Enthalpy of fusion

The enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a solid to a liquid, at constant pressure. For example, when melting 1 kg of ice (at 0 °C under a wide range of pressures), 333.55 kJ of energy is absorbed with no temperature change. The heat of solidification (when a substance changes from liquid to solid) is equal and opposite.

This energy includes the contribution required to make room for any associated change in volume by displacing its environment against ambient pressure. The temperature at which the phase transition occurs is the melting point or the freezing point, according to context. By convention, the pressure is assumed to be 1 atm (101.325 kPa) unless otherwise specified.

Enthalpies of melting and boiling for pure elements versus temperatures of transition
Enthalpies of melting and boiling for pure elements versus temperatures of transition, demonstrating Trouton's rule.


The 'enthalpy' of fusion is a latent heat, because during melting the heat energy needed to change the substance from solid to liquid at atmospheric pressure is latent heat of fusion, as the temperature remains constant during the process. The latent heat of fusion is the enthalpy change of any amount of substance when it melts. When the heat of fusion is referenced to a unit of mass, it is usually called the specific heat of fusion, while the molar heat of fusion refers to the enthalpy change per amount of substance in moles.

The liquid phase has a higher internal energy than the solid phase. This means energy must be supplied to a solid in order to melt it and energy is released from a liquid when it freezes, because the molecules in the liquid experience weaker intermolecular forces and so have a higher potential energy (a kind of bond-dissociation energy for intermolecular forces).

When liquid water is cooled, its temperature falls steadily until it drops just below the line of freezing point at 0 °C. The temperature then remains constant at the freezing point while the water crystallizes. Once the water is completely frozen, its temperature continues to fall.

The enthalpy of fusion is almost always a positive quantity; helium is the only known exception.[1] Helium-3 has a negative enthalpy of fusion at temperatures below 0.3 K. Helium-4 also has a very slightly negative enthalpy of fusion below 0.77 K (−272.380 °C). This means that, at appropriate constant pressures, these substances freeze with the addition of heat.[2] In the case of 4He, this pressure range is between 24.992 and 25.00 atm (2,533 kPa).[3]

Enthalpy of Fusion period three
Standard enthalpy change of fusion of period three.
Molar heat of fusion period two
Standard enthalpy change of fusion of period two of the periodic table of elements.
Substance Heat of fusion
Heat of fusion
water 79.72 333.55
methane 13.96 58.99
propane 19.11 79.96
glycerol 47.95 200.62
formic acid 66.05 276.35
acetic acid 45.90 192.09
acetone 23.42 97.99
benzene 30.45 127.40
myristic acid 47.49 198.70
palmitic acid 39.18 163.93
sodium acetate 63–69 264–289[4]
stearic acid 47.54 198.91
gallium 19.2 80.4
Paraffin wax (C25H52) 47.8-52.6 200–220

These values are mostly from the CRC Handbook of Chemistry and Physics, 62nd edition. The conversion between cal/g and J/g in the above table uses the thermochemical calorie (calth) = 4.184 joules rather than the International Steam Table calorie (calINT) = 4.1868 joules.


A) To heat 1 kg (1.00 liter) of water from 283.15 K to 303.15 K (10 °C to 30 °C) requires 83.6 kJ. However, to melt ice also requires energy. We can treat these two processes independently; thus, to heat 1 kg of ice from 273.15 K to water at 293.15 K (0 °C to 20 °C) requires:

(1) 333.55 J/g (heat of fusion of ice) = 333.55 kJ/kg = 333.55 kJ for 1 kg of ice to melt
(2) 4.18 J/(g·K) × 20K = 4.18 kJ/(kg·K) × 20K = 83.6 kJ for 1 kg of water to increase in temperature by 20 K
= 417.15 kJ

From these figures it can be seen that one part ice at 0 °C will cool almost exactly 4 parts water from 20 °C to 0 °C.

