Unlike other branches of Physics, Thermodynamics usually occurs inductively and not deductively. The reason for this is the difficulty of the concepts involved. It is well known that Thermodynamics is made up of three principles . But to them must be added a first postulate and the zero principle, which are as important as the three principles themselves. The virtue of this science resides in that it is very clear what it is that comes from experience, that is, that it has an empirical character, and what it is that can be deduced from empirical principles and postulates through mathematical reasoning.
The first postulate of Thermodynamics is of the utmost importance, although it is not always highlighted. What it affirms is that any isolated system finally reaches a state of equilibrium, characterized by the fact that the parameters that define it do not vary with time.
We can make the analogy of the postulates and principles of Thermodynamics with existence theorems in mathematics. In this guise, the first postulate affirms the general possibility of the existence of state functions. These are important because they are those that depend exclusively on the states of the system, without depending on the nature of the process that connects them.
The zero principle states that, if we have two systems separated by an adiabatic surface (one that does not allow the passage of heat), and we communicate them separately with a third system in such a way that they reach thermal equilibrium with it, then the separate systems, By thermally connecting them to each other, they will be in thermal equilibrium. This is a seemingly obvious, but not trivial fact. From this result it is also deduced the need to define a new macroscopic quantity called temperature. In other words: temperature is the property shared by those systems that are in thermal equilibrium with each other.
The first principle is not only an expression of the principle of conservation of energy, but also the affirmation of the existence of a concrete state function: internal energy. Once a microscopic interpretation was given to Thermodynamics through kinetic-molecular theory and statistical mechanics, this point was clarified. However, historically, Thermodynamics developed at a time when it was still a controversial issue whether matter was continuous or composed of atoms. Hence the importance of the finding of the state function that we have just discussed.
The second principle postulates the impossibility of transforming, in a cyclical process, all heat into work. In other words, heat is a degraded form of energy. Either by reasoning with ideal thermal machines (like the Carnot cycle), or by analytical reasoning (like the Caratheodory theorem), the necessity of the existence of another state function is deduced: the famous entropy. Unlike energy, it can be created and, in fact, in any spontaneous process, it increases until it reaches a maximum in equilibrium. As a corollary of the previous lines of reasoning, the need for the existence of an absolute scale of temperatures is deduced, with a lower limit, which is the absolute zero of temperatures.
Finally, the third principle relates entropy to temperature and establishes that entropy is zero at absolute zero of temperatures, allowing the calculation of absolute entropy. Until the entry into the scene of this assumption, Thermodynamics allowed only the calculation of entropy differences. A consequence of the third principle is the inaccessibility of the absolute zero of temperatures through a finite number of transformations.
David Balaguer is a doctor in Physics and content editor for the Degree in Physics at the International University of La Rioja (UNIR).
