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. It is denoted as ?S_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.

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

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

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

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

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

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

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.

See also

• Entropy of vaporization