Third law of Thermodynamics

Edited By Shivani Poonia | Updated on Jul 02, 2025 06:00 PM IST

The Third law of Thermodynamics is also known as the Nernst Theorem. It was discovered by the German chemist Walter Nernst in 1906. This law states that as the temperature of the system approaches absolute zero, the entropy of a perfectly crystalline substance approaches zero.

The third law of thermodynamics states that the entropy of a perfectly crystalline solid at absolute zero temperature(zero kelvin) is equal to zero. Entropy is called the randomness of the particles or disorder in the closed system and it is denoted by the S.

Mathematical Explanation Of Third Law

The entropy of any pure crystalline substance approaches zero as the temperature approaches absolute zero. This is called the third law of thermodynamics.

At any pressure, the entropy of every crystalline solid in thermodynamic equilibrium at absolute zero is zero.
It is impossible to reduce the temperature of any system to absolute zero by any process.
As the absolute temperature approaches zero, the increment in entropy for the isothermal process in crystalline solids approaches zero,

This Story also Contains

Mathematical Explanation Of Third Law
Some Solved Examples
Summary

Third law of Thermodynamics

i.e. S=0 at T=0

Or limT→0,S→0

If the molar heat capacities of a substance (Cp) are measured at different temperatures a graph between Cp/T vs T is drawn and it shows this type of behavior.

Now let SMo be the entropy of the substance at zero Kelvin and SM is its molar entropy at Kelvin then
ΔS=SM−SMo∴ΔS=SM(∵SMo=0, according to 3rd Law of thermodynamics) ΔS=qTΔS=∫0TCp⋅dTT,∵q=1×Cp⋅dT∴ΔS=SM=∫0TCp⋅dTT

The area under the curve or graph of Cp/T vs T determined from zero Kelvin to any desired temperature would be molar entropy change going from zero to desired T.

Some Solved Examples

Example 1. In defining the temperature scale, the standard reference point is taken as:

1)0 Kelvin

2)boiling point of water

3) (correct)Triple point of water

4)None of the above

Solution

In defining the temperature scale, the standard reference point is taken as the triple point of water.

Hence, the answer is the option (3)

Example 2. Which law states, “It is impossible to reduce any system to the absolute zero of temperature in a finite number of operations”.

1)1^st law of Thermodynamics

2)2^nd law of Thermodynamics

3) (correct)3^rd law of Thermodynamics

4)None of the above

Solution

3^rd law of thermodynamics states: The entropy change associated with any condensed system undergoing a reversible isothermal process approaches zero as the temperature at which it is performed approaches 0 K. It also says: It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute zero value in a finite number of operations.

Hence, the answer is the option (3)

Example 3. At absolute zero temperature, the entropy of a pure crystal is:

1) (correct)Zero

2)Positive

3)Negative

4)Any of the above

Solution

As we have learnt

3rd Law Of Thermodynamics -

The entropy of any pure crystalline substance approaches zero as the temperature approaches absolute zero. This is called the third law of thermodynamics.

At any pressure, the entropy of every crystalline solid in thermodynamic equilibrium at absolute zero is zero.
It is impossible to reduce the temperature of any system to absolute zero by any process.
As the absolute temperature approaches zero, the increment in entropy for the isothermal process in crystalline solids approaches zero,

i.e. S=0 at T=0
limT→0, S→0

According to the third law of thermodynamics, the entropy of pure crystal is zero at absolute zero temperature.

Therefore, Option(1) is correct.

Example 4. Which of the following laws was formulated by Nernst?

1) First law of thermodynamics
2) Second law of thermodynamics
3) (Correct)Third law of thermodynamics
4) None of the above

Solution

As we have learnt

3rd Law Of Thermodynamics -

The entropy of any pure crystalline substance approaches zero as the temperature approaches absolute zero. This is called the third law of thermodynamics. and it is discovered by Walter Nernst.

Therefore option (3) is correct.

Summary

The law helps in calculating the absolute entropy of a system and understanding the behaviour of various thermodynamic processes. It is very important to understand the material study at very low temperatures including the superconductor and many more.

Frequently Asked Questions (FAQs)

1. What is the Third Law of Thermodynamics?

The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero temperature is zero. This means that as a system approaches absolute zero, the disorder or randomness of particles approaches a minimum value.

2. Why is absolute zero temperature unattainable in practice?

Absolute zero is unattainable because it would require an infinite number of steps to remove all thermal energy from a system. As we get closer to absolute zero, it becomes increasingly difficult to remove the remaining energy, making it practically impossible to reach.

