Third Law Of Thermodynamics : Limitation On Entropy & The Concept Of Absolute Zero

As we know that thermodynamic deals with the transformation of energy from one form to another and the laws of thermodynamics describe the limits within which these transformations occur.  

"The laws of thermodynamics define a set of physical quantities, such as temperature, energy, and entropy, that characterize a thermodynamic system in thermodynamic equilibrium". 

In thermodynamics, we usually study four fundamental laws: the Zeroth Law, the First Law, the Second Law, and the Third Law of thermodynamics. 

Zeroth Law, First Law and the Second Law of Thermodynamics lead to the concepts of Temperature, Energy Conservation and The Entropy respectively. However, the third law does not lead to any new concepts. It only limits the value of the entropy of a pure, crystalline substance when the value of temperature approaches zero. 

In this article, we're interested in learning more about the "Third Law Of Thermodynamics", also known for the concept of "Absolute Zero Temperature".

All About Third Law Of Thermodynamics

Let us look at the third law of thermodynamics in detail. Like,

What is the third law of thermodynamics, how is it defined and what does it describe???

HISTORY OF THIRD LAW AND THEIR STATEMENT

When German chemist Walther Hermaan Nernst studied about the second law of thermodynamics, his mind was completely disturbed. He studied that the entropy of the universe keeps on increasing for all the processes occurring on its own. He thought that, what should be done so that the entropy of the universe will not increase and it will remain constant?

Then he studied everything about entropy. After a lot of studying and research work, he discovered the "Third Law Of Thermodynamics". 

This, the third law of thermodynamics, sometimes called Nernst's theorem or Nernst's Postulate, relates to the entropy and temperature of a physical system. He states the third law of thermodynamics as;

"The entropy of a pure & perfectly ordered crystalline substance at absolute zero temperature (or 0 Kelvin temperature) is zero". That means, only a pure and perfectly ordered crystalline substance at absolute zero temperature exhibit no molecular motion and have zero entropy. 

ASSUMPTION

The basis of the third law of thermodynamics rests on the following two assumptions;

• The system temperature must be equal to the absolute zero temperature (or approaches to absolute zero temperature).

• The substance must be a pure and perfectly crystalline substance.

➛ Both these assumptions are ideal conditions which are not really attainable. And these two conditions are the basis for the Third Law of Thermodynamics. Thus, these assumptions behave like limitations of the second law of thermodynamics because these assumptions cannot actually be obtained.

WHAT IS RANDOMNESS AND ENTROPY IN THIRD LAW???

Before starting the Third law of thermodynamics, I would like to explain two terms;

1) Randomness

2) Entropy

Let me explain to you about randomness and entropy by taking an example from daily life;

What do you do in your classroom in the presence of a teacher and without a teacher??

You sit silently and disciplined in the classroom and not moving at all when there is a teacher in the classroom. That means there is no disorder or no randomness in the classroom. But when there is no teacher in the classroom, you all are moving here & there in a classroom and not showing any discipline. That means there is disorder and randomness in the classroom.

!!!!This Is A Simple Concept Of Randomness Or Disorder. And Entropy Is Nothing But The Measure Of Randomness Or Disorder In Any SySTEM!!!!

Let us now understand about randomness and entropy by taking the example of;

States of matter like solid, liquid, gas?????????

• In solids, the molecules are properly arranged, which means it has less randomness, so the entropy of solids is least.

• In gases, the molecules move very fast throughout the container compared to liquid. It has more randomness which means it has more entropy.

• While in liquid molecules moves faster than solids and slower than gases this the entropy/randomness of liquids lies in between the solids and gases.

Thus;

RANDOMNESS (The movement of molecules is known as randomness)

              Solids ≺ Liquids ≺ Gases

ENTROPY (The measurement of randomness of the system is known as entropy)

              Solids ≺ Liquids ≺ Gases

Therefore, the greater the randomness or disorder of the system, the higher the entropy of that system. The entropy is denoted by the alphabet “S”. The unit of entropy is J/K.

STATEMENT OF THIRD LAW OF THERMODYNAMICS

The third law of thermodynamics states that, "The value of entropy of a completely pure crystalline substance is zero at absolute zero temperature". That means, at absolute zero temperature a pure crystalline substance exhibit no molecular motion and hence, have zero entropy. 

Generally, at absolute zero temperature (0 Kelvin temperature), all modes of motion stop (no translational, no rotational, no vibrational motion).

What happens when temperature rises?

In general, the molecules vibrate faster, oscillate more frequently, move more linearly and rotate more rapidly as the temperature rises. As a result, as the randomness increases, the entropy also increases.

Now, what happens when temperature decreases?

The answer is simple. Molecular vibration decreases, thus randomness of molecules also decreases and this results in a decrease of entropy.

Thus, the third law of thermodynamics tells us that for a pure crystalline solid substance if its temperature is absolute zero (0 K), its entropy will be zero.

