Thermodynamics/Applications of the second law

The second law of thermodynamics describes the irreversibility of thermodynamic phenomena. It quantifies entropy, denoted S, which is a form of the internal energy of a system that has been degraded.

• The entropy of a closed adiabatic (i.e., "isolated") system can only increase or remain constant.
• The entropy of a closed system (i.e., one that does not exchange matter with the outside world) can be decreased, but this will come at the cost of at least an equal increase in the entropy external to the system.

The Σ system exchanges energy with the reservoir and can thus decrease or increase its entropy.

As for the total isolated system, its entropy will remain constant if the exchanges are reversible ("quasi-static processes") or increase if the processes are irreversible ("non-equilibrium") because entropy is then created.

To illustrate this, imagine a glass filled with one part pure pastis (without alcohol, of course...) and a carafe filled with five parts water. If we pour the water into the pastis, a cloudy mixture will be created. There has been an increase in entropy between

the entropy of the system "1 part pure pastis" plus the entropy of the system "5 parts pure water" and

the entropy of the system "1 part pure pastis plus 5 parts pure water".

This is described by the following formula:

S(1 part pure pastis + 5 parts pure water) = S(1 part pure pastis) + S(5 parts pure water) + Δ(S)

where Δ(S) is the increase in entropy (called the "mixing entropy") of our water + pastis system.

Without the second principle of thermodynamics, there would be nothing to prevent us from pouring 1 dose of our water + pastis mixture into a glass, obtaining 5 doses of pure water in the carafe and 1 dose of pure pastis in the glass.

Another interpretation is to analyze the direction of energy transfer (thermodynamics being a science of energy transfer). Let's imagine two steel cubes, one heated to approximately 1,000°C and the other to 20°C. If we place them in contact with each other, the second law of thermodynamics dictates that the direction of heat transfer resulting from this contact is from the hot cube to the cold cube, meaning that the energy from the hot cube flows to the cold cube. Without the second law, nothing would dictate this direction, and by applying only the other principles of thermodynamics, we could have a mathematically correct equation describing that, following their contact, the cold cube cooled a little more and the hot cube heated a little more, which is intuitively an aberration.

However, by definition, since thermodynamics is an axiomatic science, we cannot prove the second principle of thermodynamics. We must admit this principle and then verify whether the consequences of this principle correspond to the phenomena observed in everyday life.

It's interesting to note that we can draw an analogy between entropy and the state of disorder of our system. Thus, since the entropy of the universe can only increase, disorder spreads all around us. This is why we believe that the universe is headed for ruin because, after an infinite amount of time, all its energy will be transformed into entropy, and therefore into disorder. If we want to continue with order, we would have to find another system (outside the universe) to which to transfer our disorder...

The second law of thermodynamics is more abstract than the first. This notion of order and disorder is quite difficult to grasp because it is mainly used at the molecular level, but these vivid examples are there to remind us of the very obviousness of this law.