Thermodynamic equilibrium and postulates

Definition
Thermodynamic equilibrium or equilibrium state is a state when the thermodynamic system is in thermal, mechanical, chemical and radiation equilibrium ( the most general state of equilibrium ). It means that all macroscopic processes such as heat exchange between individual parts of the system have ended in the given system, pressures have equalized, the concentration of various chemical substances across the system has stopped, chemical reactions, phase changes and others have stopped. An open system can theoretically acquire this state, but in practice we describe it mainly in isolated systems.

1. Postulate of Thermodynamics.
Any further macroscopic change of the system is only possible by external intervention or change in external conditions. After their change and the passage of sufficient time, the system reaches an equilibrium state again, even if the state variables are different from the original equilibrium state. It is therefore obvious that the state variables of the given equilibrium system are constant in time until the next change in external conditions. This statement is also sometimes called the Spontaneous Inviolability Postulate of Thermodynamic Equilibrium. The time required to stabilize the state after a change in external conditions is called the Relaxation Time.

Relaxation time can take on different values ​​for individual macroscopic processes. Equalization of pressures in gases takes place very quickly, on the order of 1x10 -16 s, while equalization of concentrations by means of diffusion can take up to several years. In order to achieve thermodynamic equilibrium, it is therefore not necessary for all macroscopic parameters to stabilize at once.

For the sake of completeness, it should be added that the individual instantaneous values ​​of the state quantities fluctuate around the mean value of the given quantity in the equilibrium state. An example can be the measured pressure in the equilibrium system we observe. Although the instantaneous pressure depends on the amount of molecules hitting the wall of the system (or measuring device), the output we observe from the measuring device is, so to speak, the average value of these fluctuations. If we were able to observe the time evolution of the relevant state variables, we can calculate the mean value from the relationship: $$ \bar{f_i} = \lim_{t \rightarrow \infty} \left [ \frac{1}{t} \int_{t_0}^{t_0+t} f_i (t) dt \right ] $$

If we observe the system long enough, we will find that it is in a state of thermodynamic equilibrium most of the time. From this follows the possibility of identifying the equilibrium values ​​of the macroscopic parameters of the system with the time mean values ​​defined by the relation.

Example.
To understand this knowledge, let's take a simple example of an Isolated Thermodynamic System. Let's imagine a thermos in which we have hot coffee and assume that it is an ideal isolated system, i.e. no heat or mass is gained or lost by this system. For the sake of simplicity, we will define coffee as an aqueous solution with the only dissolved substance "coffee".

Let's mark the moment when we start to describe (or observe) this system as '''Point 0. At this point, the system is in thermodynamic equilibrium.''' Coffee in a thermos is completely homogeneous in terms of heat, concentration and mechanics. In the next step, pour cold, clean water into the thermos (system). That is, a liquid that will have a significantly lower temperature than the temperature of coffee and will be composed exclusively of water molecules, i.e. without any admixtures.

Let us mark this moment as '''Point 1. At this point, the thermodynamic equilibrium of the original system was disturbed''' in several aspects. First of all, by pouring in cold water, that water gained kinetic energy. This energy will cause the originally stationary coffee to move, eg in the form of waves or turbulence. Furthermore, by supplying colder water, the system ceases to be thermally homogeneous and areas with different temperatures are created. Since it was pure water, there was also a change in the concentration of dissolved coffee, not only that the total concentration changed, but also "concentrated areas" were created where coffee is found and areas where it is not. In this Point 1, not only the properties of the given system changed, but also "started" spontaneous processes that lead to the restoration of thermodynamic equilibrium. For example, it will be a matter of heat exchange between parts with different temperatures, there will be an equalization of coffee concentrations across the system, either by diffusion or mechanical movement. The kinetic energy of the added water will also be converted into thermal energy, thanks to friction, which will also achieve balance on the mechanical side. Last but not least, the entropy of the given system will also increase.

Let's mark the next point of description (observation) as '''Point 3. At this point, all spontaneous processes have already ended.''' The system is again in thermodynamic equilibrium. The system is again thermally, concentration-wise and mechanically homogeneous, and the entropy of the given system is maximal. If we were to measure the time between point 2 and 3, we would obtain the value of the Relaxation time.

However, it is important to remember that the example of an isolated system is used for didactic reasons. The system does not have to be isolated or closed to reach thermodynamic equilibrium. The boundaries of the system can be purely imaginary, it is important that the external conditions do not change over time.

2. Postulate of Thermodynamics.
The validity of this postulate is conditioned by the fact that any part of the macroscopic system is able to exchange heat with any other part of the given system, either directly or indirectly. So it is a thermally homogeneous system.

If we mark all external parameters as α1, α2, α3 .... Then, for example, the internal energy U is expressed by the general relation U= U(α1, α2,...,αn, T). This also applies to any other internal parameter, e.g. β=β(α1, α2,...,αn, T), γ=γ(α1, α2,...,αn, T) etc.

As an example, let us consider a simple homogeneous system whose only external parameter is the volume V. According to the 2nd Postulate, it follows that, for example, Internal energy U is given by the relationship U=U(V,T) or pressure P, P=P(V,T).

It follows from the given postulate that temperature is an internal parameter. It is an intensive parameter (it does not depend on the amount of matter in the system) that physically characterizes the transfer of a special form of energy – Heat. It follows from the 1st and 2nd Postulates that we can determine the temperature only for a thermally homogeneous system in thermodynamic equilibrium.