Entropy Meaning, Definition Of Entropy, Formula, Thermodynamic- Softpik.com

Introduction of Entropy


In thermodynamics, entropy is a state function introduced in 1865 by Rudolf Clausius as part of the second principle, based on the work of Sadi Carnot. Clausius showed that the ratio Q/T (where Q is the amount of heat exchanged by a system at temperature T) corresponds, in classical thermodynamics, to the variation of a state function which he called entropy, S and whose unit is the joule per kelvin (J/K).

Statistical thermodynamics then shed new light on this abstract physical quantity: it can be interpreted as the measurement of the degree of disorder of a system at the microscopic level. The higher the entropy of the system, the less its elements are ordered, interrelated, and capable of producing mechanical effects, and the greater the share of energy unused for obtaining work; that is, wasted incoherently. Ludwig Boltzmann expressed the statistical entropy as a function of the number Ω of microscopic states, or a number of configurations, defining the equilibrium state of a given system at the macroscopic level: this is Boltzmann’s formula { S=k_B \cdot\ln(\Omega)}.

This new definition of entropy is not contradictory to that of Clausius. The two expressions of entropy simply result from two different points of view, depending on whether one considers the thermodynamic system at the macroscopic level or at the microscopic level.

More recently, the concept of entropy has been generalized and extended to many areas, such as for example Shannon’s entropy in the context of information theory in computer science; topological entropy, as well as the metric Kolmogorov-Sinai entropy, within the framework of the theory of dynamical systems in mathematics

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Entropy according to Classical Thermodynamics

The non-conservation of Entropy

The difficulty in giving an intuitive definition of the entropy of a system comes from the fact that it is not conserved. It may increase continuously during an irreversible transformation. Indeed, according to the second law of thermodynamics, the entropy of an isolated system cannot decrease, it increases or it remains constant if the transformation is reversible.

Reversible Transformations

A transformation affecting a thermodynamic system is said to be reversible if it is quasistatic and takes place without friction resulting in a heat dissipation phenomenon. Under these conditions, the transformation can be considered as consisting of a succession of states of equilibrium. If we reverse the direction of the constraint of the external environment, responsible for the transformation, we then go back through the same states of equilibrium since there have been no dissipative phenomena. We can then model the transformation and perfectly describe, it at any time.

The reversible transformation is therefore an ideal model (to be compared to the ideal model of the perfect gas), which can be approached in real transformations, by ensuring that the transformation is very slow, the imbalance of the state variables very weak, and minimizing friction.

Note: A reversible transformation that would be filmed could be projected in reverse (ie from the end to the beginning) w ithout the sequence appearing abnormal. This is the case, for example, in a first approximation, for a rubber ball that bounces once on a hard floor, it would be difficult to distinguish whether the film is projected upright or upside down. Strictly speaking, this is false because the friction during the impact and the friction of the air, however low they may be, make the process irreversible and after several bounces, the ball would stop. The reverse film would then be shocking since the ball would bounce higher and higher!

Conversely, a fundamentally irreversible transformation does not make it possible to make this observation, as in the case of an egg crashing on the same hard ground: thrown upside down we would see the broken egg reconstitute itself and then rise in the air. We find in this interpretation a manifestation of the arrow of time.

 Irreversible Transformations

The real transformations are irreversible because of dissipative phenomena. The system can never spontaneously go back. The energy lost by the system in the form of heat contributes to the increase in the overall disorder. The disorder is measured by a state function called entropy: S, introduced by the second law of thermodynamics.

While the first principle is the principle of conservation of energy, the second principle is the principle of evolution. It stipulates that any real transformation takes place with an increase in global disorder (system + external environment); disorder being measured by entropy. We also say that there is the creation of entropy.

The modern expression of the second principle formalizes this creation of entropy:

  • \Delta S_{global} = S_{cr\acute{e}\acute{e} = \Delta S_{system\grave{e}me} + \Delta S_{ext\acute{e}rieur} > 0 ~
  • In the case of the reversible ideal transformation, there is no creation of entropy:
  • S_{cr\acute{e}\acute{e}e} = \Delta S_{system\grave{e}me} + \Delta S_{ext\acute{e}rieur} = 0~


Entropy and its increase in nature, in the closed system of our environment, characterizes our path to extinction and self-destruction. From an energy point of view, the use of non-renewable energy sources, nuclear energy and means that exceed the naturalness of nature burdens our environment. This load is constantly increasing along with entropy and chaos in the form of hurricanes, excessive heat, drought or rain. Nature itself does not know chaos, it has its own fixed order, and only we create it together with an increase in entropy because we use physical laws to the extreme limits, which are not necessary for life.

For example, we create the heat of the home (20°C) in distant power stations using steam at a temperature of several hundred °C, we mine coal (we devastate the landscape and set up lives in the mines), we burn coal (which is the most primitive use of a unique chemical raw material that cannot be replaced), then we heat the steam, turn the expensive turbine with it, drive the generator with it and thereby produce electricity.

Then there is a long lossy line, and then only we, who use the rest of the expensive energy to heat the poorly insulated buildings, the expensive woodwork.

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