6.1 Absolute entropy and the third law
3 min read•august 6, 2024
and the Third Law are key concepts in thermodynamics. They help us understand how energy behaves in systems at extremely low temperatures. This knowledge is crucial for predicting material properties and designing efficient processes.
The Third Law states that perfect crystals have zero entropy at absolute zero. This gives us a starting point to calculate entropy at any temperature. Understanding absolute entropy helps us grasp energy distribution and availability in systems.
Absolute Entropy and the Third Law
The Third Law and Absolute Entropy
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- States the entropy of a perfect crystalline substance at absolute zero temperature is zero
- Provides a reference point for determining absolute entropy values
- Allows for the calculation of absolute entropy at any temperature by integrating the heat capacity from absolute zero to the desired temperature
- Absolute entropy quantifies the degree of disorder or randomness in a system
- Measured in units of joules per kelvin (J/K)
- Represents the amount of energy dispersed within a system that is unavailable for useful work
Nernst Heat Theorem and Entropy at Absolute Zero
- The Nernst heat theorem states that as a system approaches absolute zero, the change in entropy for any process approaches zero
- Implies that the entropy of a perfect crystal at absolute zero is zero
- Provides a theoretical basis for the
- At absolute zero (0 K or -273.15°C), the entropy of a perfect crystal is zero
- All atoms in the crystal are in their lowest energy state and have no thermal motion
- There is no disorder or randomness in the system at this temperature
Perfect Crystals and Zero-Point Entropy
Characteristics of Perfect Crystals
- A perfect crystal is a theoretical construct in which the atoms are arranged in a perfect lattice structure
- Each atom occupies a specific position in the lattice
- There are no defects, impurities, or thermal vibrations in the crystal
- In reality, perfect crystals do not exist due to the presence of imperfections and thermal motion at finite temperatures
- Real crystals have defects (vacancies, interstitials, dislocations) and impurities that contribute to entropy
Zero-Point Entropy and Its Implications
- Zero-point entropy refers to the residual entropy that exists in some systems even at absolute zero
- Occurs when there are multiple equivalent ground states or configurations with the same lowest energy
- Examples include certain alloys, glasses, and polymers with frozen-in disorder
- The presence of zero-point entropy indicates that the Third Law of Thermodynamics is not strictly followed in these systems
- The entropy does not reach zero at absolute zero temperature
- Highlights the limitations of the Third Law and the concept of perfect crystals
Exceptions to the Third Law
Residual Entropy and Its Causes
- Residual entropy is the entropy that remains in a system at absolute zero temperature
- Arises from the presence of multiple equivalent ground states or configurations
- Occurs in systems with frozen-in disorder, such as certain alloys (Cu-Au alloys), glasses (silica glass), and polymers (rubber)
- The existence of residual entropy challenges the strict interpretation of the Third Law
- Suggests that the entropy of these systems does not reach zero at absolute zero
- Indicates that the Third Law is an idealization that applies to perfect crystals but not all real systems
Examples and Implications of Residual Entropy
- Ice (H2O) has residual entropy due to the random orientation of hydrogen bonds in its crystal structure
- Even at absolute zero, there are multiple equivalent configurations of hydrogen bonds
- Leads to a non-zero entropy value at 0 K, estimated to be around 3.4 J/K per mole of water
- The presence of residual entropy has practical implications in materials science and engineering
- Affects the stability, mechanical properties, and thermal behavior of materials
- Needs to be considered when designing and characterizing materials for low-temperature applications
Key Terms to Review (16)
Absolute entropy: Absolute entropy is the measure of the disorder or randomness of a system at a specific temperature relative to absolute zero, based on the third law of thermodynamics. It quantifies how much thermal energy is unavailable for doing work in a thermodynamic system and reflects the microscopic configurations that correspond to a macroscopic state. This concept connects deeply with how entropy changes in reversible and irreversible processes.
As temperature approaches absolute zero, the entropy of a perfect crystal approaches zero: This principle states that as the temperature of a perfect crystalline substance nears absolute zero (0 Kelvin), the entropy, or the degree of disorder within the system, tends to approach zero. This concept is rooted in the third law of thermodynamics and implies that at absolute zero, a perfect crystal would be in its most ordered state, with only one possible microstate.
Calculating absolute entropy in calorimetry: Calculating absolute entropy in calorimetry involves determining the total entropy of a system at a given temperature, starting from a reference state at absolute zero, using calorimetric data. This process is linked to the third law of thermodynamics, which states that the entropy of a perfect crystalline substance approaches zero as the temperature approaches absolute zero. By integrating heat capacities and applying appropriate equations, one can derive the absolute entropy for substances under various conditions.
