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# Entropy

Entropy is one of the important concepts that students need to understand clearly while studying Chemistry and Physics. More significantly, entropy can be defined in several ways and thus can be applied in various stages or instances, such as in a thermodynamic stage, cosmology, and even in economics. The concept of entropy basically talks about the spontaneous changes that occur in everyday phenomena or the tendency of the universe towards disorder.

Apart from being just a scientific concept, entropy is often described as a measurable physical property that is most commonly associated with uncertainty. However, the term is also used in different fields ranging from classical thermodynamics, statistical physics and even information theory. In addition to its applications in Physics and Chemistry, it’s applied in biological systems and their relation to life, sociology, weather science and climate change, as well as to quantify the transmission of information in telecommunication.

## What Is Entropy?

Generally, entropy is defined as a measure of randomness or disorder of a system. This concept was introduced by a German physicist named Rudolf Clausius in the year 1850.

Apart from the general definition, there are several definitions that one can find for this concept. The two definitions of entropy that we will look at on this page are the thermodynamic definition and the statistical definition.

From a thermodynamics viewpoint of entropy, we do not consider the microscopic details of a system. Instead, entropy is used to describe the behaviour of a system in terms of thermodynamic properties, such as temperature, pressure, entropy, and heat capacity. This thermodynamic description took into consideration the state of equilibrium of the systems.

Besides, the statistical definition, which was developed at a later stage, focused on the thermodynamic properties, which were defined in terms of the statistics of the molecular motions of a system. Entropy is a measure of molecular disorder.

Other popular interpretations of entropy are as follows:

• If we talk about quantum statistical mechanics, Von Neumann extended the notion of entropy to the quantum domain by means of the density matrix.
• When discussing the information theory, it is a measure of the efficiency of a system in transmitting a signal or the loss of information in a transmitted signal.
• When it comes to dynamical systems, entropy defines the growing complexity of a dynamical system. It also quantifies the average flow of information per unit of time.
• Sociology states that entropy is the social decline or natural decay of structure (such as law, organisation, and convention) in a social system.
• In cosmology, entropy is described as a hypothetical tendency of the universe to attain a state of maximum homogeneity. It states that the matter should be at a uniform temperature.

In any case, today, the term entropy is used in many other sciences very much distant from Physics or Mathematics, and we must say that it no longer maintains its rigorous quantitative character.

### Properties of Entropy

• It is a thermodynamic function.
• It is a state function. It depends on the state of the system and not the path that is followed.
• It is represented by S, but in the standard state, it is represented by S°.
• Its SI unit is J/Kmol.
• Its CGS unit is cal/Kmol.
• Entropy is an extensive property which means that it scales with the size or extent of a system.

Note: The greater disorder will be seen in an isolated system; hence, entropy also increases. When chemical reactions take place, if reactants break into more products, entropy also gets increased. A system at higher temperatures has greater randomness than a system at a lower temperature. From these examples, it is clear that entropy increases with a decrease in regularity.

Entropy order: gas>liquid>solids

## Entropy Change and Calculations

During 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 given as follows:

∆S = qrev,iso/T

If we add the same quantity of heat at a higher temperature and a lower temperature, randomness will be maximum at a lower temperature. Hence, it suggests that temperature is inversely proportional to entropy.

Total entropy change, ∆Stotal =∆Ssurroundings+∆Ssystem

Total entropy change is equal to the sum of the entropy change of the system and surroundings.

If the system loses an amount of heat q at a temperature T1, which is received by surroundings at a temperature T2.

So, ∆Stotal can be calculated

∆Ssystem=-q/T1

∆Ssurrounding =q/T2

∆Stotal=-q/T1+q/T2

● If ∆Stotal is positive, the process is spontaneous.

● If ∆Stotal is negative, the process is non-spontaneous.

● If ∆Stotal is zero, the process is at equilibrium.

 Points to Remember A spontaneous process is thermodynamically irreversible. The irreversible process will attain equilibrium after some time.

Entropy change during the isothermal reversible expansion of an ideal gas

∆S = qrev,iso/T

According to the first law of thermodynamics,

∆U=q+w

For the isothermal expansion of an ideal gas, ∆U = 0

qrev = -wrev = nRTln(V2/V1)

Therefore,

∆S = nRln(V2/V1)

### Entropy Change During Reversible Adiabatic Expansion

For an adiabatic process, heat exchange will be zero(q = 0); therefore, reversible adiabatic expansion is taking place at a constant entropy (isentropic),

q = 0

Therefore,

∆S = 0

Even though the reversible adiabatic expansion is isentropic, the irreversible adiabatic expansion is not isentropic.

∆S is not equal to zero.

## Entropy and Thermodynamics

Here, we will compare or understand the relationship between entropy and the different laws of thermodynamics.

### First Law of Thermodynamics

It states that heat is a form of energy, and thermodynamic processes are, therefore, subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one place to another and converted to and from other forms of energy.

Note:

1. Entropy increases when solid changes to a liquid and a liquid changes into gases.
2. Entropy also increases when the number of moles of gaseous products increases more than the reactants.

Some things are contrary to expectations about entropy.

• A hard-boiled egg has greater entropy than an unboiled egg. It is due to the denaturation of the secondary structure of the protein (albumin). Protein changes from the helical structure into a randomly coiled form.
• If we stretch a rubber band, entropy gets decreased because macromolecules get uncoiled and arranged in a more ordered manner. Therefore, randomness will decrease.

