Third law of thermodynamics, introduced in the late 19th century, is a fundamental concept in thermodynamics and statistical mechanics. This establishes a theoretical limit for absolute zero temperature, the lowest possible temperature where the particles undergo minimal vibrational motion. The principle gives us insight into the behavior of matter at low temperatures which is of huge importance for various branches such as physics, chemistry, and materials science.

In this article, we will learn about third law of thermodynamics along with its application and limitations.

What is Third Law of Thermodynamics?

The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero temperature is exactly equal to zero. In other words, as the temperature of a perfect crystal approaches absolute zero, its entropy approaches a minimum value. This principle is the basis of calculating absolute entropy at any temperature above 0 K by summing up the ratios of heat over temperature. The Third Law has two significant consequences:

• Existence of Absolute Zero: The Third Law establishes the concept of absolute zero temperature, that is the lowest possible temperature theoretically attainable in any system.
• Entropy at Absolute Zero: The Third Law states that the entropy of a perfect crystal at absolute zero is zero.

Alternative Statement of Third law of thermodynamics

The alternate statements of the Third Law of Thermodynamics:

• Nernst statement: According to Nernst statement of third law of thermodynamics ‘it is impossible to reduce any system to absolute zero temperature in a finite number of operations’.

• Nernst-Simon heat theorem: According to this statement “As the temperature approaches absolute zero, the heat capacity of a system approaches zero for most substances.”

• Lewis-Randall Statement: As per this statement “As a system approaches absolute zero, its entropy change approaches zero“. This is because a system at zero temperature exists in its ground state, and its entropy is determined only by the degeneracy of that state.

Mathematical Derivation of Third law of thermodynamics

To mathematically derive the Third Law of Thermodynamics, we start with the definition of entropy,

S=klnΩ

Where:

• S is the entropy,
• k is the Boltzmann constant, and
• Ω is the number of microstates corresponding to a macrostate.

At absolute zero temperature, the system is in its ground state, so only one microstate is available. Therefore, Ω = 1 at absolute zero.

Next, we consider the change in entropy as the temperature approaches absolute zero. Using the definition of entropy, we have:

lim_T→0 ​S = lim_T→0 klnΩ

Since Ω = 1 at absolute zero, the above equation simplifies to:

lim_T→0​ S = lim_T→0​ kln1 = 0

This derivation proves that when the temperature approaches to absolute zero, the entropy of a perfect crystal is also approaching to zero state, which postulates the Third Law of Thermodynamics.

Why Zero Kelvin Temperature is not achievable?

As stated in the Third Law of Thermodynamics, a perfect crystal at a temperature of 0K (absolute zero) has an entropy of 0. This is because the most perfect crystal at absolute temperature has the lowest possible entropy. But, it is impossible to obtain an absolute zero because one would need infinite energy to eliminate each tiny bit of the thermal energy from a system. This is because the entropy of a substance depends on the number of microstates it can occupy, and as the temperature goes near its minimum value, that is, absolute zero, the number of microstates available to it reduces; thus, its entropy decreases.

The line in the graph shows the graphical depiction of the relationship between entropy and temperature via an entropy-temperature graph, in which the initial entropy increases with increasing temperature. From graph, we can observe that the number of steps needed to cool the substance further increases with decreasing substance temperature. The number of steps needed to cool the substance further approaches infinity as the temperature approaches 0 kelvin.

Applications of Third Law of Thermodynamics

The applications of the Third Law of Thermodynamics include:

• The calculation of absolute entropy, which is essential for determining the thermodynamic properties of substances.

• The understanding of the behavior of heat capacities as the temperature approaches zero.

• The realization that absolute zero cannot be reached, and that it is the lowest possible temperature.

• The development of atomic standards, such as atomic clocks, which use laser-cooled atoms at low temperatures

• The study of quantum effects in solids and liquids with temperatures close to absolute zero.

Limitations of Third Law of Thermodynamics

Limitations of the Third Law of Thermodynamics include:

• Perfect Crystals: The Third Law applies specifically to perfect crystals at absolute zero temperature. In reality, it is difficult to achieve absolute zero, and perfect crystals do not exist in nature.

• Non-applicability to glass and amorphous substances: The third law of thermodynamics is not relevant to glass (supercooled liquid) or amorphous substances that are conveyed solutions.

• Quantum Effects: At extremely low temperatures, quantum mechanical effects become significant. These effects, such as zero-point energy and quantum fluctuations, can influence the behavior of systems in ways that are not fully accounted by classical thermodynamics.

Also Check,

• Zeroth Law of Thermodynamics
• Second Law Of Thermodynamics
• First Law of Thermodynamics

FAQs on Third Law of Thermodynamics

What is the 3rd law of thermodynamics?

The third law of thermodynamics states that the entropy of a perfect crystal at absolute zero temperature is exactly equal to zero.

What is thermodynamics?

Thermodynamics is the branch of physics that deals with the study of energy and its transformations, particularly in relation to heat and mechanical work, and the properties of systems undergoing such transformations.

What is entropy?

Entropy is a fundamental concept in thermodynamics that measures the amount of disorder or randomness in a system. It is often described as a measure of the system’s tendency to move toward equilibrium, where the distribution of energy becomes more uniform and the system reaches a state of maximum entropy.

What is Zeroth law of thermodynamics?

The Zeroth Law of Thermodynamics states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

What is second law of thermodynamics?

The Second Law of Thermodynamics states that the total entropy of an isolated system always tends to increase over time. In other words, natural processes tend to move towards states of higher disorder or entropy.

What role does the Third Law play in materials science?

For materials scientists, the Third Law serves as a basis for understanding and predicting the material behavior at cryogenic temperatures, where the temperature must be strongly regulated and the qualities of the material must be consistently stable for applications such as superconductors and quantum computers.