Closed System: A closed system is a physical system that does not exchange matter with its surroundings but can exchange energy in the form of heat or work. This concept is crucial in understanding how energy conservation principles apply within a defined boundary, which influences various thermodynamic processes and behaviors.
Irreversible Processes: Irreversible processes are transformations that cannot return to their original state without the input of external energy, often resulting in an increase in entropy. These processes typically occur spontaneously and involve energy dissipation, leading to a permanent change in the system. They contrast with reversible processes, which can be reversed with no net change in the system or surroundings.
Isolated System: An isolated system is a type of thermodynamic system that does not exchange matter or energy with its surroundings. This means that both energy and mass are completely contained within the system, leading to a set of unique behaviors in terms of thermodynamic processes. Understanding isolated systems is crucial as they provide a simplified model for studying energy transformations, process directionality, and the foundations of entropy.
Ludwig Boltzmann: Ludwig Boltzmann was an Austrian physicist best known for his foundational contributions to statistical mechanics and the understanding of entropy. He provided a statistical interpretation of the second law of thermodynamics, which connects macroscopic and microscopic states of matter through the concept of entropy. His work laid the groundwork for the modern interpretation of thermodynamic laws and how they relate to the behavior of particles at a microscopic level.
Microstates: Microstates are distinct, specific configurations of a system at the microscopic level, often characterized by the arrangement of particles and their energy states. Understanding microstates is crucial for relating the microscopic behavior of particles to macroscopic properties like temperature and entropy, which are fundamental concepts in thermodynamics.
Reversible Processes: Reversible processes are idealized thermodynamic processes that can be reversed without leaving any change in the system or surroundings. In these processes, the system is always in thermodynamic equilibrium, allowing it to return to its original state without any net energy loss or entropy production. This concept is crucial in understanding efficiency and the maximum work that can be extracted from a system, as well as how it relates to absolute entropy and the third law of thermodynamics.
S = k * ln(ω): The equation $s = k * ln(ω)$ represents the relationship between entropy (s), Boltzmann's constant (k), and the number of microstates (ω) of a system. This formula connects statistical mechanics to thermodynamics by providing a way to quantify the disorder or randomness of a system based on its microscopic configurations. Understanding this relationship is essential in grasping how systems move toward equilibrium and how entropy changes with variations in temperature and volume.
Standard molar entropy: Standard molar entropy is the measure of the degree of disorder or randomness in a system per mole of a substance at standard conditions, typically defined as 1 bar of pressure and a specified temperature, usually 298.15 K. It is a key concept that relates to the third law of thermodynamics, which states that the entropy of a perfect crystal approaches zero as the temperature approaches absolute zero, helping us understand how entropy behaves in different states of matter.
Statistical mechanics: Statistical mechanics is a branch of physics that uses statistical methods to explain and predict the behavior of systems with a large number of particles. It connects macroscopic thermodynamic properties, such as temperature and pressure, with microscopic behaviors of individual particles, helping to derive important concepts like entropy and thermodynamic laws from first principles.
Third Law of Thermodynamics: The Third Law of Thermodynamics states that as the temperature of a system approaches absolute zero, the entropy of a perfect crystal approaches zero. This principle emphasizes that it is impossible to reach absolute zero in a finite number of steps, which has important implications for understanding absolute entropy and the behavior of materials at low temperatures.
Unattainability of absolute zero: The unattainability of absolute zero refers to the principle that it is impossible to reach a temperature of 0 Kelvin, where all molecular motion theoretically ceases. This concept underscores the limitations of thermodynamic processes and is closely tied to the behavior of entropy as temperature approaches absolute zero, emphasizing that systems can get infinitely close but never actually achieve this state.
Walther Nernst: Walther Nernst was a German physical chemist who made significant contributions to thermodynamics, particularly known for formulating the third law of thermodynamics and developing the concept of absolute entropy. His work helps bridge the understanding of energy transformations in systems and how it relates to the properties of substances at varying concentrations.
δs = q_rev/t: The equation δs = q_rev/t defines the change in entropy (δs) as the amount of reversible heat (q_rev) transferred divided by the temperature (t) at which the transfer occurs. This relationship is central to understanding how entropy measures the degree of disorder or randomness in a system and plays a crucial role in thermodynamics, particularly in the context of absolute entropy and the third law.