The second principle of thermodynamics allows us to know if a system will evolve spontaneously. It introduces a new concept: entropy. It is a rather abstract notion, often seen as a measure of disorder.

First of all, it is important to define the state of equilibrium: a system is said to be in equilibrium when it is stable and invariant, for an indefinite period of time as long as an external event does not intervene.

• A transformation is said to be reversible if at any time there is equilibrium between the internal elements of the system and equilibrium with the external elements of the system considered.
• To show that a transformation is irreversible, it is sufficient to point to an instant during the transformation when an equilibrium condition is not verified. Often, the simplest way is to analyze the situation at the initial moment: in most cases, the evolution is induced by a break of equilibrium.
• A transformation will be said to be quasi-static if there is an equilibrium at any time between the internal elements of the system.

# Statement of the second principle

During a transformation of a quantity of heat into an energy which is macroscopically ordered, it is never possible to have an efficiency of 100%, a part remains in disordered form. Thus, as the transformations proceed, there is an irreversible evolution towards an increase of disorder.

The second principle then introduces the notion of entropy which allows to quantify the tendency to go towards a disordered state. Thus, to any system is associated a state function S, called entropy. When the isolated system and the seat of an irreversible transformation, its entropy increases. When the maximum is reached, the system is in equilibrium.

To use the concept of entropy, it is fundamental that the system is isolated, otherwise if it is not isolated, its entropy can very well increase or decrease or remain invariant.

To calculate its entropy, we use the relation of the second principle: dS = 𝛅Q/T

In reality, the measurement of entropy is more a notion of probability.

For heat pumps, we will use several notions, including that of the heat source: it is a system that has a constant temperature, and whatever interactions it may have with the system under study, the temperature does not vary, it can only exchange heat. To designate this heat source, we often use the term thermostat.

This second principle also allows us to obtain Laplace's law: during an adiabatic transformation (when heat exchange with the outside is negligible) and reversible, a fixed quantity of perfect gas, the quantity PV𝜸 is constant.

We will see in the next chapters why all these notions are important and in what context we can use them. In particular, we will see the properties of the pure body.

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