# 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 ΔSfus 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.

$\Delta G_{fus} = \Delta H_{fus} - T \times \Delta S_{fus} < 0$, where $\Delta H_{fus}$ is the enthalpy or heat of fusion.

Since this is a thermodynamic equation, the symbol T refers to the absolute thermodynamic temperature, measured in Kelvin (K).

Equilibrium occurs when the temperature is equal to the melting point $T = T_f$ so that

$\Delta G_{fus} = \Delta H_{fus} - T_f \times \Delta S_{fus} = 0$,

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

$\Delta S_{fus} = \frac {\Delta H_{fus}} {T_f}$

## 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