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# Third Law of Thermodynamics

Thermodynamics means the flow of heat and it deals with quantitative relationships existing between heat and other forms of energy in physico-chemical transformations.
We have already studied about the relationship between the heat and the work done in first law of thermodynamics, and about energy and work done in second law of thermodynamics.
Let us study about change in entropy in third law of thermodynamics where we will discuss the concept of entropy.

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## Third Law of Thermodynamics Definition

We know that entropy is the rate of change of disorder occurring in a system. Walther Nernst introduced the concept of entropy in the third law of thermodynamics which states that:
For a perfect crystal at the absolute zero temperature, the entropy would be exactly equal to zero.When only one minimum energy state is possessed by a perfect crystal the law would hold true.
If we consider systems such as glasses which are not perfect crystal then a generalized form of 3rd law would be:
When the temperature approaches zero, the randomness or entropy of a system would approach a constant value.
The Constant value of entropy is called Residual Entropy and it should be noted that it is not necessarily zero.

## Third Law of Thermodynamics Equation

The Third law can be expressed as:
$\lim_{T \to 0}$ S = 0 ...............................(a)Here,
S = entropy which is expressed as J s-1K-1.
T = absolute temperature which is expressed in K.
It can also be written as:
T $\to$ 0 $\Rightarrow$ S $\to$ Smin .....................................(b) Hence we can say if the temperature approaches zero then the entropy approaches to its minimum value.
Another application of third law of thermodynamics:
S = 2.303 Cp log T ..........................................(c)Using this we can find the absolute entropy of any substance at a given temperature T.
Here Cp is the heat capacity of the substance at a constant pressure.

Limitations of the law:
1. Even at 0 K Glassy solids have entropy which is greater than zero.
2. Solids that have mixtures of isotopes do not possess zero entropy at 0 K.
For example: Solid chlorine does not have zero entropy at 0 K.
3. Crystals of CO, N2O, NO, H2O, etc., do not possess perfect order even at 0 K, thus their entropy is not equal to zero.

## Third Law of Thermodynamics Examples

We can consider H2O if we want to understand the concept of the third law of thermodynamics.
Water exists in three different states:
1. Gaseous state
2. Liquid state
3. Solid state

In Gaseous state
The entropy or randomness is very high. Here we are talking about the randomness in motion of the molecules of which the water is made up of. They move with very high entropy.

In Liquid state
Now the randomness is reduced. It is not as free as the gaseous state and hence we can say that entropy of the molecules is reduced. This is because the movement between the molecules is reduced.

In Solid state
In this state the moment between molecules is almost zero. The entropy approaches almost zero value. This is because the molecules are packed very tightly in the solid state and hence the randomness is very low. This is when it is cooled at very low temperature or at an absolute zero temperature.

Now if it cooled further then all the motion between the molecules would stop. This is because these are no free spaces for the motion of the particles. And hence the entropy becomes almost zero.
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