### Second Law of Thermodynamics

According to the concepts of entropy and spontaneity, the second law of thermodynamics has a number of definitions.

1. All naturally occurring spontaneous processes are thermodynamically irreversible.
2. Complete transmission of heat into work is thermodynamically not feasible without the wastage of a certain amount of energy.
3. The entropy of the universe is continuously increasing.
4. Total entropy change is always positive. The entropy of a system plus the entropy of its surroundings will be greater than zero.

∆Stotal =∆Ssurroundings+∆Ssystem >0

### Third Law of Thermodynamics

The entropy of any crystalline solid approaches zero as the temperature approaches absolute temperature. It is because there is a perfect order in a crystal at absolute zero.

The limitation of this law is that many solids do not have zero entropy at absolute zero.

For example, a glassy solid and a solid containing a mixture of isotopes.

## Entropy Changes During Phase Transition

### Entropy of Fusion

It is the increase in entropy when a solid melt into liquid. The entropy increases as the freedom of movement of molecules increases with phase change.

The entropy of fusion is equal to the enthalpy of fusion divided by the melting point (fusion temperature)

fusS=∆fusH / Tf

A natural process such as a phase transition (for example, fusion) will occur when the associated change in the Gibbs free energy is negative.

Most of the time, ∆fusS is positive

Exception

Helium-3 has a negative entropy of fusion at temperatures below 0.3 K. Helium-4 also has a very slightly negative entropy of fusion below 0.8 K.

### Entropy of Vaporisation

The entropy of vaporisation is a state when there is an increase in entropy as liquid changes into a vapour. This is due to an increase in molecular movement which creates a randomness of motion.

The entropy of vaporisation is equal to the enthalpy of vaporisation divided by boiling point. It can be represented as,

vapS=∆vapH / Tb

## Standard Entropy of Formation of a Compound

It is the entropy change that takes place when one mole of a compound in the standard state is formed from the elements in the standard state.

## Spontaneity

● Exothermic reactions are spontaneous because ∆Ssurrounding is positive, which makes ∆Stotal positive.

● Endothermic reactions are spontaneous because ∆Ssystem is positive and ∆Ssurroundings is negative, but overall ∆Stotal is positive.

● Free energy change criteria for predicting spontaneity is better than entropy change criteria because the former requires only free energy change of the system, whereas the latter needs entropy change of both system and surroundings.

## Negentropy

It is the reverse of entropy. It means things becoming more in order. By ‘order’, it means organisation, structure and function. It is the opposite of randomness or chaos.

One example of negentropy is a star system such as a solar system.

### Solved Questions

1. The entropy of an isolated system can never ____.

a) increase

b) decrease

c) be zero

d) none of the mentioned

Explanation: The entropy of an isolated system always increases and remains constant only when the process is reversible.

2. According to the entropy principle, the entropy of an isolated system can never decrease and remains constant only when the process is reversible.

a) true

b) false

Explanation: This is the statement for the principle of increase of entropy.

3. Entropy may decrease locally in some regions within the isolated system. How can this statement be justified?

a) This cannot be possible.

b) This is possible because the entropy of an isolated system can decrease.

c) It must be compensated by a greater increase of entropy somewhere within the system.

d) None of the above.

Explanation: The net effect of an irreversible process is an entropy increase in the whole system.

4. Clausius summarised the first and second laws of thermodynamics as _____.

a) the energy of the world is constant

b) the entropy of the world tends towards a maximum

c) both of the above

d) none of the above

Explanation: These two statements were given by Clausius.

5. The entropy of an isolated system always ____ and becomes a ____ at the state of equilibrium.

a) decreases, minimum

b) increases, maximum

c) increases, minimum

d) decreases, maximum

Explanation: If the entropy of an isolated system varies with some parameter, then there is a certain value of that parameter that maximises the entropy.

## Entropy as Disorder

Even though there are many new and different interpretations of entropy, in general, it is defined as a measure of disorder and chaos. Chaos, as such, is the state of a physical or dynamic system wherein elements of all types are mixed evenly throughout the space, and so it becomes homogeneous.

Q1

### Why is entropy constant at the triple point of water?

The triple point defines a situation of simultaneous equilibrium between the solid, liquid and gas phases. The entropy of the gas phase is higher than the entropy of the liquid phase.

Q2

### Does freezing increase entropy?

Water has a greater entropy than ice, and so entropy favours melting. Freezing is an exothermic process; energy is lost from the water and dissipated to the surroundings. Therefore, as the surroundings get hotter, they gain more energy, and thus the entropy of the surroundings increases.

Q3

### Can entropy ever decrease?

It just says that the total entropy of the universe can never decrease. Entropy can decrease somewhere, provided it increases somewhere else by at least as much. The entropy of a system decreases only when it interacts with some other system whose entropy increases in the process. That is the law.

Q4

### Can entropy be infinite?

Since no finite system can have an infinite number of microstates, it’s impossible for the entropy of the system to be infinite. In fact, entropy tends towards finite maximum values as a system approaches equilibrium.

Q5

### Can entropy be negative?

If entropy is the amount of disorder, negative entropy means something has less disorder or more order. The shirt is now less disordered and in a state of negative entropy, but you are more disordered and thus, the system as a whole is in a state of either zero entropy or positive entropy.

Q6

### What causes entropy?

Several factors affect the amount of entropy in a system. If you increase temperature, you increase entropy.

• More energy put into a system excites the molecules and the amount of random activity.
• As the gas expands in a system, entropy increases.