 # 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 the everyday phenomenon or the tendency of the universe towards disorder.

## 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 here 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.

Meanwhile, 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 the molecular disorder.

### 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°.
• It’s SI unit is J/Kmol.
• It’s 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 number of 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. Entropy formula is given as;

∆S = qrev,iso/T

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

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

Total entropy change is equal to the sum of entropy change of 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, irreversible adiabatic expansion is not isentropic.

∆S 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 liquid change into gases.
2. Entropy also increases when the number of moles of gaseous products increases more than the reactants.

Some things 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 random coiled form.
• If we stretch a rubber band entropy get decreased because macromolecules get uncoiled and arranged in a more ordered manner. Therefore randomness will decrease.

### Second Law of Thermodynamics

According to 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 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 entropy of surrounding will be greater than zero.

∆Stotal =∆Ssurroundings+∆Ssystem >0

### Third Law of Thermodynamics

The entropy of any crystalline solid approaches to 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.

Example: glassy solid, 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 due to freedom of movement of molecules get increased with phase change.

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

fusS=∆fusH / Tf

A natural process such as a phase transition (eg.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 Vaporization

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

The entropy of vaporization is equal to the enthalpy of vaporization 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 ∆Ssurr is positive which make ∆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 system whereas the latter needs entropy change of both system and surroundings.

## Negentropy

It is a reverse of entropy. It means things becoming more in order. By ‘order’ it means in organisation, structure and function. It is 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 region 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 mentioned

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

4. Clausius summarized 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 mentioned

d) none of the mentioned

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 which maximizes the entropy.

### 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

### 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 are gaining more energy and thus the entropy of the surroundings is increasing.

### 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.

### 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 toward finite maximum values as a system approaches equilibrium.

### Can entropy be negative?

So 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.

### 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.