3. How does the Third Law of Thermodynamics relate to entropy?

The Third Law provides a reference point for entropy calculations by defining the minimum possible entropy at absolute zero. It allows us to calculate absolute entropies of substances, rather than just changes in entropy.

4. What is the significance of perfect crystals in the Third Law?

Perfect crystals are used in the statement of the Third Law because they represent the most ordered state of matter. At absolute zero, a perfect crystal would have all atoms in their exact lattice positions with no thermal motion, resulting in zero entropy.

5. Can substances have negative absolute entropy?

No, substances cannot have negative absolute entropy. The Third Law establishes zero as the lower limit for entropy, corresponding to a perfect crystal at absolute zero. All real substances have positive entropy values above this limit.

6. How does the Third Law affect chemical reactions at very low temperatures?

As temperatures approach absolute zero, chemical reactions tend to slow down or stop altogether. This is because particles have less thermal energy to overcome activation barriers, and the system's entropy change becomes a more significant factor in determining reaction spontaneity.

7. How does the Third Law affect the behavior of gases at extremely low temperatures?

As gases approach extremely low temperatures, they tend to condense into liquids or solids. This is because the particles lose kinetic energy and the attractive forces between them become more significant, leading to a more ordered state with lower entropy.

8. Why do some substances, like glasses, appear to violate the Third Law?

Glasses and other amorphous solids appear to violate the Third Law because they don't form perfect crystals at absolute zero. However, they don't truly violate the law; they simply approach a higher, non-zero entropy value as they're cooled, due to their disordered structure.

9. What is the relationship between the Third Law and Bose-Einstein condensates?

Bose-Einstein condensates, where particles collapse into the lowest quantum state at extremely low temperatures, demonstrate the principles of the Third Law. As the temperature approaches absolute zero, the particles' entropy approaches a minimum, consistent with the law.

10. Why is the Third Law sometimes called the Nernst-Planck statement?

The Third Law is sometimes called the Nernst-Planck statement because it combines Walther Nernst's heat theorem with Max Planck's quantum theory. Nernst proposed the behavior of entropy at low temperatures, while Planck's work explained why this behavior occurs at the atomic level.

11. How does the Third Law affect our understanding of the thermodynamic properties of black holes?

The Third Law has implications for black hole thermodynamics, suggesting that it's impossible to reduce a black hole's temperature to absolute zero. This aligns with other thermodynamic properties of black holes, such as Hawking radiation, and helps connect gravity with thermodynamics.

12. How does the Third Law help in calculating standard entropies?

The Third Law provides a reference point (zero entropy at 0 K) from which we can calculate standard entropies of substances at any temperature. This is done by integrating the heat capacity of the substance from 0 K to the temperature of interest.

13. What is the Nernst Heat Theorem and how does it relate to the Third Law?

The Nernst Heat Theorem, which forms the basis of the Third Law, states that the change in entropy approaching absolute zero for any isothermal process approaches zero. This implies that entropy itself approaches a constant value (zero for perfect crystals) as temperature approaches absolute zero.

14. How does the Third Law influence our understanding of phase transitions?

The Third Law helps explain why some phase transitions, like melting, become less likely as temperature decreases. As we approach absolute zero, the entropy difference between solid and liquid phases diminishes, making the transition energetically unfavorable.

15. What is residual entropy and how does it relate to the Third Law?

Residual entropy is the entropy that remains in a substance at absolute zero due to structural disorder or multiple equivalent ground states. While it seems to contradict the Third Law, it's consistent with the law's more general formulation that entropy approaches a constant (not necessarily zero) at absolute zero.

16. How does quantum mechanics support the Third Law of Thermodynamics?

Quantum mechanics supports the Third Law by explaining the discreteness of energy levels in atoms and molecules. As temperature approaches absolute zero, particles occupy the lowest energy state (ground state), leading to minimum disorder and entropy.

17. Why is the Third Law important for understanding low-temperature physics?

The Third Law is crucial for low-temperature physics because it explains phenomena like superconductivity and superfluidity, which occur when materials approach very low temperatures and their entropy becomes extremely small.

18. How does the Third Law affect the efficiency of heat engines at very low temperatures?

As temperatures approach absolute zero, the efficiency of heat engines theoretically approaches 100% according to the Carnot cycle. However, the Third Law implies that reaching absolute zero is impossible, setting a practical limit on maximum efficiency.

19. What is the connection between the Third Law and Planck's quantum hypothesis?

Planck's quantum hypothesis, which states that energy is quantized, supports the Third Law by explaining why entropy approaches zero at absolute zero. As temperature decreases, fewer energy states become available, reducing the system's entropy.

