder. The more disorder, the more entropy there is, just the opposite occurs if a system is very ordered, in this case the entropy decreases.

The state of thermal equilibrium is precisely the state of maximum entropy, which means that any isolated system goes spontaneously towards a state of greater disorder.

Now, the transfer of thermal energy in the system is governed by the change in its entropy. Let S be the entropy and let us denote with the Greek letter "delta" the change in it: ΔS. The change that takes the system from an initial state to a final state is defined as:

This equation is valid only for reversible processes. Process in which the system can fully return to its initial conditions and is in thermodynamic equilibrium at each point along the way.

Examples of systems with increasing entropy

- In the transfer of heat from a hotter body to a colder one, the entropy increases until the temperature of both is the same, after which its value remains constant if the system is isolated.

- Another example of increasing entropy is the dissolution of sodium chloride in water, until reaching equilibrium as soon as the salt has completely dissolved.

- In a solid that melts, the entropy is also increasing, since the molecules are moving from a more orderly situation, which is a solid, to a more disordered one as a liquid.

- In some types of spontaneous radioactive decay, the resulting number of particles increases and with it the entropy of the system. In other decays in which particle annihilation occurs, there is a transformation from mass to kinetic energy that eventually dissipates heat, and entropy also increases.

Such examples highlight the fact that thermodynamic equilibrium is relative: a system can be in thermodynamic equilibrium locally, for example if the cup of coffee + teaspoon system is considered.

However, the coffee cup + spoon + environment system may not be in thermal equilibrium until the coffee has completely cooled down.

References

1. Bauer, W. 2011. Physics for Engineering and Sciences. Volume 1. Mc Graw Hill. 650-672.
2. Cengel, Y. 2012. Thermodynamics. 7 ^ma Edition. McGraw Hill. 15-25 and 332-334.
3. Thermodynamics. Recovered from: ugr.es.
4. National University of Rosario. Physicochemical I. Recovered from: rephip.unr.edu.ar
5. Watkins, T. Entropy and the Second Law of Thermodynamics in Particle and Nuclear Interactions. San Jose State University. Recovered from: sjsu.edu.
6. Wikipedia. Thermodynamic equilibrium. Recovered from: en.wikipedia.org.