B) Silicon has a heat of fusion of 50.21 kJ/mol. 50 kW of power can supply the energy required to melt about 100 kg of silicon in one hour, after it is brought to the melting point temperature:

50 kW = 50kJ/s = 180000kJ/h

180000kJ/h * (1 mol Si)/50.21kJ * 28gSi/(mol Si) * 1kgSi/1000gSi = 100.4kg/h

Solubility prediction

The heat of fusion can also be used to predict solubility for solids in liquids. Provided an ideal solution is obtained the mole fraction of solute at saturation is a function of the heat of fusion, the melting point of the solid and the temperature (T) of the solution:

Here, R is the gas constant. For example, the solubility of paracetamol in water at 298 K is predicted to be:

This equals to a solubility in grams per liter of:

which is a deviation from the real solubility (240 g/L) of 11%. This error can be reduced when an additional heat capacity parameter is taken into account.[5]


At equilibrium the chemical potentials for the pure solvent and pure solid are identical:


with the gas constant and the temperature.

Rearranging gives:

and since

the heat of fusion being the difference in chemical potential between the pure liquid and the pure solid, it follows that

Application of the Gibbs–Helmholtz equation:

ultimately gives:


and with integration:

the end result is obtained:

See also


  1. ^ Atkins & Jones 2008, p. 236.
  2. ^ Ott & Boerio-Goates 2000, pp. 92–93.
  3. ^ Hoffer, J. K.; Gardner, W. R.; Waterfield, C. G.; Phillips, N. E. (April 1976). "Thermodynamic properties of 4He. II. The bcc phase and the P-T and VT phase diagrams below 2 K". Journal of Low Temperature Physics. 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245.
  4. ^ Ibrahim Dincer and Marc A. Rosen. Thermal Energy Storage: Systems and Applications, page 155
  5. ^ Measurement and Prediction of Solubility of Paracetamol in Water-Isopropanol Solution. Part 2. Prediction H. Hojjati and S. Rohani Org. Process Res. Dev.; 2006; 10(6) pp 1110–1118; (Article) doi:10.1021/op060074g


  • 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, BJ. Bevan; Boerio-Goates, Juliana (2000), Chemical Thermodynamics: Advanced Applications, Academic Press, ISBN 0-12-530985-6
Absolute zero

Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as 0. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15° on the Celsius scale (International System of Units), which equals −459.67° on the Fahrenheit scale (United States customary units or Imperial units). The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition.

It is commonly thought of as the lowest temperature possible, but it is not the lowest enthalpy state possible, because all real substances begin to depart from the ideal gas when cooled as they approach the change of state to liquid, and then to solid; and the sum of the enthalpy of vaporization (gas to liquid) and enthalpy of fusion (liquid to solid) exceeds the ideal gas's change in enthalpy to absolute zero. In the quantum-mechanical description, matter (solid) at absolute zero is in its ground state, the point of lowest internal energy.

The laws of thermodynamics indicate that absolute zero cannot be reached using only thermodynamic means, because the temperature of the substance being cooled approaches the temperature of the cooling agent asymptotically, and a system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state at absolute zero. The kinetic energy of the ground state cannot be removed.

Scientists and technologists routinely achieve temperatures close to absolute zero, where matter exhibits quantum effects such as superconductivity and superfluidity.


The mineral cristobalite is a high-temperature polymorph of silica, meaning that it has the same chemical formula as quartz, SiO2, but a distinct crystal structure. Both quartz and cristobalite are polymorphs with all the members of the quartz group, which also include coesite, tridymite and stishovite. Cristobalite occurs as white octahedra or spherulites in acidic volcanic rocks and in converted diatomaceous deposits in the Monterey Formation of the US state of California and similar areas. Cristobalite is stable only above 1470 °C, but can crystallize and persist metastably at lower temperatures. It is named after Cerro San Cristóbal in Pachuca Municipality, Hidalgo, Mexico.

The persistence of cristobalite outside its thermodynamic stability range occurs because the transition from cristobalite to quartz or tridymite is "reconstructive", requiring the breaking up and reforming of the silica framework. These frameworks are composed of SiO4 tetrahedra in which every oxygen atom is shared with a neighbouring tetrahedron, so that the chemical formula of silica is SiO2. The breaking of these bonds required to convert cristobalite to tridymite and quartz requires considerable activation energy and may not happen on a human time frame. Framework silicates are also known as tectosilicates.

