# Third Law of Thermodynamics

This law was developed by the German chemist Walther Nernst between the years 1906 and 1912. According to this law-

*Entropy of a perfect crystal is zero when the temperature of the crystal is equal to absolute zero (i.e. zero Kelvin)*. Third law of thermodynamics explains entropy.

At a temperature of zero Kelvin, the following phenomena can be observed in a closed system-

1. The system does not contain any heat.

2. All the atoms and molecules in the system are at their lowest energy points.

Therefore, a system at absolute zero has only one accessible microstate – it's ground state. As per the third law of thermodynamics, the entropy of such a system is exactly zero.

In actual practice, no object or system can have a temperature of zero Kelvin, because of the Second law of thermodynamics. The Second law, in part, implies that heat can never spontaneously move from a colder body to a hotter body. So, as a system approaches absolute zero, it will eventually have to draw energy from whatever systems are nearby. If it draws energy, it can never obtain absolute zero. So, this state is not physically possible, but is a mathematical limit of the universe.

## Mathematical Explanation of the Third Law

As per the statistical mechanics, the entropy of any system is a function of initial entropy, which is-

S – S_{o} = k_{B} lnΩ

S is the Entropy of the system, S_{o} is the initial Entropy, k_{B} is the Boltzmann constant, Ω is the total number of microstates that consist of the macroscopic configuration of the system.

Now, for a perfect crystal that has exactly one unique ground state, Ω = 1. Therefore, the equation can be rewritten as follows-

S – S_{o} = k_{B} ln(1) = 0 [As ln(1) = 0]

When the initial entropy of the system is taken as zero, the following value of 'S' can be obtained-

S – 0 = 0

or, S = 0

Thus, the entropy of a perfect crystal at absolute zero is zero.

## Statements of Third Law of Thermodynamics

Different scientists postulated the third law of thermodynamics differently, describing the system's behavior at absolute zero temperature.

The important theorems and statements of the third law of thermodynamics-

**Nernst theorem:** It is impossible to reach the absolute entropy of a system to its absolute zero value in a finite number of steps.

**Nernst-Simon statement:** The entropy change of a system in a reversible isothermal process approaches zero as the temperature approaches zero.

**Planck statement:** In any system in equilibrium, the entropy tends to become constant, independent of the other thermodynamic variables, as the temperature approaches zero.

## Consequences of Third Law of Thermodynamics

The absolute zero temperature can not be reached in finite steps and the value of heat capacity, coefficient of thermal expansion, and other thermodynamic coefficients reach zero as the temperature reaches absolute zero.

## Limitations of Third Law of Thermodynamics

Third law of thermodynamics also has some limitations which are given below-

- Third law is applicable only at absolute zero temperature which is practically not possible to acieve. The lowest temperature achieved in a lab is about one Pico Kelvin, which is still far from absolute zero.
- Third law doesn't apply to all substances. It is applicable only for pure, perfect and crystal substances.
- Third law doesn't provide information about entropy of a substance at temperatures other than absolute zero.
- It is not possible to achieve absolute zero temperature means it is impossible to build a perpetual motion machine.

Residual Entropy

First Law of Thermodynamics and Limitations

Second Law of Thermodynamics and Limitations

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