Third Law of Thermodynamics: Introduction, Entropy, Calculations

Third Law of Thermodynamics: Translational, rotational, and vibrational molecular motions can occur among the atoms, molecules, or ions that make up a chemical system. The entropy of a system increases as the molecular motion of the system increases. The entropy of a fully ordered system would be zero. A perfect crystal at absolute zero temperature is the only system that fits this requirement \((0 \mathrm{~K})\). Let us understand what entropy and absolute temperature are and how they define the third law of thermodynamics.

What is Entropy?

Entropy is a physical quantity that represents a system’s molecular disorder or randomness. It is the amount of thermal energy in a system that cannot be used to perform useful work. This is due to the fact that work is obtained from a system’s ordered movement of molecules. Entropy describes the spontaneity of any process and aids in determining whether or not a process is thermally viable. This explains the phenomenon of the irreversibility of reactions.

The entropy of a system is proportional to its temperature. It increases with the increase in temperature and decreases with a decrease in temperature. The entropy and heat of a system are related as-

\({\rm{\Delta S = \Delta Q/T}}\)

Where:

\({\rm{\Delta S}}\) represents the entropy change in the system, \({\rm{Q}}\) represents the heat absorbed, and \({\rm{T}}\) is the temperature 

Order of entropy of solid, liquid and gas having same molar mass –

\({{\rm{S}}_{\rm{0}}}{\rm{ (gas)  > }}{{\rm{S}}_{\rm{0}}}{\rm{ (liquid)  >  > }}{{\rm{S}}_{\rm{0}}}{\rm{ (solid) }}\)

Calculating \(\Delta {{\text{S}}_{{\text{sys}}}}\)

For values calculated for one mole of substance at a pressure of \(1\) bar and a temperature of \(298 \mathrm{~K}\) standard entropies are labelled \({\rm{S}}_{\rm{0}}^{{\rm{298}}}\). Any process’ standard entropy change \(\left( {{{\rm{S}}_{\rm{0}}}} \right)\) can be calculated using the standard entropies of its reactant and product species, as shown below:

\({\rm{\Delta }}{{\rm{S}}_{\rm{0}}}{\rm{ = }}\sum {\rm{v}} {\rm{S}}_{\rm{0}}^{{\rm{298}}}\) (Products) – \({\rm{ – }}\sum {\rm{v}} {\rm{S}}_{\rm{0}}^{{\rm{298}}}\) (Reactants)

What is Absolute Temperature?

Absolute zero is the lowest temperature, i.e \({\rm{0K}}\) on the Kelvin Scale. On a Celsius scale, this is \(-273.15\) and on a Fahrenheit scale, it is \(-459.7\). Absolute zero is an unattainable ideal temperature, and a perfect crystalline structure is another unattainable ideal. Nonetheless, the third law of thermodynamics is based on the combination of these two ideals: at absolute zero, the entropy of any perfectly ordered, crystalline substance is zero.

Third Law of Thermodynamics

As the temperature approaches absolute zero, the entropy of any pure crystalline solid approaches zero. This is referred to as the third law of thermodynamics.

This means that at absolute zero temperature, a system’s randomness will be minimum. The heat of a system, which is merely a collection of the kinetic energy of the system, reduces as the temperature decreases. As a result, the kinetic energy eventually comes to a complete stop, implying that there is no randomness.

The third law of thermodynamics, in particular, discusses the universe as a whole and the degree of randomness that exists inside it.

Applications

There are two major applications of the Third law of thermodynamics. These are-

Using the third law of thermodynamics, we can find whether the substance is pure crystalline or not?

The third law of thermodynamics is all about perfectly crystalline substances which states that the entropy of a perfectly Crystalline substance will be zero at \(0\) Kelvin temperature. 

This means if the substance is not perfectly crystalline, then at \(0\) Kelvin temperature its entropy will not be zero.

Substances with some imperfections in their crystal structure will show some disorder or randomness and are not pure crystalline substances.

In this way, we can find whether the substances are pure crystalline or not.

We can find the absolute entropy of any substance at a given temperature.

The absolute entropy of any substance at a given temperature can be calculated by using the third law of thermodynamics.

We need to compare the entropy of a given substance at \({\text{T}}\) temperature with the entropy of that substance at zero Kelvin temperature. 

We have to calculate the change in entropy between these temperatures.

\({{\rm{S}}_{\rm{T}}}{\rm{ – }}{{\rm{S}}_{\rm{0}}}{\rm{ = \Delta S}}…………{\rm{(1)}}\)

Now, we know that at \({\rm{0K}}\) temperature, the entropy will be zero. So, \(\left( {{{\rm{S}}_{\rm{0}}}{\rm{ = 0}}} \right)\)

We can easily find the change in entropy \({\rm{(\Delta S)}}\), using the formula.

\({{\rm{S}}_{\rm{T}}}{\rm{ – }}{{\rm{S}}_{\rm{0}}}{\rm{ = \Delta S = }}\int_{\rm{T}}^{\rm{0}} {{{\rm{C}}_{\rm{p}}}} {\rm{dT/T}}\)

Now, after getting this entropy change \({\rm{(\Delta S)}}\), we can easily get the entropy at a given temperature \(\left( {{{\rm{S}}_{\rm{T}}}} \right)\) from the above equation \((1)\).

Summary

At \({\rm{298K}}\) and \(1\) atm pressure, the enthalpy or internal energy of an element in its most stable form is zero. The entropy of a substance decreases as its absolute temperature approaches zero. The Third Law of Thermodynamics is based on this principle, which states that the entropy of a perfectly ordered solid at \({\rm{0K}}\) is zero. The second law of thermodynamics states that a spontaneous process increases the entropy of the universe, \({\rm{\Delta }}{{\rm{S}}_{{\rm{univ }}}}{\rm{ > 0}}\). If \({\rm{\Delta }}{{\rm{S}}_{{\rm{univ }}}}{\rm{ < 0}}\), the process is non-spontaneous, and if \({\rm{\Delta }}{{\rm{S}}_{{\rm{univ }}}}{\rm{ = 0}}\), the system is at equilibrium.

FAQs

Q.1. What does the third law of thermodynamics state?
Ans: As the temperature approaches absolute zero, the entropy of any pure crystalline solid approaches zero. This is referred to as the third law of thermodynamics.

Q.2. What is the best example of the third law of thermodynamics?
Ans: Vapours of water are the gaseous forms of water at high temperatures, which illustrates the third law of thermodynamics. Within the steam, the molecules move in random motion. As a result, it has high entropy.

Q,3, Which property is evaluated using the third law of thermodynamics?
Ans: The third law of thermodynamics serves as an absolute baseline for calculating entropy. The entropy determined relative to this point is the absolute entropy.

Q.4. What is the significance of the 3rd law of thermodynamics?
Ans: The third law of thermodynamics has two essential implications: it defines the sign of any object’s entropy at temperatures above absolute zero as positive, and it establishes a fixed reference point for measuring the absolute entropy of any substance at any temperature.

Q.5. What are the applications of the Third Law of Thermodynamics?
Ans: There are two major applications of the Third law of thermodynamics, which are mentioned below:
1. Using the third law of thermodynamics, we can determine whether the substance is pure crystalline or not.
2. We can find the absolute entropy of any substance at a given temperature.

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