There is more than one form of the cristobalite framework. At high temperatures, the structure is cubic, Fd3m, No. 227, Pearson symbol cF104. A tetragonal form of cristobalite (P41212, No. 92, Pearson symbol tP12) occurs on cooling below about 250 °C at ambient pressure and is related to the cubic form by a static tilting of the silica tetrahedra in the framework. This transition is variously called the low-high or transition. It may be termed "displacive"; i.e., it is not generally possible to prevent the cubic β-form from becoming tetragonal by rapid cooling. Under rare circumstances the cubic form may be preserved if the crystal grain is pinned in a matrix that does not allow for the considerable spontaneous strain that is involved in the transition, which causes a change in shape of the crystal. This transition is highly discontinuous. The exact transition temperature depends on the crystallinity of the cristobalite sample, which itself depends on factors such as how long it has been annealed at a particular temperature.

The cubic β phase consists of dynamically disordered silica tetrahedra. The tetrahedra remain fairly regular and are displaced from their ideal static orientations due to the action of a class of low-frequency phonons called rigid unit modes. It is the "freezing" of one of these rigid unit modes that is the soft mode for the α–β transition.

In the α–β phase transition only one of the three degenerate cubic crystallographic axes retains a fourfold rotational axis in the tetragonal form. The choice of axis is arbitrary, so that various twins can form within the same grain. These different twin orientations coupled with the discontinuous nature of the transition can cause considerable mechanical damage to materials in which cristobalite is present and that pass repeatedly through the transition temperature, such as refractory bricks.

When devitrifying silica, cristobalite is usually the first phase to form, even when well outside its thermodynamic stability range. This is an example of Ostwald's step rule. The dynamically disordered nature of the β-phase is partly responsible for the low enthalpy of fusion of silica.

The micrometre-scale spheres that make up precious opal exhibit some x-ray diffraction patterns that are similar to that of cristobalite, but lack any long-range order so they are not considered true cristobalite. In addition, the presence of structural water in opal makes it doubtful that opal consists of cristobalite.

Enthalpy change of solution

The enthalpy of solution, enthalpy of dissolution, or heat of solution is the enthalpy change associated with the dissolution of a substance in a solvent at constant pressure resulting in infinite dilution.

The enthalpy of solution is most often expressed in kJ/mol at constant temperature. The energy change can be regarded as being made of three parts, the endothermic breaking of bonds within the solute and within the solvent, and the formation of attractions between the solute and the solvent. An ideal solution has a null enthalpy of mixing. For a non-ideal solution it is an excess molar quantity.

Enthalpy of vaporization

The enthalpy of vaporization, (symbol ∆Hvap) also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance, to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

The enthalpy of vaporization is often quoted for the normal boiling temperature of the substance; although tabulated values are usually corrected to 298 K, that correction is often smaller than the uncertainty in the measured value.

The heat of vaporization is temperature-dependent, though a constant heat of vaporization can be assumed for small temperature ranges and for reduced temperature T r {\displaystyle T_{r}} . The heat of vaporization diminishes with increasing temperature and it vanishes completely at a certain point called the critical temperature (). Above the critical temperature, the liquid and vapor phases are indistinguishable, and the substance is called a supercritical fluid.


Freezing is a phase transition in which a liquid turns into a solid when its temperature is lowered below its freezing point. In contrast, solidification is a similar process where a liquid turns into a solid, not by lowering its temperature, but by increasing the pressure that it is under. Despite this technical distinction, the two processes are very similar and the two terms are often used interchangeably.

For most substances, the melting and freezing points are the same temperature; however, certain substances possess differing solid–liquid transition temperatures. For example, agar displays a hysteresis in its melting point and freezing point. It melts at 85 °C (185 °F) and solidifies from 32 °C to 40 °C (89.6 °F to 104 °F).

Frigorific mixture

A frigorific mixture is a mixture of two or more phases in a chemical system that, so long as none of the phases is consumed during equilibration, reaches an equilibrium temperature that is independent of the starting temperature of the phases before they are mixed. The equilibrium temperature is also independent of the quantities of the phases used as long as sufficient amounts of each are present to reach equilibrium without consuming one or more.

