🥵Thermodynamics Unit 7 – The Third Law of Thermodynamics
The Third Law of Thermodynamics explores the behavior of systems as they approach absolute zero temperature. It establishes that a perfect crystal's entropy becomes zero at this point, providing a reference for entropy calculations and insights into low-temperature phenomena.
This law has far-reaching implications, from cryogenic technologies to chemical equilibria. It sets limits on refrigeration efficiency, helps predict reaction spontaneity, and plays a crucial role in understanding extreme environments in astrophysics and condensed matter physics.
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Key Concepts and Definitions
Entropy is a measure of the disorder or randomness in a system and increases as temperature increases
At absolute zero (0 K), a perfect crystal has zero entropy since there is no disorder
Absolute zero is the lowest possible temperature where all molecular motion ceases
Corresponds to -273.15°C or -459.67°F
Heat capacity is the amount of heat required to raise the temperature of a substance by one degree
Approaches zero as temperature approaches absolute zero
Residual entropy refers to the entropy that remains in a system even at absolute zero due to degeneracy or disorder
Thermal equilibrium occurs when two systems in contact have the same temperature and no net heat flow between them
Historical Context and Development
The Third Law of Thermodynamics was developed in the early 20th century to address the behavior of systems at very low temperatures
Walther Nernst, a German chemist, proposed the heat theorem in 1906 which stated that entropy changes approach zero as temperature approaches absolute zero
This laid the groundwork for the Third Law
The Nernst-Simon statement, formulated by Franz Simon in 1937, provided a more rigorous mathematical formulation of the Third Law
Experimental work by Giauque and others in the 1920s and 1930s provided strong evidence supporting the Third Law
Measurements of heat capacities of various substances at low temperatures confirmed the predicted behavior
The development of the Third Law helped to establish the absolute temperature scale and provided insights into the quantum mechanical nature of matter
Statement of the Third Law
The entropy of a perfect crystal at absolute zero is exactly equal to zero
In other words, the entropy of a system approaches a constant value as the temperature approaches absolute zero
For systems with non-zero entropy at absolute zero (residual entropy), the change in entropy approaches zero as temperature approaches absolute zero
Mathematically, limT→0ΔS=0
The Third Law provides an absolute reference point for the determination of entropy
It is impossible to reach absolute zero in a finite number of steps or in a finite amount of time
Known as the unattainability principle
Mathematical Formulation
The mathematical statement of the Third Law is given by limT→0(∂T∂S)V=0
This means that the change in entropy with respect to temperature approaches zero as temperature approaches absolute zero
The heat capacity of a system is related to the change in entropy with temperature by C=T(∂T∂S)V
As T→0, C→0 according to the Third Law
For a perfect crystal, the entropy at absolute zero is given by S(0)=0
This serves as a reference point for calculating absolute entropies
The Third Law can be used to calculate the absolute entropy of a substance at any temperature by integrating the heat capacity: S(T)=∫0TT′C(T′)dT′
Implications and Applications
The Third Law has important implications for the behavior of materials at low temperatures
Superconductivity and superfluidity are phenomena that occur near absolute zero
Understanding the Third Law is crucial for the development of cryogenic technologies and the study of condensed matter physics
The Third Law provides a fundamental limit on the efficiency of refrigeration and heat engines
It is impossible to achieve 100% efficiency in a heat engine or to reach absolute zero in a refrigerator
The Third Law is used in the calculation of chemical equilibria and reaction feasibility at low temperatures
Helps predict the spontaneity and direction of chemical reactions
The Third Law has applications in astrophysics, particularly in understanding the behavior of matter in extreme environments like neutron stars and white dwarfs
Experimental Verification
Experimental measurements of heat capacities at low temperatures have provided strong support for the Third Law
Heat capacities of various substances (metals, dielectrics, superconductors) approach zero as T→0
Measurements of the entropy changes in chemical reactions and phase transitions near absolute zero are consistent with the Third Law
Entropy changes become very small at low temperatures
Spectroscopic studies of materials at low temperatures have confirmed the decrease in molecular motion and vibrational modes predicted by the Third Law
Investigations of the magnetic properties of materials at low temperatures (magnetization, susceptibility) have also verified the Third Law
Magnetic entropy contributions vanish as T→0
Limitations and Exceptions
The Third Law applies strictly to perfect crystalline solids at absolute zero
Real materials may have defects, impurities, or other sources of disorder that lead to non-zero entropy at T=0
Systems with degenerate ground states (multiple lowest energy configurations) can have residual entropy at absolute zero
Examples include ice, carbon monoxide, and certain alloys
Glasses and other amorphous materials do not have a unique ground state and may violate the Third Law
They have a non-zero residual entropy due to structural disorder
Quantum systems with strongly correlated electrons or frustrated interactions can exhibit unusual low-temperature behavior that deviates from the Third Law
Examples include spin liquids and quantum spin ice
Connection to Other Laws of Thermodynamics
The Third Law is closely related to the Second Law of Thermodynamics, which states that the entropy of an isolated system always increases
The Third Law provides an absolute reference point for entropy and sets a lower limit on the entropy of a system
The Third Law is consistent with the First Law of Thermodynamics (conservation of energy) and the Zeroth Law (thermal equilibrium)
It describes the behavior of entropy as a system approaches thermal equilibrium at absolute zero
The Third Law has implications for the efficiency of heat engines and refrigerators, which are governed by the Second Law
It sets a fundamental limit on the minimum temperature that can be achieved in a refrigeration cycle
The Third Law is important for understanding the microscopic basis of the other laws of thermodynamics
It relates the macroscopic properties of a system (entropy, temperature) to the microscopic behavior of its constituent particles