Entropy of fusion

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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-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]

See also[edit]


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


  • 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