Third law of thermodynamics

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Law of thermodynamics regarding entropy at absolute zero

The Third law of thermodynamics is a fundamental principle in thermodynamics that describes the behavior of entropy as the temperature of a system approaches absolute zero. This law states that the entropy of a perfect crystal at absolute zero is exactly zero. This principle has significant implications for the study of physical chemistry, statistical mechanics, and quantum mechanics.

Statement of the Law

The Third law of thermodynamics can be formally stated as:

• As the temperature of a system approaches absolute zero, the entropy of the system approaches a constant minimum.

In mathematical terms, this can be expressed as: \[ \lim_{T \to 0} S = S_0 \] where \( S \) is the entropy and \( S_0 \) is the constant minimum entropy, which is zero for a perfect crystal.

Implications

The Third law of thermodynamics has several important implications:

• **Absolute Zero**: It implies that it is impossible to reach absolute zero in a finite number of steps because the entropy change would become infinitely small.
• **Heat Capacity**: The heat capacity of a system approaches zero as the temperature approaches absolute zero.
• **Chemical Reactions**: The law affects the behavior of chemical reactions at very low temperatures, influencing reaction rates and equilibrium positions.

Applications

The Third law of thermodynamics is crucial in various fields:

• **Cryogenics**: The study of materials at very low temperatures relies on the principles of the Third law.
• **Quantum Computing**: Understanding entropy at near absolute zero temperatures is essential for the development of quantum computers.
• **Material Science**: The properties of materials at low temperatures are influenced by their entropy behavior as described by the Third law.

History

The Third law of thermodynamics was formulated by Walther Nernst in 1906, and it is sometimes referred to as the Nernst heat theorem. Nernst's work laid the foundation for the development of modern thermodynamics and statistical mechanics.

See Also

• First law of thermodynamics
• Second law of thermodynamics
• Zeroth law of thermodynamics
• Entropy
• Absolute zero
• Cryogenics
• Quantum mechanics