20. How does the Third Law influence our understanding of chemical equilibrium at low temperatures?

At very low temperatures, chemical equilibrium shifts towards the side with fewer moles of gas or the more ordered state, as predicted by the Third Law. This is because the entropy term in the Gibbs free energy equation becomes more significant at low temperatures.

21. Why do some scientists consider the Third Law to be more fundamental than the other laws of thermodynamics?

Some scientists consider the Third Law more fundamental because it provides an absolute reference point for entropy, unlike the other laws which deal with relative changes. It also connects macroscopic thermodynamics with the microscopic behavior of particles.

22. How does the Third Law affect our ability to reach absolute zero in practice?

The Third Law implies that reaching absolute zero requires an infinite number of steps, each removing less energy than the last. This makes it practically impossible to reach absolute zero, although we can get very close using techniques like laser cooling and magnetic cooling.

23. How does the Third Law influence the behavior of electrons in materials at very low temperatures?

At very low temperatures, electrons in materials tend to occupy lower energy states, reducing their overall entropy. This behavior, predicted by the Third Law, leads to phenomena like superconductivity, where electrons form ordered pairs with zero electrical resistance.

24. What role does the Third Law play in understanding the heat capacity of solids at low temperatures?

The Third Law explains why the heat capacity of solids approaches zero as temperature nears absolute zero. This is because fewer vibrational modes are excited at lower temperatures, reducing the material's ability to absorb heat.

25. How does the Third Law relate to the concept of absolute entropy in statistical mechanics?

The Third Law provides a macroscopic foundation for the concept of absolute entropy in statistical mechanics. It establishes that the number of accessible microstates (and thus entropy) approaches a minimum at absolute zero, aligning with statistical mechanical predictions.

26. How does the Third Law affect our understanding of magnetic ordering in materials at low temperatures?

The Third Law predicts that materials tend towards more ordered states at very low temperatures. In magnetic materials, this often leads to spontaneous alignment of magnetic moments (ferromagnetism or antiferromagnetism) as the system tries to minimize its entropy.

27. What is the significance of the Third Law for cryogenic engineering?

The Third Law is crucial for cryogenic engineering as it sets fundamental limits on cooling processes. It explains why achieving temperatures close to absolute zero becomes increasingly difficult and energy-intensive, informing the design of cryogenic systems.

28. How does the Third Law influence the behavior of mixtures and solutions at extremely low temperatures?

As temperatures approach absolute zero, mixtures and solutions tend to separate into pure components or form ordered structures to minimize entropy, as predicted by the Third Law. This behavior is important in understanding phase diagrams and crystallization processes at low temperatures.

29. What is the connection between the Third Law and the concept of perfect order?

The Third Law implies that perfect order (zero entropy) is theoretically achievable only at absolute zero temperature for a perfect crystal. This concept of perfect order serves as an idealized reference point for understanding real-world systems and their entropy.

30. How does the Third Law affect our understanding of the universe's heat death?

The Third Law suggests that the universe can never reach a state of absolute zero entropy (perfect order). This implies that the heat death of the universe, where all energy is evenly distributed, would be a state of maximum disorder rather than perfect order.

31. Why is the Third Law important for understanding the behavior of quantum computers at low temperatures?

Quantum computers often operate at extremely low temperatures to minimize thermal noise and maintain quantum coherence. The Third Law helps explain why cooling beyond certain temperatures becomes increasingly difficult, setting practical limits on quantum computer operation.

32. How does the Third Law relate to the concept of entanglement entropy in quantum systems?

While the Third Law deals with thermodynamic entropy, it has implications for entanglement entropy in quantum systems. As temperature approaches absolute zero, quantum systems tend towards their ground state, which can be highly entangled, showcasing the interplay between quantum and thermodynamic concepts.

33. What is the significance of the Third Law for understanding the properties of helium at low temperatures?

The Third Law helps explain the unique behavior of helium at low temperatures, such as its refusal to solidify under normal pressures. This is related to helium's quantum properties and its retention of some entropy (zero-point motion) even as it approaches absolute zero.

34. How does the Third Law influence our understanding of chemical reactions that produce or consume gases?

The Third Law predicts that reactions producing gases become less favorable at very low temperatures, while those consuming gases become more favorable. This is because gases have higher entropy than solids or liquids, and systems tend towards lower entropy states as temperature decreases.

