# Latent heat

Latent heat is the energy released or absorbed by a body or a thermodynamic system during a constant-temperature process. A typical example is a change of state of matter, meaning a phase transition such as the melting of ice or the boiling of water.[1][2] The term was introduced around 1762 by Scottish chemist Joseph Black. It is derived from the Latin latere (to lie hidden). Black used the term in the context of calorimetry when referring to the heat transferred that caused a change of volume while the thermodynamic system was held at constant temperature.

In contrast to latent heat, an energy is called a sensible energy or heat when it causes processes that do result in a change of the temperature of the system.

## Usage

Two of the more common forms of latent heat (or enthalpies or energies) encountered are latent heat of fusion (melting) and latent heat of vaporization (boiling). These names describe the direction of energy flow when changing from one phase to the next: from solid to liquid, and liquid to gas.

In both cases the change is endothermic, meaning that the system absorbs energy on going from solid to liquid to gas. The change is exothermic (the process releases energy) for the opposite direction. For example, in the atmosphere, when a molecule of water evaporates from the surface of any body of water, energy is transported by the water molecule into a lower temperature air parcel that contains less water vapor than its surroundings. Because energy is needed to overcome the molecular forces of attraction between water particles, the process of transition from a parcel of water to a parcel of vapor requires the input of energy causing a drop in temperature in its surroundings. If the water vapor condenses back to a liquid or solid phase onto a surface, the latent energy absorbed during evaporation is released as sensible heat onto the surface. The large value of the enthalpy of condensation of water vapor is the reason that steam is a far more effective heating medium than boiling water, and is more hazardous.

The terms sensible heat and latent heat are not special forms of energy; instead they characterize the same form of energy, heat, in terms of their effect on a material or a thermodynamic system. A good way to remember the distinction is that a change in sensible heat may be ″sensed″ with a thermometer, and a change in latent heat is invisible to a thermometer – the temperature reading doesn't change. Heat is thermal energy in the process of transfer between a system and its surroundings or between two systems with a different temperature.

Both sensible and latent heats are observed in many processes while transporting energy in nature. Latent heat is associated with the phase changes of atmospheric water vapor, mostly vaporization and condensation, whereas sensible heat is energy transferred that affects the temperature of the atmosphere.

The original usage of the term, as introduced by Black, was applied to systems that were intentionally held at constant temperature. Such usage referred to latent heat of expansion and several other related latent heats. These latent heats are defined independently of the conceptual framework of thermodynamics.[3]

When a body is heated at constant temperature by thermal radiation in a microwave field for example, it may expand by an amount described by its latent heat with respect to volume or latent heat of expansion, or increase its pressure by an amount described by its latent heat with respect to pressure.[4]

### Meteorology

In meteorology, latent heat flux is the flux of heat from the Earth's surface to the atmosphere that is associated with evaporation or transpiration of water at the surface and subsequent condensation of water vapor in the troposphere. It is an important component of Earth's surface energy budget. Latent heat flux has been commonly measured with the Bowen ratio technique, or more recently since the mid-1900s by the eddy covariance method.

## History

The English word latent comes from Latin latēns, meaning lying hid.[5][6] The term latent heat was introduced into calorimetry around 1750 when Joseph Black, commissioned by producers of Scotch whisky in search of ideal quantities of fuel and water for their distilling process,[7] to studying system changes, such as of volume and pressure, when the thermodynamic system was held at constant temperature in a thermal bath. James Prescott Joule characterised latent energy as the energy of interaction in a given configuration of particles, i.e. a form of potential energy, and the sensible heat as an energy that was indicated by the thermometer,[8] relating the latter to thermal energy.

## Specific latent heat

A specific latent heat (L) expresses the amount of energy in the form of heat (Q) required to completely effect a phase change of a unit of mass (m), usually 1kg, of a substance as an intensive property:

$L = \frac {Q}{m}.$

Intensive properties are material characteristics and are not dependent on the size or extent of the sample. Commonly quoted and tabulated in the literature are the specific latent heat of fusion and the specific latent heat of vaporization for many substances.

From this definition, the latent heat for a given mass of a substance is calculated by

$Q = {m} {L}$

where:

Q is the amount of energy released or absorbed during the change of phase of the substance (in kJ or in BTU),
m is the mass of the substance (in kg or in lb), and
L is the specific latent heat for a particular substance (kJ-kgm−1 or in BTU-lbm−1), either Lf for fusion, or Lv for vaporization.

## Table of latent heats

The following table shows the latent heats and change of phase temperatures of some common fluids and gases.[citation needed]

SubstanceLatent Heat
Fusion
kJ/kg
Melting
Point
°C
Latent Heat
Vaporization
kJ/kg
Boiling
Point
°C
Alcohol, ethyl108−11485578.3
Ammonia339−751369−33.34
Carbon dioxide184−78574−57
Helium  21−268.93
Hydrogen(2)58−259455−253
Nitrogen25.7−210200−196
Oxygen13.9−219213−183
R134a −101215.9−26.6
R152a −116326.511.3
Toluene72.1−93351110.6
Turpentine  293
Water33402260100

## Latent heat for condensation of water

The latent heat of condensation of water in the temperature range from −25 °C to 40 °C is approximated by the following empirical cubic function:

$L_\text{water}(T) = (2500.8 - 2.36 T + 0.0016 T^2 - 0.00006 T^3)~\text{J/g},$[10]

where the temperature $T$ is taken to be the numerical value in °C.

For sublimation and deposition from and into ice, the latent heat is almost constant in the temperature range from −40 °C to 0 °C and can be approximated by the following empirical quadratic function:

$L_\text{ice}(T) = (2834.1 - 0.29 T - 0.004 T^2)~\text{J/g}.$[10]

## References

1. ^ Perrot, Pierre (1998). A to Z of Thermodynamics. Oxford University Press. ISBN 0-19-856552-6.
2. ^ Clark, John, O.E. (2004). The Essential Dictionary of Science. Barnes & Noble Books. ISBN 0-7607-4616-8.
3. ^ Bryan, G.H. (1907). Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications, B.G. Tuebner, Leipzig, pages 9, 20–22.
4. ^ Maxwell, J.C. (1872). Theory of Heat, third edition, Longmans, Green, and Co., London, page 73.
5. ^ Harper, Douglas. "latent". Online Etymology Dictionary.
6. ^ Lewis, Charlton T. (1890). An Elementary Latin Dictionary. Entry for latens.
7. ^ James Burke (1979). "Credit Where It's Due" (in English). The Day the Universe Changed. Episode 6. 34 minutes in. BBC.
8. ^ J. P. Joule (1884), The Scientific Paper of James Prescott Joule, The Physical Society of London, p. 274, "I am inclined to believe that both of these hypotheses will be found to hold good,—that in some instances, particularly in the case of sensible heat, or such as is indicated by the thermometer, heat will be found to consist in the living force of the particles of the bodies in which it is induced; whilst in others, particularly in the case of latent heat, the phenomena are produced by the separation of particle from particle, so as to cause them to attract one another through a greater space.", Lecture on Matter, Living Force, and Heat. May 5 and 12, 1847
9. ^ Yaws' Handbook of Properties of the Chemical Elements 2011 Knovel
10. ^ a b Polynomial curve fits to Table 2.1. R. R. Rogers & M. K. Yau (1989). A Short Course in Cloud Physics (3rd ed.). Pergamon Press. p. 16. ISBN 0-7506-3215-1.