# Third Law of Thermodynamics

## Rationale and Statement

For a given system, we cannot give an absolute value of the internal energy, U, because that value needs to know the precise internal state. Therefore, we always use the difference, either ΔU or dU. And since the enthalpy, H, is based on the internal the same is true for enthalpy.

However, that is not true for the entropy, S. The absolute value of entropy is defined by the Third Law of Thermodynamics

The entropy of a pure crystalline solid at absolute zero is an arbitrary constant which can be set to zero

## Simplified Statement

An easier statement (but not quite as precise) is

The entropy at absolute zero is zero

This statement is useful in calculating entropies.

## Calculation of Entropy

We can now calculate the absolute entropy at any T > 0 by integrating the Clausis inequality from 0 to T and using the third law at T = 0.

## Crystalline solids

Let us now take a look at the first statement. Note that it says a pure crystalline solid. In other words a perfectly ordered solid. This would not include amorphous solids (an amorphous solid is one which is not a crystal, for example, glass).

All substances we know of, with one exception, become crystalline as they approach absolute zero. Therefore, as far as we know all observations agree with the third law.

The one exception is helium. As helium approaches absolute zero it becomes a strange behaving liquid called a superfluid. It has no viscosity and will crawl up the side of a beaker. It however has an ordered structure [1] about equal to a crystalline solid.

## Notes

1. more correctly, a density of energy states