6.1 Third Law and absolute entropy
4 min read•july 30, 2024
The is all about . It says a perfect crystal has zero entropy at 0 K, giving us a starting point to measure . This law helps us understand how substances behave at super low temps.
Calculating absolute entropy involves measuring and integrating from 0 K to the desired temperature. This connects to quantum effects like and , which pop up near . The Third Law complements the other thermodynamic laws nicely.
Absolute Entropy and the Third Law
Definition and Relationship
Top images from around the web for Definition and Relationship
The Third Law of Thermodynamics | Boundless Physics View original
Is this image relevant?
Third law of thermodynamics - Wikipedia View original
Is this image relevant?
The Third Law of Thermodynamics | Boundless Physics View original
Is this image relevant?
The Third Law of Thermodynamics | Boundless Physics View original
Is this image relevant?
Third law of thermodynamics - Wikipedia View original
Is this image relevant?
1 of 3
Top images from around the web for Definition and Relationship
The Third Law of Thermodynamics | Boundless Physics View original
Is this image relevant?
Third law of thermodynamics - Wikipedia View original
Is this image relevant?
The Third Law of Thermodynamics | Boundless Physics View original
Is this image relevant?
The Third Law of Thermodynamics | Boundless Physics View original
Is this image relevant?
Third law of thermodynamics - Wikipedia View original
Is this image relevant?
1 of 3
- Absolute entropy measures the total entropy content of a substance at a given temperature
- Reference point is zero entropy at absolute zero (0 K)
- The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero is zero
- Provides a reference point for measuring absolute entropy
- As temperature increases, the absolute entropy of a substance increases
- Due to increased molecular motion and disorder (vibrations, rotations, translations)
Temperature Dependence and Calculation
- The Third Law allows for the calculation of absolute entropy values
- Measure the heat capacity of a substance over a range of temperatures
- Integrate from absolute zero to the desired temperature
- Heat capacity is the amount of heat required to raise the temperature of a substance by one degree
- Measured in units of joules per kelvin (J/K)
- The relationship between heat capacity and absolute entropy is given by:
- is the absolute entropy at temperature
- is the heat capacity
Implications of the Third Law at Absolute Zero
Molecular Behavior and Energy
- At absolute zero (0 K), the entropy of a perfect crystal is zero
- The system is in its most ordered state with minimal molecular motion
- The Third Law implies that reaching absolute zero temperature in a finite number of steps is impossible
- Would require an infinite amount of energy to remove all thermal motion from a system
- As temperature approaches absolute zero, the heat capacity of a substance approaches zero
- The substance becomes less responsive to added heat energy
Quantum Mechanical Effects
- become more prominent near absolute zero
- Leading to phenomena such as superfluidity and superconductivity in certain materials
- Superfluidity occurs in liquids (helium-4) at extremely low temperatures
- The liquid flows without friction and has infinite thermal conductivity
- Superconductivity occurs in certain materials (lead, mercury) at low temperatures
- The material has zero electrical resistance and can conduct electricity without energy loss
Calculating Absolute Entropy
Experimental Techniques and Data
- To calculate the absolute entropy of a substance at a given temperature, integrate from absolute zero to the desired temperature
- The heat capacity of a substance can be measured experimentally
- Techniques such as calorimetry or differential scanning calorimetry (DSC)
- Accurate heat capacity data over a wide range of temperatures is essential for precise absolute entropy calculations
Integration and Equations
- The integration of requires the use of a reference point
- Provided by the Third Law (zero entropy at absolute zero for a perfect crystal)
- The absolute entropy calculation involves the following equation:
- is the absolute entropy at temperature
- is the heat capacity
- Numerical integration techniques (trapezoidal rule, Simpson's rule) are often used to evaluate the integral
- Due to the complexity of heat capacity functions
Third Law vs Other Thermodynamic Laws
Focus and Scope
- The Third Law deals with the behavior of matter at absolute zero temperature and provides a reference point for entropy
- The other laws focus on the relationships between heat, work, and energy in thermodynamic systems
- First Law: energy conservation
- Second Law: entropy and spontaneity
- Zeroth Law: thermal equilibrium and temperature
Specific Comparisons
- The First Law states that energy cannot be created or destroyed, only converted
- The Third Law specifically addresses the entropy content of matter at absolute zero
- The Second Law states that the total entropy of an isolated system always increases over time
- The Third Law provides a lower limit for entropy at absolute zero
- The Zeroth Law deals with thermal equilibrium and the concept of temperature
- Essential for understanding the Third Law's implications on matter near absolute zero
- The Third Law is most relevant when considering the properties of matter at extremely low temperatures
- The First and Second Laws are applicable to a wide range of thermodynamic systems and processes
Key Terms to Review (19)
Absolute entropy: Absolute entropy is a measure of the disorder or randomness of a system at a specific temperature, typically defined at absolute zero. It reflects the total energy dispersion within a system and is quantified in units of joules per mole per kelvin (J/mol·K). Understanding absolute entropy is essential for thermodynamic calculations, as it connects to the Third Law of Thermodynamics and standard molar entropies, which help quantify the entropy changes in chemical reactions and physical processes.
Absolute zero: Absolute zero is the theoretical lowest temperature possible, defined as 0 Kelvin (K), where molecular motion ceases completely. At this point, a system's entropy reaches its minimum value, making it a key concept in thermodynamics and statistical mechanics. Understanding absolute zero helps in measuring temperature accurately and forms the foundation for discussions around the third law of thermodynamics, particularly regarding absolute entropy.
