The entropy of a system refers to the amount of thermal energy per unit temperature that cannot be used. Molecular motion results in work; thus, entropy is also a measure of the disorder or randomness of a system. It calculates the energy an object is not able to use to do work. It also measures the number of arrangements that an atom can take in a system. According to the Second Law of Thermodynamics, entropy remains the same regardless of the direction of time. The entropy can only be constant if the system is in the most disorderly state possible. At the triple point, three phases of a particular substance can coexist simultaneously, such as gaseous, liquid, and solid. Therefore, the entropy is constant at the triple point of water. The direction of spontaneous change based on entropy can explain several phenomena. The German physicist Rudolf Clausius introduced a key element of 19th-century physics in 1850.

Interpretations of Entropy

• Von Neumann used a density matrix to extend the concept of entropy to the quantum domain in quantum statistical mechanics.
• It refers to a measure of how efficiently a system transmits a signal or the quantity of information lost in a transmitted signal in the context of information theory.
• In dynamic systems, entropy represents the increasing complexity of a system. It also calculates the average rate of information flow per unit of time.
• According to sociology, entropy is the social deterioration or natural decay of structure in a social system (such as law, organisation, and convention).
• The tendency of the cosmos to approach a state of maximum homogeneity is referred to as entropy in cosmology. A constant temperature implies a constant entropy.
• However, entropy is now used in many other fields unrelated to physics or mathematics, and we have to admit that it has lost its rigorous quantitative character.

Entropy and Its Properties

• Entropy is a function of thermodynamics.
• It is a state function. Instead of the path chosen, the outcome is determined by the system’s condition.
• It is generally represented by S; however, in the normal state, it is represented by S°.
• J/Kmol is the SI unit.
• Cal/Kmol is the CGS unit.
• The entropy of a system is an extensive quality, meaning it expands in proportion to its size or scope.

An isolated system will have more disorder, leading to a greater entropy. Entropy also increases when chemical reactions break down into more products. In a system at a higher temperature, randomness is greater than at a lower temperature. With these examples, it is clear that entropy increases with a decrease in regularity.

                                       Entropy order: gas > liquid > solids

Change in Entropy and Its Calculations

As part of an entropy change, a process is defined as the amount of heat emitted or absorbed isothermally and reversibly divided by the absolute temperature. The entropy formula is as follows:

∆S = qrev,iso/T.

When the same quantity of heat is added at higher and lower temperatures, randomness will be highest at the lower temperature. It follows that temperature is inversely proportional to entropy. 

•  Thermodynamically, spontaneous processes are irreversible.

• After some time, the irreversible process will reach equilibrium.

Total entropy change, ∆Total = ∆Surroundings + ∆System

The total entropy change is equal to the sum of the entropy changes in the system and its surroundings.

If a system loses heat q at a temperature T1, which is received by surroundings at a temperature T2, ∆S total can be calculated as,

∆System = -q/T1

∆Surrounding = q/T2

∆Total = -q/T1 + q/T2

• When ∆Total is positive, the process is spontaneous.
• If ∆Total is negative, then the process is non-spontaneous.
• When ∆Total is zero, the process is in equilibrium.

When an ideal gas expands isothermally reversibly, the entropy changes

∆S = qrev,iso/T.

Following the first law of thermodynamics,

∆U = q + w

The isothermal expansion of an ideal gas is, ∆U = 0

qrev = -wrev = nRTln(V2/V1)

Therefore,

∆S = nRln(V2/V1)

Role of Vapourisation Entropy

As liquids change into vapours, there is an increase in entropy. An increase in molecular movement causes a random motion.

The entropy of vaporisation equals enthalpy of vaporisation divided by boiling point. It can be expressed as follows;

∆vapS = ∆vapH/Tb

Standard Entropy of Formation of a Compound

An entropy change occurs when one mole of a compound in the standard state is made from the elements in the standard state.

Role of Spontaneity

• In exothermic reactions, there are spontaneous reactions because the external environment is positive, which leads to a positive total.
• The endothermic reaction occurs when the system is positive, the surroundings are negative, but the overall total is positive.
• Using free energy change criteria is better than using entropy change criteria because the former requires only free energy change of the system, whereas the latter requires entropy change of both the system and surroundings.

Influence of Negentropy In Entropy

Negentropy is the reverse of entropy. It indicates that things are becoming more ordered. By order, we mean structure, organisation, and function. They are opposed to randomness or chaos.

A star system such as the solar system is an example of negentropy.

The Triple Point of Water

• A substance’s triple point is the temperature and pressure at which it can exist in all three phases (solid, liquid, and gas) in equilibrium. 
• In a three-way junction, the three phases (solid, liquid, and vapour) of a substance can co-exist in thermal equilibrium. 
• Thermal equilibrium can only occur at two (or one) phases at all other temperatures. Eventually, the ice, water and the water vapour will all reach the same temperature. 
• The air present throws the balance off.

Entropy Constant at the Triple Point of Water

The triple point is a state of simultaneous equilibrium between the solid, liquid, and gas phases.

In such a case, one can simply write:

                                     ΔS = ΔH/T

A consequence of ΔG = 0. In the case of water molar (m) enthalpies at 273 K,