2.3 Third law of thermodynamics
8 min read•august 21, 2024
The third law of thermodynamics is a cornerstone of statistical mechanics, providing insights into system behavior at extremely low temperatures. It establishes fundamental limits on thermodynamic processes as temperature approaches , connecting macroscopic properties to microscopic quantum mechanics.
This law explores entropy behavior near absolute zero, introducing concepts like zero-point and . It's crucial for understanding , , and phase transitions, with applications in , quantum computing, and advanced materials research.
Definition and statement
- Third law of thermodynamics forms a crucial part of statistical mechanics, providing insights into the behavior of systems at extremely low temperatures
- Establishes fundamental limits on thermodynamic processes and properties as temperature approaches absolute zero
- Connects macroscopic thermodynamic behavior to microscopic quantum mechanical properties of matter
Absolute zero temperature
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- Defines the lowest theoretically possible temperature at or
- Represents the state where all thermal motion of particles ceases
- Quantum mechanical prevents particles from becoming completely motionless
- Serves as a reference point for many thermodynamic calculations and measurements
Unattainable perfect crystal
- Describes an idealized system with perfect atomic/molecular ordering at absolute zero
- Actual materials retain some disorder due to quantum effects and imperfections
- Concept helps in understanding the theoretical limits of entropy and other thermodynamic properties
- Provides a basis for comparing real materials to ideal behavior at low temperatures
Entropy at absolute zero
- Entropy, a key concept in statistical mechanics, approaches a constant value as temperature nears absolute zero
- Third law provides insights into the fundamental nature of entropy and its relation to microscopic states
- Understanding entropy behavior at extreme low temperatures crucial for various applications in low-temperature physics
Zero-point entropy
- Represents the residual entropy of a system at absolute zero temperature
- Arises from quantum mechanical effects and
- Calculated using statistical mechanics principles and quantum state counting
- Varies depending on the material's structure and composition (crystalline vs. amorphous)
Residual entropy
- Refers to the non-zero entropy that remains in some systems even at absolute zero
- Occurs in materials with multiple equivalent ground states (ice, carbon monoxide crystals)
- Quantified using Boltzmann's entropy formula: , where is the number of microstates
- Impacts thermodynamic calculations and predictions for low-temperature behavior
Nernst heat theorem
- Formulated by in 1906 as a precursor to the third law of thermodynamics
- Provides a mathematical framework for understanding entropy changes near absolute zero
- Crucial for developing accurate models of low-temperature thermodynamic behavior in statistical mechanics
Implications for heat capacity
- Predicts that heat capacity approaches zero as temperature approaches absolute zero
- Explains the observed decrease in specific heat of materials at very low temperatures
- Leads to the development of the Debye model for heat capacity in solids
- Helps in understanding quantum effects on thermodynamic properties (Einstein and Debye temperatures)
Entropy changes near 0K
- States that entropy changes approach zero for any isothermal process as temperature approaches absolute zero
- Implies that all substances have the same if they form perfect crystals
- Provides a method for calculating absolute entropies by integrating specific heat data
- Crucial for understanding phase transitions and chemical reactions at extremely low temperatures
Applications in statistical mechanics
- Third law principles are fundamental in developing statistical mechanical models of low-temperature systems
- Enables accurate predictions of thermodynamic properties and behavior near absolute zero
- Crucial for understanding quantum effects on macroscopic observables in many-body systems
Partition function behavior
- Describes how the partition function, a key concept in statistical mechanics, behaves as temperature approaches zero
- Demonstrates the dominance of contributions at very low temperatures
- Allows for simplified calculations of thermodynamic properties in the low-temperature limit
- Provides insights into the quantum mechanical nature of systems near absolute zero
Free energy considerations
- Examines how Gibbs and Helmholtz free energies behave in the limit of absolute zero
- Shows that free energy approaches the ground state energy of the system as temperature decreases
- Helps in predicting spontaneity of processes and equilibrium conditions at very low temperatures
- Crucial for understanding phase transitions and chemical equilibria in cryogenic systems
Experimental verification
- Experimental tests of the third law have been crucial in confirming its validity and refining our understanding
- Challenges in reaching extremely low temperatures have led to innovative experimental techniques
- Verification experiments have provided insights into quantum effects and low-temperature physics
Calorimetry at low temperatures
- Involves precise measurements of heat capacity and enthalpy changes near absolute zero
- Requires specialized equipment capable of operating at cryogenic temperatures (dilution refrigerators)
