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
Δ
S
fus
{\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.
Δ
G
fus
=
Δ
H
fus
−
T
×
Δ
S
fus
<
0
,
{\displaystyle \Delta G_{\text{fus}}=\Delta H_{\text{fus}}-T\times \Delta S_{\text{fus}}<0,}
where
Δ
H
fus
{\displaystyle \Delta H_{\text{fus}}}
is the enthalpy of fusion.
Since this is a thermodynamic equation, the symbol
T
{\displaystyle 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
{\displaystyle T=T_{f}}
so that
Δ
G
fus
=
Δ
H
fus
−
T
f
×
Δ
S
fus
=
0
,
{\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:
Δ
S
fus
=
Δ
H
fus
T
f
{\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.