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Entropy of fusion

Increase in entropy when a solid melts

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Inthermodynamics, the entropy of fusion is the increase in entropy when meltingasolid substance. This is almost always positive since the degree of disorder increases in the transition from an organized crystalline solid to the disorganized structure of a liquid; the only known exception is helium.^[1] It is denoted as ${\displaystyle \Delta S_{\text{fus}}}$ and normally expressed in joules per mole-kelvin, J/(mol·K).

A natural process such as a phase transition will occur when the associated change in the Gibbs free energy is negative.

${\displaystyle \Delta G_{\text{fus}}=\Delta H_{\text{fus}}-T\times \Delta S_{\text{fus}}<0,}$

where ${\displaystyle \Delta H_{\text{fus}}}$ is the enthalpy of fusion. Since this is a thermodynamic equation, the symbol ${\displaystyle T}$ refers to the absolute thermodynamic temperature, measured in kelvins (K).

Equilibrium occurs when the temperature is equal to the melting point ${\displaystyle T=T_{f}}$ so that

${\displaystyle \Delta G_{\text{fus}}=\Delta H_{\text{fus}}-T_{f}\times \Delta S_{\text{fus}}=0,}$

and the entropy of fusion is the heat of fusion divided by the melting point:

${\displaystyle \Delta S_{\text{fus}}={\frac {\Delta H_{\text{fus}}}{T_{f}}}}$

Helium[edit]

Helium-3 has a negative entropy of fusion at temperatures below 0.3 K. Helium-4 also has a very slightly negative entropy of fusion below 0.8 K. This means that, at appropriate constant pressures, these substances freeze with the addition of heat.^[2]

See also[edit]

• Entropy of vaporization

Notes[edit]

References[edit]

• Atkins, Peter; Jones, Loretta (2008), Chemical Principles: The Quest for Insight (4th ed.), W. H. Freeman and Company, p. 236, ISBN 978-0-7167-7355-9
• Ott, J. Bevan; Boerio-Goates, Juliana (2000), Chemical Thermodynamics: Advanced Applications, Academic Press, ISBN 0-12-530985-6

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