- Utilizes adiabatic demagnetization and other techniques to achieve ultra-low temperatures
- Provides data for calculating absolute entropies and verifying third law predictions
Specific heat measurements
- Measures how the specific heat of materials approaches zero as temperature decreases
- Reveals deviations from classical behavior due to quantum effects (electronic, magnetic contributions)
- Helps in identifying and characterizing phase transitions at low temperatures
- Provides experimental data for testing and refining theoretical models in statistical mechanics
Limitations and exceptions
- While widely applicable, the third law has some limitations and exceptions in certain systems
- Understanding these cases helps refine our knowledge of low-temperature physics and quantum effects
- Provides insights into exotic states of matter and novel quantum phenomena
Quantum effects
- Explains how quantum phenomena can lead to deviations from classical third law predictions
- Discusses the role of zero-point energy in preventing true absolute zero attainment
- Examines quantum tunneling and its effects on low-temperature thermodynamic properties
- Explores that occur at absolute zero (quantum critical points)
Non-crystalline materials
- Addresses how amorphous materials and glasses deviate from perfect crystal behavior
- Explains the concept of configurational entropy in disordered systems
- Discusses the Kauzmann paradox and its implications for the third law in supercooled liquids
- Examines how structural relaxation affects thermodynamic properties at low temperatures
Connection to other laws
- Third law complements and extends the first and second laws of thermodynamics
- Provides a more complete picture of thermodynamic behavior across all temperature ranges
- Essential for understanding the fundamental limits of thermal processes and energy conversion
First and second laws
- Explains how the third law relates to energy conservation (first law) and entropy increase (second law)
- Discusses the implications of the third law for the efficiency of heat engines and refrigerators
- Examines how the third law affects the concept of absolute temperature scales
- Explores the role of the third law in understanding irreversibility and the arrow of time
Statistical interpretation
- Relates the third law to the microscopic behavior of particles and quantum states
- Explains how the third law emerges from statistical mechanical principles (Boltzmann's entropy formula)
- Discusses the connection between entropy and information theory in the context of the third law
- Examines how the third law influences our understanding of ergodicity and equilibration in many-body systems
Implications for phase transitions
- Third law provides crucial insights into the behavior of materials undergoing phase changes at low temperatures
- Helps in understanding the fundamental nature of different types of phase transitions
- Crucial for predicting and explaining low-temperature phenomena in condensed matter physics
Order-disorder transitions
- Examines how the third law affects transitions between ordered and disordered states
- Discusses the concept of critical exponents and universality in the context of low-temperature phase transitions
- Explores the role of symmetry breaking in order-disorder transitions near absolute zero
- Analyzes specific examples (ferromagnetic transitions, superconducting transitions)
Quantum phase transitions
- Describes phase transitions driven by quantum fluctuations at absolute zero
- Explains the concept of quantum critical points and their influence on material properties
- Discusses experimental techniques for studying quantum phase transitions (neutron scattering, NMR)
- Examines applications in understanding exotic states of matter (quantum spin liquids, topological insulators)
Third law in quantum systems
- Explores how the third law manifests in systems dominated by quantum mechanical effects
- Provides insights into the fundamental nature of quantum states and their thermodynamic properties
- Crucial for understanding low-temperature behavior in quantum computing and quantum information systems
Ground state degeneracy
- Explains how multiple ground states can lead to non-zero entropy at absolute zero
- Discusses the concept of topological degeneracy in certain quantum systems
- Examines the implications for quantum computing and error correction (topological qubits)
- Analyzes specific examples of systems with ground state degeneracy (frustrated magnets, quantum Hall systems)
Quantum entanglement effects
- Describes how entanglement influences the thermodynamic properties of quantum systems at low temperatures
- Discusses the concept of entanglement entropy and its relation to the third law
- Examines the role of entanglement in quantum phase transitions and critical phenomena
- Explores potential applications in quantum sensing and metrology at ultra-low temperatures
Technological applications
- Third law principles have significant implications for various technological applications
- Understanding low-temperature behavior crucial for developing advanced cooling systems and sensors
- Enables exploration of quantum phenomena for next-generation technologies
Cryogenics
- Discusses the development of cryogenic cooling techniques based on third law principles
- Examines applications in superconducting magnets for MRI machines and particle accelerators
- Explores cryogenic preservation techniques for biological samples and organs
