THIRD LAW OF THERMODYNAMICS

1. Introduction

The Third Law of Thermodynamics deals with the behavior of entropy at very low temperatures, especially as temperature approaches absolute zero (0 K). While the first and second laws explain energy conservation and direction of processes, the third law provides a reference point for entropy and explains why absolute zero cannot be achieved in practice.

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2. Statement of the Third Law of Thermodynamics

The Third Law of Thermodynamics can be stated in the following equivalent forms:

(a) Entropy Statement

The entropy of a perfectly crystalline pure substance is zero at absolute zero temperature (0 K).

(b) Unattainability Statement

It is impossible to reduce the temperature of any system to absolute zero in a finite number of processes.

Both statements are thermodynamically equivalent and widely accepted.

3. Concept of Absolute Zero

• Absolute zero (0 K or −273.15°C) is the lowest theoretical temperature
• At this temperature, molecular motion is at its minimum possible level
• No heat energy can be extracted from a system at 0 K

Absolute zero is a theoretical limit and cannot be reached experimentally.

4. Entropy at Absolute Zero

4.1 Perfect Crystal Concept

A perfect crystal is one in which:

• All atoms are arranged in a perfectly ordered manner
• There is only one possible microscopic arrangement (microstate)

Since entropy is a measure of disorder:$$S = k \ln W$$

Where:

• $S$S = entropy
• $k$k = Boltzmann constant
• $W$W = number of microstates

For a perfect crystal at 0 K:$$W = 1 \Rightarrow S = 0$$

Entropy–Temperature (S–T) Diagram Explanation

6. Importance of the Third Law

The Third Law provides:

• A fixed reference point for entropy calculations
• A basis for absolute entropy values, not just entropy change
• Understanding of low-temperature behavior of materials

Without the Third Law, entropy values would be relative and arbitrary.

7. Practical Implications of the Third Law

7.1 Impossibility of Reaching Absolute Zero

• Infinite steps or infinite time would be required
• Cooling methods become less effective as temperature decreases

7.2 Cryogenics

• Third law governs the design of cryogenic systems
• Used in liquefaction of gases like helium and hydrogen

7.3 Material Properties at Low Temperature

• Electrical resistance of metals decreases
• Superconductivity phenomena occur near absolute zero

8. Mathematical Interpretation

For any reversible process:$$dS = \frac{\delta Q_{rev}}{T}$$dS=TδQrev​​

As:$$T \rightarrow 0, \quad dS \rightarrow 0$$T→0,dS→0

Thus, entropy change becomes negligible near absolute zero.

9. Comparison with Other Laws of Thermodynamics

Law	Main Focus
Zeroth Law	Thermal equilibrium and temperature
First Law	Conservation of energy
Second Law	Direction of heat transfer and entropy increase
Third Law	Entropy behavior at absolute zero

10. Limitations of the Third Law

• Applies strictly to perfect crystalline substances
• Real substances may have residual entropy due to imperfections
• Not applicable to amorphous solids like glass

11. Engineering Applications

• Low-temperature physics
• Cryogenic engines and storage tanks
• Space technology
• Material science research

12. Numerical Relevance (Exam Point of View)

• Mostly theoretical questions
• Short notes and conceptual explanations
• Linked with entropy and second law concepts

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