|A latent heat diagram by English science writer Chris Woodford, depicting the isothermal (constant temperature) aspect of latent heat, namely that there is a certain period of phase change (solid → liquid; liquid → gas) where heat is being added, but where no temperature change is measured. |
In 1757, Joseph Black, in his lectures, to account for inconsistencies in the then theories on how heating and melting occurred in relation to heat movements and temperature recordings, introduced the concept of latent heat.  The older established view of heat flow in relation to phase change, according to Black, when he began to lecture, was that:
“Fluidity was universally considered as produced by a small addition to the quantity of heat which a body contains, when it is once heated up to its melting point; and the return of such a body to a solid state, as depending on a very small diminution of the quantity of heat, after it is cooled to the same degree; that a solid body, when it is changed into a fluid, receives no greater addition to the heat within it than what is measured by the elevation of temperature indicated after fusion by the thermometer; and that, when the melted body is again made to congeal, by a diminution of its heat, it suffers no greater loss of heat than what is indicated also by the simple application to it of the same instrument.”
The newer view of heat in relation to a solid to liquid phase change, according Black's recent experiments, is that:
“The opinion I formed from attentive observation of the facts and phenomena, is as follows. When ice, for example, or any other solid substance, is changing into a fluid by heat, I am of opinion that it receives a much greater quantity of heat than what is perceptible in it immediately after by the thermometer. A great quantity of heat enters into it, on this occasion, without making it apparently warmer, when tried by that instrument. This heat, however, must be thrown into it, in order to give it the form of a fluid; and I affirm, that this great addition of heat is the principal, and most immediate cause of the fluidity induced.”
Conversely, the newer view of heat in relation to a liquid to solid phase change, according to Black, is that:
“On the other hand, when we deprive such a body of its fluidity again, by a diminution of its heat, a very great quantity of heat comes out of it, while it is assuming a solid form, the loss of which heat is not to be perceived by the common manner of using the thermometer. The apparent heat of the body, as measured by that instrument, is not diminished, or not in proportion to the loss of heat which the body actually gives out on this occasion; and it appears from a number of facts, that the state of solidity cannot be induced without the abstraction of this great quantity of heat. And this confirms the opinion, that this quantity of heat, absorbed, and, as it were, concealed in the composition of fluids, is the most necessary and immediate cause of their fluidity.”
To sum his view up, he introduces a new term:
“[In the] common process of freezing water, the extrication and emergence of the latent heat, if I may be allowed to use these terms, is performed by such minute steps, or rather with such a smooth progress, that many may find difficulty in apprehending it; but [other] example[s] [occur], in which this extrication of the concealed heat becomes manifest and striking.”
In 1772, Johan Wilcke (1732-1796) (Ѻ), a Swedish physicist,, independent of Black, whom he was then unaware of, published his discovery of the latent heat of fusion of ice; later, in 1781, Wilcke coined the concept and term of "specific heat" (Specifica-varme), in analogy with the term "specific gravity" (Specifica-tyngd), drawing up a list of specific heats of different mixtures, obtained experimentally by the method of mixtures. 
Heat of evaporation
The observation that the temperature of water, in open, air began to remain fixed as soon as it reached the boiling point and that addition of more heat only seemed to produce more ebullition and rapid evaporation was first noted by Robert Hooke in circa 1680. 
Into the 1860s, German physicist Rudolf Clausius expressed his views on heat and latent heat, to the effect “the heat actually present in a unit weight of [a] substance [is] the vis viva of it molecular motions” and that latent heat “is not only, as its name imports, hidden from our perceptions, but has actually no physical existence … it has been converted into work.” 
Modern terminology, for phase transitions that occur at constant temperature and pressure, the term “enthalpy of transformation” is used instead of the more obsolete term “latent heat”, as the enthalpy function (U + PV) is the so-called "heat content" of bodies.
Social latent heat
See main: Social latent heatIn 2019, Guilherme Arrude, et al, in their “Social Contagion Models on Hypergraphs”, attempted a blurry derivation attempt at “social latent heat”, using hypergraphs, Poisson process model ideas, a Fourier transform, etc., which gives them the following so-called social latent heat equation:
where is the energy released or absorbed; the following are a few excerpts:
“Phenomenologically, a discontinuity implies that our system possesses a ‘social latent heat’, that is released or accumulated at a constant value of λ. In terms of a social process, the latent heat interpretation is the fraction of individuals we have to add or remove to move the dynamics from one solution to the other.”
The following are related quotes:
“When water is boiling the temperature, as Amontons showed, remains constant, yet heat must be entering it all the time. Black calls this heat, which produces no sensible effect on the thermometer, the ‘latent heat’, and it is specifically associated with change of state. An exactly similar argument indicates that the melting of ice is associated with the absorption of latent heat.”— Donald Cardwell (1971), From Watt to Clausius (pgs. 37-38)
“The methods Black used to measure latent heats were extremely simple. He compared the time take to heat up a certain amount of water from a known temperature to boiling point with the time taken for the water to boil away. Assuming the heat was entering the water at a constant rate, he computed by simple arithmetic the temperature that the water would have reached had it not been turned into steam. The excess of this temperature above the boiling point is his measure of the latent heat of vaporization of water. In other words, it is the measure of the heat that has entered the water during the time it was boiling; the value he obtained for it was about 960 degrees Fahrenheit. His method for determining the latent heat of fusion of ice is essentially the same: he compares the time taken for a piece of ice at freezing point to melt with the time taken for it, in the form of water, to heat up from freezing point to a given temperature. The figure he gets for the latent heat of fusion is 140 degrees Fahrenheit.”
— Donald Cardwell (1971), From Watt to Clausius (pg. 38) 
● Specific heat
● Heat capacity
1. Giunta, Carmen. (2003). “Black heat capacity”, Le Moyne College, Department of Chemistry.
2. Perrot, Pierre. (1998). A to Z of Thermodynamics, Oxford: Oxford University Press.
3. Black, Joseph. (1803). “Lectures on the Elements of Chemistry” (excerpts on “latent heat” and “specific heat”), University of Edinburgh, published from his manuscripts by John Robison (1803) [as excerpted by William Francis Magie, A Source Book in Physics (New York: McGraw-Hill, 1935)].
4. Maxwell, James C. (1878). “Tait’s ‘Thermodynamics’ (I)”, (pgs. 257-59). Nature, Jan. 31.
5. Rees, Abraham. (1819). “Section: M. Amonton’s Fire-Wheel”, The Cyclopedia (pg. 40). Longman, Hurst, Rees, Orme & Brown.
6. Woodford, Chris. (2012). “Heat: Latent Heat”, ExpainThatStuff.com.
7. (a) McKie, Douglas and Heathcote, Niels. (1975). The Discovery of Specific and Latent Heats (pg. 15). Arno Press.
(b) Cardwell, Donald S.L. (1971). From Watt to Clausius: the Rise of Thermodynamics in the Early Industrial Age (pg. 38). Cornell University Press.
8. Arrude, Guilherme; Petri, Giovanni; Moreno, Yamir. (2019). “Social Contagion Models on Hypergraphs” (pdf), ArXiv, Sep 29.
9. Cardwell, Donald S.L. (1971). From Watt to Clausius: the Rise of Thermodynamics in the Early Industrial Age (pg. 40). Cornell University Press.
● McKie, Douglas. (1935). Discovery of Specific and Latent Heats. E. Arnold & Co.
● Latent heat – Wikipedia.