- Analyzes the challenges and limitations of achieving ultra-low temperatures in practical systems
Low-temperature physics
- Describes experimental techniques for studying materials at extremely low temperatures
- Discusses applications in superconductivity research and development of high-temperature superconductors
- Examines the use of low-temperature environments for precision measurements (atomic clocks, gravitational wave detectors)
- Explores potential applications in quantum computing and quantum simulation using ultra-cold atoms and ions
Historical development
- Traces the evolution of our understanding of low-temperature thermodynamics and the third law
- Provides context for the development of statistical mechanics and quantum theory
- Highlights key experiments and theoretical advances that shaped our current understanding
Walther Nernst's contribution
- Describes Nernst's formulation of the heat theorem in 1906, which laid the foundation for the third law
- Discusses Nernst's experimental work on specific heats and chemical equilibria at low temperatures
- Examines the controversy and debates surrounding the initial formulation of the third law
- Analyzes the impact of Nernst's work on the development of quantum theory and statistical mechanics
Refinements and generalizations
- Traces the evolution of the third law from Nernst's original formulation to its modern understanding
- Discusses contributions from other scientists (Planck, Einstein, Debye) in refining the third law
- Examines how advances in low-temperature physics led to more precise formulations of the third law
- Explores ongoing research and open questions related to the third law in quantum many-body systems
Key Terms to Review (20)
Absolute Zero: Absolute zero is the theoretical lowest temperature possible, measured at 0 Kelvin (or -273.15°C), where the motion of atoms theoretically comes to a complete stop. This concept is crucial in understanding thermodynamic behavior, as it sets a baseline for the third law of thermodynamics, which states that as the temperature of a perfect crystalline substance approaches absolute zero, the entropy approaches a minimum value.
Cryogenics: Cryogenics is the study and application of materials and processes at extremely low temperatures, typically below -150°C (-238°F). This field plays a crucial role in various scientific and industrial applications, such as preserving biological samples, conducting experiments in superconductivity, and enhancing the efficiency of certain technologies. It intersects significantly with the principles of thermodynamics, particularly in understanding the behavior of materials as they approach absolute zero.
Entropy at Absolute Zero: Entropy at absolute zero refers to the concept that the entropy of a perfect crystalline substance approaches zero as the temperature approaches absolute zero (0 Kelvin). This idea is a cornerstone of the third law of thermodynamics, which states that the entropy of a perfect crystal is zero when the temperature is absolute zero, reflecting a state of perfect order and minimal energy.
Ground State: The ground state is the lowest energy state of a quantum mechanical system, where all particles occupy their minimum energy levels. In this state, the system is at its most stable configuration, with no additional energy available for transition to higher energy states. Understanding the ground state is crucial in various fields, particularly in thermodynamics and statistical mechanics, as it relates to entropy and the distribution of particles among energy levels.
Ground State Degeneracy: Ground state degeneracy refers to the phenomenon where multiple distinct quantum states exist at the same lowest energy level of a system. This concept is essential because it highlights how systems can have several configurations or arrangements that yield the same energy, which has implications for entropy and thermodynamic behavior, especially as systems approach absolute zero.
Inaccessibility of Absolute Zero: The inaccessibility of absolute zero refers to the principle that it is impossible to reach a temperature of absolute zero, which is 0 Kelvin or -273.15 degrees Celsius. This concept is tied to the third law of thermodynamics, which states that as a system approaches absolute zero, the entropy of the system approaches a minimum value, but can never actually be reduced to zero in a finite number of steps. Essentially, while we can get very close to absolute zero, we can never achieve it due to physical constraints.
Lim t→0 s = 0: The expression 'lim t→0 s = 0' indicates that as the time variable 't' approaches zero, the entropy 's' of a system approaches zero. This concept is pivotal in understanding the third law of thermodynamics, which asserts that the entropy of a perfect crystal at absolute zero temperature is exactly zero. It highlights how systems behave as they cool down to absolute zero, revealing essential insights about the nature of entropy and its relationship with temperature.
Low-temperature physics: Low-temperature physics is the study of the behavior of matter at temperatures close to absolute zero, where quantum effects become significant. At these low temperatures, systems exhibit unique phenomena such as superconductivity and superfluidity, which differ dramatically from their behavior at higher temperatures. Understanding these effects is crucial for exploring fundamental questions in quantum mechanics and thermodynamics.