Ice pack

An ice pack or gel pack is a portable plastic bag filled with water, refrigerant gel, or liquid. For use the contents are frozen in a freezer. Both ice and other non-toxic refrigerants (mostly water) can absorb a considerable amount of heat before they warm above 0 °C, due to the high latent heat of fusion of water. These packs are commonly used to keep food cool in portable coolers, or as a cold compress to alleviate the pain of minor injuries, or in insulated shipping containers to keep products cool during transport.Ice packs are used in coolers to keep perishable foods (especially meats, dairy products, eggs, etc.) below the 5–75 °C (41–167 °F) danger zone when outside a refrigerator or freezer, and to keep drinks pleasantly cool. The amount of ice needed varies with the amount of food, its initial temperature, the thermal insulation of the cooler, and the ambient temperature and exposure to direct sunlight. Ice initially well below freezing temperature will last a little longer.

Water has a much higher latent heat of fusion than most substances, and a melting temperature which is convenient and easily attained with, for example, a household freezer. Additives to improve the properties of water are often used. For example, substances can be added to prevent bacterial growth in the pack, or to prevent the water from solidifying so it remains a thick gel throughout use.

Gel packs are often made of non-toxic materials that will remain a slow-flowing gel, and therefore will not spill easily or cause contamination if the container breaks. Gel packs may be made by adding hydroxyethyl cellulose (Cellusize), sodium polyacrylate, or vinyl-coated silica gel.

Introduction to entropy

Entropy is an important concept in the branch of physics known as thermodynamics. The idea of "irreversibility" is central to the understanding of entropy. Everyone has an intuitive understanding of irreversibility. If one watches a movie of everyday life running forward and in reverse, it is easy to distinguish between the two. The movie running in reverse shows impossible things happening – water jumping out of a glass into a pitcher above it, smoke going down a chimney, water in a glass freezing to form ice cubes, crashed cars reassembling themselves, and so on. The intuitive meaning of expressions such as "you can't unscramble an egg", or "you can't take the cream out of the coffee" is that these are irreversible processes. No matter how long you wait, the cream won't jump out of the coffee into the creamer.

In thermodynamics, one says that the "forward" processes – pouring water from a pitcher, smoke going up a chimney, etc. – are "irreversible": they cannot happen in reverse. All real physical processes involving systems in everyday life, with many atoms or molecules, are irreversible. For an irreversible process in an isolated system (a system not subject to outside influence), the thermodynamic state variable known as entropy is never decreasing. In everyday life, there may be processes in which the increase of entropy is practically unobservable, almost zero. In these cases, a movie of the process run in reverse will not seem unlikely. For example, in a 1-second video of the collision of two billiard balls, it will be hard to distinguish the forward and the backward case, because the increase of entropy during that time is relatively small. In thermodynamics, one says that this process is practically "reversible", with an entropy increase that is practically zero. The statement of the fact that the entropy of an isolated system never decreases is known as the second law of thermodynamics.

Classical thermodynamics is a physical theory which describes a "system" in terms of the thermodynamic variables of the system or its parts. Some thermodynamic variables are familiar: temperature, pressure, volume. Entropy is a thermodynamic variable which is less familiar and not as easily understood. A "system" is any region of space containing matter and energy: A cup of coffee, a glass of icewater, an automobile, an egg. Thermodynamic variables do not give a "complete" picture of the system. Thermodynamics makes no assumptions about the microscopic nature of a system and does not describe nor does it take into account the positions and velocities of the individual atoms and molecules which make up the system. Thermodynamics deals with matter in a macroscopic sense; it would be valid even if the atomic theory of matter were wrong. This is an important quality, because it means that reasoning based on thermodynamics is unlikely to require alteration as new facts about atomic structure and atomic interactions are found. The essence of thermodynamics is embodied in the four laws of thermodynamics.

Unfortunately, thermodynamics provides little insight into what is happening at a microscopic level. Statistical mechanics is a physical theory which explains thermodynamics in microscopic terms. It explains thermodynamics in terms of the possible detailed microscopic situations the system may be in when the thermodynamic variables of the system are known. These are known as "microstates" whereas the description of the system in thermodynamic terms specifies the "macrostate" of the system. Many different microstates can yield the same macrostate. It is important to understand that statistical mechanics does not define temperature, pressure, entropy, etc. They are already defined by thermodynamics. Statistical mechanics serves to explain thermodynamics in terms of microscopic behavior of the atoms and molecules in the system.