35. What is the relationship between the Third Law and the concept of degeneracy in quantum systems?

The Third Law is closely related to the concept of degeneracy in quantum systems. At absolute zero, a system with degenerate ground states (multiple states with the same lowest energy) will have non-zero entropy, known as residual entropy. This is consistent with the more general formulation of the Third Law.

36. How does the Third Law affect our understanding of the behavior of electrons in metals at low temperatures?

The Third Law helps explain phenomena like the formation of electron 'Fermi seas' in metals at low temperatures. As temperature decreases, electrons fill energy states up to the Fermi level, minimizing their entropy in accordance with the Third Law.

37. What is the significance of the Third Law for understanding phase transitions in quantum critical systems?

The Third Law is crucial for understanding quantum phase transitions, which occur at absolute zero. Unlike classical phase transitions driven by thermal fluctuations, quantum phase transitions are driven by quantum fluctuations and showcase the interplay between quantum mechanics and thermodynamics predicted by the Third Law.

38. How does the Third Law relate to the concept of information in thermodynamics?

The Third Law connects to information theory through the concept of entropy. As a system approaches absolute zero, it contains maximum information (minimum uncertainty about particle positions and momenta), corresponding to minimum entropy as predicted by the Third Law.

39. What is the importance of the Third Law in understanding the limits of refrigeration?

The Third Law sets fundamental limits on refrigeration by implying that it's impossible to cool a system to absolute zero in a finite number of steps. This informs the design and theoretical limits of cooling systems, from household refrigerators to advanced cryogenic equipment.

40. How does the Third Law influence our understanding of the behavior of superconductors?

The Third Law helps explain the behavior of superconductors, where electrons form ordered Cooper pairs at low temperatures. This ordering process, which reduces the system's entropy, is consistent with the Third Law's prediction of increased order as temperature approaches absolute zero.

41. What is the relationship between the Third Law and the concept of ground state in quantum mechanics?

The Third Law aligns with the quantum mechanical concept of ground state - the lowest energy state of a system. As temperature approaches absolute zero, quantum systems tend to occupy their ground state, minimizing both energy and entropy as predicted by the Third Law.

42. What is the significance of the Third Law for understanding the behavior of quantum gases?

The Third Law is crucial for understanding quantum gases like Bose-Einstein condensates. It explains why these gases undergo phase transitions to highly ordered states at extremely low temperatures, as the system attempts to minimize its entropy.

43. How does the Third Law influence our understanding of the thermodynamic arrow of time?

The Third Law supports the concept of the thermodynamic arrow of time by establishing an absolute lower bound for entropy. It implies that the universe started in a low-entropy state and is progressing towards higher entropy, giving a direction to time from a thermodynamic perspective.

44. What is the connection between the Third Law and the unattainability of absolute zero in open systems?

The Third Law implies that absolute zero is unattainable in any real (open) system because the process of measurement or interaction with the environment would introduce some energy and entropy. This underscores the theoretical nature of absolute zero and its importance as a limiting case.

45. How does the Third Law affect our understanding of the behavior of polymers at low temperatures?

The Third Law helps explain why polymers become brittle at very low temperatures. As temperature decreases, polymer chains lose mobility and tend towards more ordered configurations to minimize entropy, leading to a loss of flexibility and increased brittleness.

46. What is the significance of the Third Law for understanding the behavior of quantum dots?

The Third Law is important for understanding quantum dots, particularly their electronic and optical properties at low temperatures. As temperature decreases, the discrete energy levels in quantum dots become more pronounced, leading to sharper spectral features and reduced entropy.

47. How does the Third Law relate to the concept of zero-point energy?

The Third Law is closely related to zero-point energy - the lowest possible energy that a quantum mechanical system can have. Even at absolute zero, quantum systems retain this zero-point energy, which contributes to residual entropy and prevents the achievement of perfect order.

48. What is the importance of the Third Law in understanding the limits of quantum computing?

The Third Law sets fundamental limits on quantum computing by implying that absolute zero (and thus perfect quantum state preparation) is unattainable. This informs our understanding of quantum error correction and the practical challenges in building large-scale quantum computers.

49. How does the Third Law influence our understanding of the behavior of topological materials at low temperatures?

The Third Law helps explain the unique properties of topological materials at low temperatures. As these materials approach absolute zero, they maintain certain topological states with non-zero entropy, showcasing the interplay between quantum topology and thermodynamics.

50. What is the significance of the Third Law for understanding the ultimate fate of the universe?

The Third Law informs our understanding of the universe's ultimate fate by suggesting that a state of absolute zero entropy (perfect order) is unattainable. This implies that even in a "heat death" scenario, the universe would retain some residual entropy, preventing a state of perfect equilibrium.