Ludwig Boltzmann: Ludwig Boltzmann was an Austrian physicist known for his foundational contributions to statistical mechanics and thermodynamics, particularly his formulation of the relationship between entropy and probability. His work laid the groundwork for understanding how macroscopic properties of systems emerge from the behavior of microscopic particles, connecting concepts such as microstates, phase space, and ensembles.
Nernst Heat Theorem: The Nernst Heat Theorem states that as a system approaches absolute zero, the entropy of a perfect crystalline substance approaches zero. This theorem is crucial in understanding the behavior of systems at very low temperatures and establishes a fundamental connection to the third law of thermodynamics, which reinforces the idea that it is impossible to reach absolute zero in a finite number of steps.
Order-disorder transition: An order-disorder transition is a change in the arrangement of particles in a system, where particles shift from an ordered state, characterized by a regular and repeating pattern, to a disordered state with random arrangements. This transition is significant in various physical systems, influencing properties like entropy and phase stability, and connects to concepts such as thermodynamic limits and phase behaviors.
Quantum Effects: Quantum effects refer to the physical phenomena that arise from the principles of quantum mechanics, which govern the behavior of matter and energy at the microscopic scale. These effects include wave-particle duality, superposition, and entanglement, which can lead to behaviors that deviate significantly from classical physics predictions. Understanding quantum effects is crucial for interpreting thermodynamic behaviors at low temperatures and the behavior of systems approaching absolute zero, where traditional thermodynamic laws become less applicable.
Quantum Entanglement Effects: Quantum entanglement effects refer to the phenomenon where two or more particles become interconnected in such a way that the state of one particle instantly influences the state of another, regardless of the distance separating them. This fascinating aspect of quantum mechanics challenges classical intuitions about locality and separability, leading to implications for information transfer, quantum computing, and the foundational principles of thermodynamics.
Quantum Phase Transitions: Quantum phase transitions occur at absolute zero temperature and are driven by quantum fluctuations rather than thermal fluctuations. These transitions are significant in understanding how materials change their state due to changes in external parameters like pressure or magnetic field, linking them to fundamental concepts like the third law of thermodynamics and critical phenomena in materials.
Residual Entropy: Residual entropy refers to the entropy that remains in a system at absolute zero temperature, indicating that the system can still have multiple ground states. This concept is closely related to the idea that not all systems reach a unique state of order as they cool, which contradicts the expectations set by the Third Law of Thermodynamics. Essentially, residual entropy highlights the limitations of classical thermodynamic behavior in certain materials, particularly those with complex structures or degeneracies.
S(t) = k ln ω: The equation $$s(t) = k \ln \omega$$ represents the entropy of a system, where $$s(t)$$ is the entropy, $$k$$ is the Boltzmann constant, and $$\omega$$ is the number of accessible microstates. This relationship highlights the connection between microscopic configurations of particles and the macroscopic property of entropy, emphasizing how disorder or randomness in a system correlates to its entropy. This concept is foundational for understanding the statistical interpretation of thermodynamics and connects deeply with principles that govern the behavior of matter as it approaches absolute zero.
Thermodynamic limit: The thermodynamic limit refers to the behavior of a system as the number of particles approaches infinity while keeping the volume constant, leading to a smoother and more predictable set of macroscopic properties. This concept is critical for understanding how systems transition from microscopic behavior to macroscopic thermodynamic laws, revealing underlying patterns in statistical mechanics.
Walther Nernst: Walther Nernst was a German physical chemist known for his contributions to thermodynamics, particularly the formulation of the third law of thermodynamics. He developed the Nernst heat theorem, which states that as the temperature of a perfect crystal approaches absolute zero, the entropy approaches a constant minimum value, often considered to be zero. His work laid the foundation for understanding how systems behave at low temperatures and influenced later advancements in statistical mechanics and quantum physics.
Zero-Point Energy: Zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess, which is not zero due to the uncertainty principle. It reflects the inherent fluctuations of energy present in a system at absolute zero temperature, where classical physics would suggest that all motion stops. This concept is crucial for understanding how systems behave at very low temperatures, how particles fill available energy states, and the behavior of oscillators in quantum mechanics.
Zero-point entropy: Zero-point entropy refers to the residual entropy of a system at absolute zero temperature, where the third law of thermodynamics states that the entropy of a perfect crystal approaches zero. Despite this, quantum mechanics predicts that there can still be multiple ground states, which results in a non-zero entropy value even at absolute zero. This concept highlights the limitations of classical thermodynamics and introduces the importance of quantum effects in understanding the behavior of matter at very low temperatures.