In statistical mechanics, the entropy of a system is described as a measure of how many different microstates there are that could give rise to the macrostate that the system is in. The entropy of the system is given by Ludwig Boltzmann's famous equation:

where S is the entropy of the macrostate, k is Boltzmann's constant, and W is the total number of possible microstates that might yield the macrostate. The concept of irreversibility stems from the idea that if you have a system in an "unlikely" macrostate (log(W ) is relatively small) it will soon move to the "most likely" macrostate (with larger log(W )) and the entropy S will increase. A glass of warm water with an ice cube in it is unlikely to just happen, it must have been recently created, and the system will move to a more likely macrostate in which the ice cube is partially or entirely melted and the water is cooled. Statistical mechanics shows that the number of microstates which give ice and warm water is much smaller than the number of microstates that give the reduced ice mass and cooler water.

Latent heat

Latent heat is thermal energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition.

Latent heat can be understood as heat energy in hidden form which is supplied or extracted to change the state of a substance without changing its temperature. Examples are latent heat of fusion and latent heat of vaporization involved in phase changes, i.e. a substance condensing or vaporizing at a specified temperature and pressure.The term was introduced around 1762 by British chemist Joseph Black. It is derived from the Latin latere (to lie hidden). Black used the term in the context of calorimetry where a heat transfer caused a volume change in a body while its temperature was constant.

In contrast to latent heat, sensible heat is a heat transfer that results in a temperature change in a body.

Material properties (thermodynamics)

The thermodynamic properties of materials are intensive thermodynamic parameters which are specific to a given material. Each is directly related to a second order differential of a thermodynamic potential. Examples for a simple 1-component system are:

  • Isothermal compressibility
  • Adiabatic compressibility
  • Specific heat at constant pressure
  • Specific heat at constant volume

where P  is pressure, V  is volume, T  is temperature, S  is entropy, and N  is the number of particles.

For a single component system, only three second derivatives are needed in order to derive all others, and so only three material properties are needed to derive all others. For a single component system, the "standard" three parameters are the isothermal compressibility , the specific heat at constant pressure , and the coefficient of thermal expansion .

For example, the following equations are true:

The three "standard" properties are in fact the three possible second derivatives of the Gibbs free energy with respect to temperature and pressure.


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 increases the substance's temperature to the melting point. At the melting point, the ordering of ions or molecules in the solid breaks down to a less ordered state, and the solid melts to become a liquid.

Substances in the molten state generally have reduced viscosity as the temperature increases. An exception to this principle is the element sulfur, whose viscosity increases to a point due to polymerization and then decreases with higher temperatures in its molten state.Some organic compounds melt through mesophases, states of partial order between solid and liquid.

Melting point

The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at a standard pressure such as 1 atmosphere or 100 kPa.

When considered as the temperature of the reverse change from liquid to solid, it is referred to as the freezing point or crystallization point. Because of the ability of some substances to supercool, the freezing point is not considered as a characteristic property of a substance. When the "characteristic freezing point" of a substance is determined, in fact the actual methodology is almost always "the principle of observing the disappearance rather than the formation of ice", that is, the melting point.


Neopentane, also called 2,2-dimethylpropane, is a double-branched-chain alkane with five carbon atoms. Neopentane is a flammable gas at room temperature and pressure which can condense into a highly volatile liquid on a cold day, in an ice bath, or when compressed to a higher pressure.

Neopentane is the simplest alkane with a quaternary carbon, and has achiral tetrahedral symmetry. It is one of the three structural isomers with the molecular formula C5H12 (pentanes), the other two being n-pentane and isopentane. Out of these three, it is the only one to be a gas at standard conditions; the other being liquids.

Phase (matter)

In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase. (See state of matter § Glass)

The term phase is sometimes used as a synonym for state of matter, but there can be several immiscible phases of the same state of matter. Also, the term phase is sometimes used to refer to a set of equilibrium states demarcated in terms of state variables such as pressure and temperature by a phase boundary on a phase diagram. Because phase boundaries relate to changes in the organization of matter, such as a change from liquid to solid or a more subtle change from one crystal structure to another, this latter usage is similar to the use of "phase" as a synonym for state of matter. However, the state of matter and phase diagram usages are not commensurate with the formal definition given above and the intended meaning must be determined in part from the context in which the term is used.


