third law of thermodynamics statement, formula and examples

Statement of the Third Law of Thermodynamics

The third law of thermodynamics states that as the temperature of a system approaches absolute zero (0 Kelvin or -273celsius), the entropy of a perfect crystalline substance approaches zero. In simpler terms, it implies that it is impossible to reach absolute zero in a finite number of steps, and at absolute zero, a perfect crystal would have no randomness or disorder.

Formula

While the third law primarily deals with concepts of absolute entropy, it can be related to the entropy change (

$S$

$$S=k\ln \mathrm{\Omega }$$

where:

• $S$
• $k$
• $\mathrm{\Omega }$

At absolute zero, for a perfect crystal, 

$\mathrm{\Omega }=1$

$$S=k\ln (1)=0$$

Examples of the Third Law of Thermodynamics

1. Perfect Crystals: In theory, a perfect crystal made of a single type of atom will have zero entropy at absolute zero because all particles are in a perfectly ordered arrangement with no randomness.

2. Helium-3 and Helium-4: These isotopes of helium exhibit very different behaviors as they approach absolute zero due to quantum mechanical effects. Helium-4 remains liquid and does not become a perfect crystal until much lower temperatures than helium-3, which can form a crystalline solid at higher temperatures.

3. Specific Heat Capacity: The concept extends to the behavior of materials. At temperatures approaching absolute zero, the specific heat capacity of materials tends to zero, implying that adding heat does not change their temperature significantly.

4. Cryogenics: In experiments involving cryogenics, scientists manipulate substances at near absolute zero temperatures. As they cool materials to these temperatures, their entropy decreases, and they reach states that reflect the principles of the third law.

5. Entropy Calculations: In calculating the entropy change for processes involving low temperatures, the third law is crucial. For example, when transitioning a substance from a liquid phase to a solid phase at very low temperatures, the calculations for entropy will utilize the understanding that at absolute zero, the entropy is effectively zero for a perfect crystalline solid.

These examples demonstrate the implications of the third law of thermodynamics in physical systems, especially regarding the behavior of substances at extremely low temperatures.