The Second Law of Thermodynamics

When a hot object comes into contact with a cold object, heat flows from the hotter to the colder, never from colder to hotter spontaneously. Energy may still be conserved if heat left the cooler object and went to the hotter one. That’s where one encounters the second law of thermodynamics.

The second law of thermodynamics states that the entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible in nature. The systems are isolated and spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy.

The entropy which is of the total surroundings and the system can remain constant in ideal cases that are where the system is in thermodynamic equilibrium, or we can say is undergoing a (fictitious) reversible process in nature. In all processes that are occurring, including spontaneous processes, the total entropy of the system and its surroundings increases and the process is irreversible in nature and also in the thermodynamic sense. The entropy increase accounts for the irreversibility of natural processes, and the asymmetry which is between past and future.

Historically, if we look at the second law, it was an empirical finding that was accepted as an axiom of thermodynamic theory. classical mechanics, statistical mechanics, or quantum mechanics, explains the microscopic origin of the law.

The second law of thermodynamics has been expressed in numerous ways. This law’s first formulation is credited to the French scientist named Sadi Carnot, who in 1824 showed that there is an upper limit to the efficiency of conversion of heat to work in a heat engine. This aspect of the second law of thermodynamics is often named after Carnot.

Various Statements

The second law of thermodynamics can be expressed in numeric specific ways, the most prominent classical statements being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin in1851, and by the statement in axiomatic thermodynamics by Constantin Caratheodory in 1909. These statements of different scientists cast the law in general physical terms citing the impossibility of certain processes. The scientists,  Clausius, and Kelvin's statements have been shown to be of equal importance.

Equation for Second Law of Thermodynamics

Stoichiometrically, the second law of thermodynamics is represented as:

ΔS(univ) > 0

where ΔS(univ) is the change in the entropy of the universe.

Entropy is a measure of a system's randomness, as well as a measure of energy or chaos within a closed system. It may be thought of as a quantitative metric for describing energy quality.

Meanwhile, there are just a few causes that cause the closed system's entropy to rise. To begin with, in a closed system, heat is exchanged with the environment while the mass remains constant. This change in heat content causes a disruption in the system, increasing the entropy of the system.

Second, intrinsic modifications in the system's molecular motions are possible. This produces disruptions, which in turn cause irreversibilities inside the system, increasing the entropy of the system.

Carnot's Principle

As per history, the origin of the second law of thermodynamics was in scientists Carnot's principle only. The law refers to a cycle of a Carnot heat engine, fictively operated in the limiting mode of extreme slowness known as quasi-static so that the work and heat transfers are only between subsystems that are always in their own internal states of thermodynamic equilibrium. The engine of Carnot is an idealized device that is of special interest to engineers who are concerned with the efficiency of heat engines. The principle of Carnot was recognized by Carnot at a time when the caloric theory of heat was seriously taken into consideration, before the recognition of the first law of thermodynamics, and before the expression of mathematics of the entropy concept.  Interpreted iIn the light of the law, it is physically equivalent to the second law of thermodynamics and remains valid today. Carnot's original arguments were considered from the viewpoint of the caloric theory and before the discovery of the first law of thermodynamics. Some samples from his book are given below:

The German scientist Rudolf Clausius in 1850 had also laid the foundation stone for the second law of thermodynamics by examining the relationship between heat transfer and work. His formulation of the second law of thermodynamics, which was published in Germany in 1854, is known as the Clausius statement:

Heat can never pass from a colder to a warmer body without having some of the other changes which are connected, occurring at the same time.

Planks Proposition

Planck offered the following proposition which was derived directly from his own experience. This is sometimes regarded as his statement of the second law of thermodynamics, but he postulated it as a starting point for the derivation of the second law.

It is impossible to construct an engine that will work in a complete cycle, and produce no effect except the cooling of a heat reservoir and raising of a weight. 

The relationship was between Kelvin's statement and Planck's proposition.

It is almost customary in textbooks nowadays, to speak of the "Kelvin–-Planck statement" of the second law, as if we take an example in the text by Ter Haar and Wergeland.

The Kelvin–Planck statement or we also call it the heat engine statement of the second law of thermodynamics states that:

It is impossible to devise a device that is cyclically operating and the sole effect is- to absorb energy in the form of heat from a single thermal reservoir and to deliver an equivalent work to all.

Planck's Statement

The statement in which Planck stated the second law is as follows:

Every process which is occurring in nature proceeds in the sense in which the sum of the entropies of all bodies taking part in that process is increased. In the limit, for example for reversible processes, the sum of the entropies remains unchanged.

Planck's Principle

Max Planck in 1926 wrote a very important paper on the basics of thermodynamics. He indicated the principle as follows:

The internal energy of a closed system is increased by an adiabatic process, throughout the duration of which, the volume of the system remains constant.

This formulation does not mention temperature and does not mention heat, nor even entropy, and does not necessarily implicitly rely on those concepts, but it implies the content of the second law in thermodynamics. A statement that is closely related is that "Frictional pressure never does positive work." Planck also wrote: "The production of heat by the friction is irreversible."

If we are not mentioning entropy, this principle of Planck is stated in physical terms. It is very closely related to the Kelvin statement which was explained above. It is relevant that for a system at a mole number and constant volume, entropy is a monotonic function of the internal energy.

Clausius's Statement

It is impossible to construct a device operating in a cycle that can transfer heat from a colder body to a warmer one without consuming any work. Also, energy will not flow spontaneously from a low-temperature object to a higher-temperature object. It's vital to understand that we're talking about energy transfer on a net basis. Transfer of energetic particles or electromagnetic radiation can transfer energy from a cold object to a hot object. In any spontaneous process, however, the net transfer will occur from the hot object to the cold object. In order to move the net energy to the heated item, some type of labour is required. In other words, the refrigerator will not work unless the compressor is powered by an external source. Clausius's statement is used by the heat pump and refrigerator.

Conclusion

The thermodynamics second law states that the entropy of an isolated system can never decrease over time and is constant if and only if all processes are reversible in nature. Entropy is a measure of a system's randomness, as well as energy or chaos within a closed system.