Specific may refer to:

Specificity (disambiguation)

Specific, a cure or therapy for a specific illness

Sublimation (phase transition)

Sublimation is the transition of a substance directly from the solid to the gas phase, without passing through the intermediate liquid phase. Sublimation is an endothermic process that occurs at temperatures and pressures below a substance's triple point in its phase diagram, which corresponds to the lowest pressure at which the substance can exist as a liquid. The reverse process of sublimation is deposition or desublimation, in which a substance passes directly from a gas to a solid phase. Sublimation has also been used as a generic term to describe a solid-to-gas transition (sublimation) followed by a gas-to-solid transition (deposition). While a transition from liquid to gas is described as evaporation if it occurs below the boiling point of the liquid, and as boiling if it occurs at the boiling point, there is no such distinction within the solid-to-gas transition, which is always described as sublimation.

At normal pressures, most chemical compounds and elements possess three different states at different temperatures. In these cases, the transition from the solid to the gaseous state requires an intermediate liquid state. The pressure referred to is the partial pressure of the substance, not the total (e.g. atmospheric) pressure of the entire system. So, all solids that possess an appreciable vapour pressure at a certain temperature usually can sublime in air (e.g. water ice just below 0 °C). For some substances, such as carbon and arsenic, sublimation is much easier than evaporation from the melt, because the pressure of their triple point is very high, and it is difficult to obtain them as liquids.

The term sublimation refers to a physical change of state and is not used to describe the transformation of a solid to a gas in a chemical reaction. For example, the dissociation on heating of solid ammonium chloride into hydrogen chloride and ammonia is not sublimation but a chemical reaction. Similarly the combustion of candles, containing paraffin wax, to carbon dioxide and water vapor is not sublimation but a chemical reaction with oxygen.

Sublimation is caused by the absorption of heat which provides enough energy for some molecules to overcome the attractive forces of their neighbors and escape into the vapor phase. Since the process requires additional energy, it is an endothermic change. The enthalpy of sublimation (also called heat of sublimation) can be calculated by adding the enthalpy of fusion and the enthalpy of vaporization.

Thermal Battery

A thermal energy battery is a physical structure used for the purpose of storing and releasing thermal energy—see also thermal energy storage. Such a thermal battery (a.k.a. TBat) allows energy available at one time to be temporarily stored and then released at another time. The basic principles involved in a thermal battery occur at the atomic level of matter, with energy being added to or taken from either a solid mass or a liquid volume which causes the substance's temperature to change. Some thermal batteries also involve causing a substance to transition thermally through a phase transition which causes even more energy to be stored and released due to the delta enthalpy of fusion or delta enthalpy of vaporization.

Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.

Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the particle constituents of matter have minimal motion and can become no colder. In the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy. Thermodynamic temperature is often also called absolute temperature, for two reasons: one, proposed by Kelvin, that it does not depend on the properties of a particular material; two that it refers to an absolute zero according to the properties of the ideal gas.

The International System of Units specifies a particular scale for thermodynamic temperature. It uses the kelvin scale for measurement and selects the triple point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically. The Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a practical means of estimating the thermodynamic temperature to a very high degree of accuracy.

Roughly, the temperature of a body at rest is a measure of the mean of the energy of the translational, vibrational and rotational motions of matter's particle constituents, such as molecules, atoms, and subatomic particles. The full variety of these kinetic motions, along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these, make up the total internal energy of a substance. Internal energy is loosely called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings, or by the substance upon the surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a "degree of freedom". At equilibrium, each degree of freedom will have on average the same energy: where is the Boltzmann constant, unless that degree of freedom is in the quantum regime. The internal degrees of freedom (rotation, vibration, etc.) may be in the quantum regime at room temperature, but the translational degrees of freedom will be in the classical regime except at extremely low temperatures (fractions of kelvins) and it may be said that, for most situations, the thermodynamic temperature is specified by the average translational kinetic energy of the particles.

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