# Entropy of fusion

The entropy of fusion is the increase in entropy when melting a 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 J mol−1 K−1

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 or heat of fusion.

Since this is a thermodynamic equation, the symbol 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

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]

## Notes

1. ^ Atkins & Jones 2008, p. 236.
2. ^ Ott & Boerio-Goates 2000, pp. 92–93.

## References

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