PERFECT CRYSTALLINE SUBSTANCE

The perfect crystal is a substance with almost no imperfections. Third law of thermodynamics is all about these pure crystalline substances. The atoms in a perfect crystalline substance look something like this. All the atoms are of same size and they are arranging in a perfect order.

This type of substance is known as a perfect crystalline substance or pure crystalline substance. Third law of thermodynamics is not applicable to all substances. There are many substances which do not obey the 3rd law of thermodynamics. 

ABSOLUTE ZERO TEMPERATURE

In practice, it is not possible to achieve absolute zero temperature. Generally, the Kelvin Scale is known as the Absolute Temperature Scale. "Absolute zero temperature is the coldest possible temperature ever which is a theoretical assumption and is measured on the Kelvin scale". Kelvin scale doesn't have a negative value of temperature.

          { 0 K ＝ –273.15 °C ＝ –459.67 °F }

At absolute zero temperature, the thermodynamic system must be in a state with minimum thermal energy and all molecular motion within the system will stop. And also no heat energy within the system at this temperature. Thus, the entropy of the system becomes zero at this temperature.

SIGNIFICANCE/CONSEQUENCES OF THIRD LAW

(1) It provides a Fixed Reference Point (means zero entropy at zero Kelvin temperature) that allows us to measure the absolute entropy of any substance at any given temperature, "T".

(2) It states that the sign of entropy of any substance is always positive at any temperature above absolute zero temperature. Therefore, entropy is always increasing (or zero) and never decreasing.

Thus, "The Absolute Entropy of a pure substance at a given temperature,T will be the sum of the total entropy obtained by heating it from absolute zero temperature to a particular temperature,T ".

MATHEMATICAL EXPLANATION AND EQUATION

L.Boltzmann and J.W. Gibbs developed a quantitative method for expressing the disorder of a thermodynamic system by means of a quantity "Ω". Where "Ω" is defined as the number of different ways that microscopic particles can be distributed among "States" that are accessible to them.

According to Boltzmann, entropy is related to the number of possible microscopic states and is given by an equation,

     Entropy, [ ∆S ＝ S –S₀ ＝ k ln(Ω) ]

Here,

       S is the entropy of the system

       S₀ is the initial entropy of system

       k is the Boltzmann constant

       Ω is the number of possible microstates

For a perfect crystalline substance, the number of possible microstates is exactly one (which has the minimum energy called Ground state) at absolute zero temperature. The microstate in which the energy of the system is at its minimum is called the Ground State.

Thus, Entropy of the system;

                    ➩ ∆S ＝ S –S₀ ＝ k ln(1) 

                    ➩ ∆S ＝ S –S₀ ＝ k×0

                    ➩ ∆S ＝ S –S₀ ＝ 0

If the initial entropy 'S₀' selected as 0 then;

                    ➩ { Entropy, S ＝ 0 }

Thus, the entropy of a pure perfectly crystalline substance is “ZERO” at absolute zero temperature. This happens because the atoms, molecules or ions that compose a chemical system (or a substance) can undergo a variety of molecular motions including "Translational, Rotational and Vibrational Motion". And the higher the molecular motion in a system, the higher the number of possible microstates and hence, the higher the entropy of the system. And for a perfect crystalline substance at absolute zero temperature, the system has only a single micro-state and hence the entropy of a system become zero.

Now, when the initial entropy of the system is taken as zero, the value of Absolute Entropy 'S' can be calculated easily. 

APPLICATION OF THIRD LAW

An important application of the third law of thermodynamic is that it helps us in the calculation of the Absolute Entropy of a system/substance at any given temperature,T. 

Here, 

S₀ is the entropy at zero Kelvin temperature and Sт is the entropy of substance/system at a given temperature,T

Since, S₀=0 because of third law;

The above value of integral can be obtained by plotting the graph of "Cр /T Vs T " and then finding the area of this curve from "0 to T" Kelvin.

FAQs

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

Third law of thermodynamics is all about perfectly crystalline substances. It states that the entropy of a perfectly Crystalline substance will be zero at 0 Kelvin temperature. That means if the substance is not perfectly crystalline, then its entropy will not be zero at 0 Kelvin temperature. And such substances are not pure crystalline substances. These substances will have some imperfections in their crystal structure. These substances will show some disorder or randomness. And this disorder or randomness is also known as residual entropy.

Why are you studying third law? What are its applications?

As we know, we only find the change in the entropy of a system not the entropy alone of the system. But, with the help of third law of thermodynamics, we can easily find the absolute entropy of any substance at a given temperature by comparing the entropy of a given substance at T temperature with the entropy of that substance at zero Kelvin temperature which is zero.

Which substances do not follow the third law of thermodynamics?

In general, diatomic molecules may not obey the third law of thermodynamics because there is a possibility that diatomic molecules can arrange themselves in an alternative way, so that they show some randomness/disorder as we have seen in the example of CO (carbon monoxide).

Thus such diatomic molecules may not show zero entropy at absolute zero temperature.

     

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