thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

, the entropy of fusion is the increase in

entropy Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...

when

melting Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which inc ...

solid Solid is a state of matter where molecules are closely packed and can not slide past each other. Solids resist compression, expansion, or external forces that would alter its shape, with the degree to which they are resisted dependent upon the ...

substance. This is almost always positive since the degree of disorder increases in the transition from an organized

crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

line solid to the disorganized structure of a

liquid Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to th ...

; the only known exception is

helium Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is ...

. It is denoted as

\Delta S_

and normally expressed in

joules The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work don ...

per mole-

kelvin The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...

, J/(mol·K). A natural process such as a phase transition will occur when the associated change in the

Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol is a thermodynamic potential that can be used to calculate the maximum amount of Work (thermodynamics), work, other than Work (thermodynamics)#Pressure–v ...

is negative. :

\Delta G_ = \Delta H_ - T \times \Delta S_ < 0,

where is the enthalpy of fusion. Since this is a thermodynamic equation, the symbol refers to the absolute

thermodynamic temperature Thermodynamic temperature, also known as absolute temperature, is a physical quantity which measures temperature starting from absolute zero, the point at which particles have minimal thermal motion. Thermodynamic temperature is typically expres ...

, measured in

s (K). Equilibrium occurs when the temperature is equal to the

melting point The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state of matter, state from solid to liquid. At the melting point the solid and liquid phase (matter), phase exist in Thermodynamic equilib ...

T = T_f

so that :

\Delta G_ = \Delta H_ - T_f \times \Delta S_ = 0,

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

\Delta S_ = \frac

Helium

Helium-3 Helium-3 (3He see also helion) is a light, stable isotope of helium with two protons and one neutron. (In contrast, the most common isotope, helium-4, has two protons and two neutrons.) Helium-3 and hydrogen-1 are the only stable nuclides with ...

has a negative entropy of fusion at temperatures below 0.3 K.

Helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consi ...

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.

Notes

References

* * {{DEFAULTSORT:Entropy Of Fusion Thermodynamic entropy Thermodynamic properties

Helium

See also

Notes

References