The third law of thermodynamics states that absolute zero (0 K) cannot be reached in a finite number of steps. This principle is based on the relationship between entropy and temperature of a physical system.
According to this law, when a system reaches absolute zero, its entropy approaches a constant minimum value. In an ideal system (such as a perfect crystal), this value is zero . This is because at 0 K, the system is in its ground state, with no thermal motion or additional configurations generating entropy.
Limitations of the third law of thermodynamics
Impossibility of reaching absolute zero
One of the main limitations of the third law is that absolute zero is not reachable in a finite number of steps.
This principle, known as the absolute zero inaccessibility theorem, implies that any attempt to cool a system to 0 K will only succeed in asymptotically approaching this temperature.
Consequently, there will always be a small remnant of thermal motion and hence a residual entropy.
Limitations in real systems
Another significant limitation is found in real systems , such as crystals.
Although the theory assumes perfect crystals with no structural defects, real crystals contain imperfections that generate additional configurations and increase entropy, even at temperatures close to absolute zero. These defects are unavoidable, since crystals form at temperatures above 0 K.
Incompatibility with metastable states
The third law cannot describe systems in metastable states or outside thermodynamic equilibrium, such as glasses or amorphous polymers.
In these cases, the residual entropy is not uniquely defined, which complicates the application of the law.
Theorems and statements of the third law of thermodynamics
The third law of thermodynamics is supported by several formulations that explain its relationship with entropy and temperature. The key theorems and statements associated with this principle are detailed below.
1. Nernst's theorem
Nernst's theorem states that a chemical reaction between pure crystalline phases does not generate changes in entropy when it occurs at absolute zero. That is, at 0 K, systems reach a state of maximum stability where there are no fluctuations that alter their configuration.
This theorem is also interpreted as the impossibility of reducing the absolute entropy of a system to zero by a finite number of operations. This formulation highlights that there is always a practical limit to the reduction of entropy in thermodynamic processes, especially under conditions close to absolute zero.
2. Nernst-Simon statement
The Nernst-Simon statement states that any entropy change associated with a reversible isothermal transformation of a system tends to zero as the temperature approaches absolute zero.
In practical terms, this means that reactions or processes that occur at extremely low temperatures do not produce appreciable changes in entropy, since the system is in its ground state and the possible configurations are extremely limited.
3. Planck's statement
Max Planck, one of the most influential physicists in formulating the laws of thermodynamics, reinterpreted Nernst's theorem in terms of entropy. According to this statement, the entropy of a system in equilibrium tends to a well-defined constant as the temperature approaches 0 K.
Planck postulated that this constant is independent of the other thermodynamic variables of the system, such as pressure or volume. This implies that, in the state of absolute zero, the system reaches a perfect and predictable order, where there is no uncertainty associated with its configuration.
4. Absolute Zero Inaccessibility Theorem
This theorem states that it is impossible to reduce the temperature of a system to absolute zero in a finite number of steps.
For example, in cooling processes, each step reduces the temperature asymptotically, but never reaches exactly 0 K. This theorem has profound practical implications, as it limits the ability of experimental systems to reach absolute zero, regardless of the technology used.
Consequences of the third principle
The third law implies the following consequences:
1. Impossibility of reaching absolute zero temperatures
It follows from the third law of thermodynamics that absolute zero temperature cannot be achieved in any final process associated with a change in entropy. It can only be approached asymptotically.
Therefore, the third law of thermodynamics is sometimes formulated as the principle of the impossibility of reaching absolute zero temperature.
2. The behavior of thermodynamic coefficients
A number of thermodynamic consequences follow from the third law of thermodynamics: as T → 0, it must also tend to zero:
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Heat capacity at constant pressure and constant volume
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coefficients of thermal expansion and some similar values.
The validity of the third law of thermodynamics was questioned at one time, but it was later discovered that all apparent contradictions are associated with metastable states of matter that cannot be considered to be in thermodynamic equilibrium.