# Third Law of Thermodynamics

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## What is The Third Law of Thermodynamics?

The bench of chemical science which deals with the study of different forms of energy and the quantitative relationships between them is known as thermodynamics. The confined study of chemical changes and chemical substances only, the restricted branch of thermodynamics is known as chemical thermodynamics.

The third law of thermodynamics states that the entropy of a pure crystal at absolute zero is zero. The 3rd law of thermodynamics explains entropy. Entropy is the measure of the disorder in a system, and while a perfect crystal is by definition perfectly ordered so that the entropy of that crystal is zero. Whenever asked to explain the third law of thermodynamics it is necessary to mention the pure crystal state of the matter.

### Absolute Zero

The temperature at which all particle motion almost stops. The temperature is known as absolute zero, and it’s the lowest possible temperature. It is equal to -273.15 degrees Celsius, -459.67 degrees Fahrenheit, and 0 kelvin.

### Entropy

Entropy is a degree of disorder or randomness of a system. An ordered system has low entropy. A disordered system has high entropy. Any change in entropy or disorder accompanying a process from start to finish is represented by ΔS.

When the products of a reaction are less complex or more disordered than the reactants, the reaction is said to proceed with gain in entropy (+ΔS) or vice versa (-ΔS). In all spontaneous reactions such as oxidation of glucose or melting of ice, the ΔS is positive.

Nature tends to form chaos (disorder) than order- ageing, decaying, rusting etc. Usable energy is transformed to unusable energy when work is performed. The higher energy dispersal means higher entropy.

The entropy of the substance depends on its state.

### Entropy Trends and Physical Properties

• Entropy increases with melting and vaporization.

• Entropy increases when solids or liquids mixed in water.

• Entropy decreases when gas is dissolved in water.

• Entropy is lower in hard and brittle material than in malleable solids like metals.

• Entropy increases with chemical complexity.

• In an isothermal process, the change in entropy (ΔS) is the change in heat (Q) divided by the absolute temperature (T). The SI units of entropy are J/K (joules/degrees Kelvin).

ΔS = Q/T

### Mathematical Explanation of the Third Law

In mechanics, the third law of thermodynamics equation is expressed as:

S – S0 = kB lnΩ

In the above equation, S is the entropy of the system, S0 is the initial entropy, KB is the Boltzmann constant, Ω is the total number of microstates which are consisted of the macroscopic configuration of the system.

### Application of the Third Law of Thermodynamics

• It helps in the calculation of the absolute entropy of a substance at any temperature. These determinations are based upon the heat capacity measurements. For a solid, if So is the entropy at 0 K and S is the entropy at T K, then

ΔS = S - So = $\int_{0}^{T}$ Cp dT/T

As according to the third law, So = 0 at 0 k, therefore,

S =  $\int_{0}^{T}$ Cp/T . dT

The value of this integral can be obtained by plotting Cp/T versus T and then finding the area under the curve from 0 k to T K.

However, a simplified expression for the absolute entropy of solids at temperature T is given below:

S = $\int_{0}^{T}$ Cp dT/T = $\int_{0}^{T}$ Cp d ln T

= Cp ln T = 2.303 Cp log T

Where Cp is the heat capacity of the substance at constant pressure and is supposed to remain constant in the range 0 to T K.

• It defines the sign of entropy.

### Third Law of Thermodynamics Example

Steam/vapours of water are the gaseous forms of water at high temperature. The molecules within the steam move randomly. Therefore, it has high entropy. If these vapours set for cooling this steam to below 100 degrees Celsius it will get transformed into water, where the movement of the molecules will be restricted resulting in a decrease in entropy.

### Limitations of the 3rd Law of Thermodynamics

Some molecules like carbon dioxide, carbon monoxide, nitric oxide, nitrous oxide, solid chlorine, and ice do not follow this law.

### Did You Know?

• For non-reacting substances on mixing entropy, the system always increases.

• Entropy is an extensive property.

• The process proceeds spontaneously in the direction in which randomness or disorderness increases.