# Difference between revisions of "Third law of thermodynamics"

Carl McBride (talk | contribs) (New page: The '''third law of thermodynamics''' (or '''Nernst's theorem''' after the experimental work of Walther Nernst) states that the entropy of a system approaches a minimum (that of its gr...) |
Carl McBride (talk | contribs) m (Corrected typos.) |
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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. | + | The [[heat capacity]] (for either [[pressure]] or volume) tends to zero as one approaches absolute zero. From |

:<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 [[thermal expansion coefficient]] | + | Similarly for the [[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> |

## Revision as of 12:22, 22 January 2010

The **third law of thermodynamics** (or **Nernst's theorem** after the experimental work of Walther Nernst) states that the entropy of a system approaches a minimum (that of its ground state) as one approaches the temperature of absolute zero. One can write

where 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

The heat capacity (for either pressure or volume) tends to zero as one approaches absolute zero. From

one has

thus as , otherwise the integrand would become infinite.

Similarly for the thermal expansion coefficient