Adiabatic Process: An adiabatic process is a thermodynamic change in which no heat is exchanged with the surroundings. During this process, any change in the system's internal energy is solely due to work done on or by the system, which makes it a critical concept in understanding how energy is conserved and transformed in various thermodynamic systems.
Entropy at absolute zero: Entropy at absolute zero refers to the state where a system's entropy theoretically approaches zero as temperature reaches 0 Kelvin. This concept is tied to the Third Law of Thermodynamics, which states that as a system approaches absolute zero, the entropy of a perfect crystal becomes constant and minimal, leading to implications for the calculation of absolute entropy and standard molar entropies.
First Law vs. Third Law: The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another, emphasizing the conservation of energy in a closed system. In contrast, the Third Law of Thermodynamics establishes that as the temperature of a system approaches absolute zero, the entropy of a perfect crystal approaches zero, highlighting the behavior of systems at extremely low temperatures and providing a reference point for absolute entropy.
Heat Capacity: Heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). This concept is vital in understanding how substances interact with thermal energy and connects to ideas like thermal equilibrium and temperature measurements, as well as internal energy and enthalpy changes in chemical reactions.
Isothermal Process: An isothermal process is a thermodynamic process in which the temperature of a system remains constant while heat is exchanged with its surroundings. This constancy of temperature has profound implications for how energy, heat, and work interact within a system, linking it closely to concepts like internal energy and enthalpy changes.
Macrostates: Macrostates refer to the overall, observable conditions of a system, characterized by macroscopic properties like temperature, pressure, and volume. These properties define the state of a system in thermodynamics and can correspond to numerous microscopic configurations or arrangements of particles. Understanding macrostates is crucial for relating microscopic behavior to thermodynamic quantities, especially in the context of entropy and the Third Law.
Microstate: A microstate refers to a specific arrangement of a system's particles that corresponds to a particular energy level, contributing to the overall entropy of the system. In statistical mechanics, the concept of microstates is crucial for understanding how the macroscopic properties of a system emerge from the microscopic configurations of its components. Each microstate represents a distinct way in which particles can be organized while maintaining the same total energy.
Nernst Equation: The Nernst Equation is a mathematical relationship that describes the electrochemical potential of a cell based on the concentrations of reactants and products involved in a redox reaction. This equation is vital in understanding how variations in concentration affect the voltage produced by electrochemical cells, allowing for insights into thermodynamic stability, reaction spontaneity, and performance in energy storage systems.
Perfect crystalline structure: A perfect crystalline structure is an ideal arrangement of atoms in a solid where the atoms are positioned in a repeating, orderly pattern without any defects or irregularities. This concept is crucial for understanding the fundamental behavior of materials at low temperatures and connects deeply to the calculations of absolute entropy and the Third Law of Thermodynamics.
Quantum mechanical effects: Quantum mechanical effects refer to the phenomena that arise from the principles of quantum mechanics, particularly at the atomic and subatomic levels. These effects often lead to behaviors that cannot be explained by classical physics, such as wave-particle duality, superposition, and quantization of energy levels. Understanding these effects is crucial when analyzing systems at low temperatures or small scales, particularly in how they relate to thermodynamic concepts like entropy and absolute zero.
S(t) = ∫_{0}^{t} c/t dt: The equation s(t) = ∫_{0}^{t} c/t dt represents the process of calculating the entropy of a system over time, where 's' is the entropy, 'c' is a constant that characterizes the system, and 't' is the time variable. This integral highlights how entropy evolves as a function of time, emphasizing the relationship between entropy and the thermodynamic processes occurring in a system. Understanding this equation is crucial for grasping how absolute entropy is defined and calculated at different temperatures.
Second Law Implications on Entropy: The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, leading to the concept that natural processes tend to move towards a state of maximum disorder or randomness. This principle implies that in any energy transfer or transformation, some energy becomes unavailable for doing work, thus increasing the system's overall entropy and reinforcing the idea that entropy is a measure of energy dispersal in a system.
Standard molar entropy: Standard molar entropy is a measure of the degree of disorder or randomness in a substance at standard conditions, typically defined as 1 bar of pressure and a specified temperature, often 298.15 K (25°C). This concept is deeply 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. Standard molar entropies provide a way to quantify the entropy associated with one mole of a substance, reflecting its microscopic configurations and the energy dispersal among those configurations.
Superconductivity: Superconductivity is a phenomenon in which certain materials exhibit zero electrical resistance and the expulsion of magnetic fields when cooled below a specific critical temperature. This behavior allows for the efficient transfer of electrical current without energy loss, making superconductors highly desirable for applications such as magnetic levitation and advanced electronic devices.
Superfluidity: Superfluidity is a phase of matter characterized by the complete absence of viscosity, allowing it to flow without dissipating energy. This unique state occurs at extremely low temperatures, where quantum mechanical effects become significant, enabling the fluid to exhibit remarkable properties such as the ability to climb walls and flow through tiny openings without resistance.
Third Law of Thermodynamics: The Third Law of Thermodynamics states that as the temperature of a perfect crystal approaches absolute zero, the entropy of the system approaches a constant minimum. This principle is essential in understanding the behavior of systems at very low temperatures and helps define absolute entropy, which is a key concept in thermodynamic calculations.
Walther Nernst: Walther Nernst was a German chemist who is best known for his formulation of the Third Law of Thermodynamics, which states that the entropy of a perfect crystal approaches zero as the temperature approaches absolute zero. His work laid the foundation for understanding absolute entropy and its implications for thermodynamic systems, bridging the gap between statistical mechanics and classical thermodynamics.