Editing Third law of thermodynamics

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where <math>N</math> is the number of particles. Note that there are systems whose ground state entropy is not zero, for example metastable states or glasses, or systems with weakly or non-coupled spins that are not subject to an ordering field.
 
where <math>N</math> is the number of particles. Note that there are systems whose ground state entropy is not zero, for example metastable states or glasses, or systems with weakly or non-coupled spins that are not subject to an ordering field.
 
==Implications==
 
==Implications==
The [[heat capacity]] (for either [[pressure]] or volume) tends to zero as one approaches absolute zero. From
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The [[heat capacity]] (for either [[pressure]] or volume) tends to zero as one approaches absolute zero. Form
  
 
:<math>C_{p,V}(T)= T \left. \frac{\partial S}{\partial T} \right\vert_{p,V}  </math>
 
:<math>C_{p,V}(T)= T \left. \frac{\partial S}{\partial T} \right\vert_{p,V}  </math>
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thus <math>C \rightarrow 0</math> as <math>T \rightarrow 0</math>, otherwise the integrand would become infinite.
 
thus <math>C \rightarrow 0</math> as <math>T \rightarrow 0</math>, otherwise the integrand would become infinite.
  
Similarly for the [[thermal expansion coefficient]]
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Similarly for [[thermal expansion coefficient]]
  
 
:<math>\alpha := \frac{1}{V} \left. \frac{\partial V}{\partial T} \right\vert_p = -\frac{1}{V} \left. \frac{\partial S}{\partial p} \right\vert_T \rightarrow 0</math>
 
:<math>\alpha := \frac{1}{V} \left. \frac{\partial V}{\partial T} \right\vert_p = -\frac{1}{V} \left. \frac{\partial S}{\partial p} \right\vert_T \rightarrow 0</math>

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