Entropy of fusion

In thermodynamics, the entropy of fusion is the increase in entropy when melting a solid 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 $\Delta S_{\text{fus}}$ 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.

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

where ⁠$\Delta H_{\text{fus}}$⁠ is the enthalpy 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 $T=T_f$ 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