Third Law of Thermodynamics

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• One consequence of Boltzmann’s proposal is thata perfectly ordered crystal will have an entropy of 0.
• This gives us the Third Law of Thermodynamics

  The entropy of a perfectly ordered crystal at \(0K\) is zero.

• This suggests that absolute molar entropies can be calculated \(S=\int_0^T \frac{C}{T}\, dT\)

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Example 5.7

\({SiO_2}\) is found to have a molar heat capacity of \(0.777 \frac{J}{mol\,K}\) at \(15 K\) (Yamashita, et al., 2001). Calculate the molar entropy of \({SiO_2}\) at \(15 K\).

Note: The Debye extrapolation says that at low temperatures, the heat capacity is proportional to \(T^3\), that is \(C\propto T^3 \therefore C = aT^3\) at very low temperatures.