# Original Writings of Joseph Black on the Melting of Ice

Confusion in the meaning of “heat” and “temperature” led to a gross error in estimates of the amount of heat required to melt water, until the experiments of Joseph Black (1728-99)[1] which are described in the scientist’s own words [2] below.

Figure $$\PageIndex{1}$$ Joseph Black[3]

Figure $$\PageIndex{2}$$ The original ice-calorimeter, used by Antoine Lavoisier and Pierre-Simon Laplace in used in 1782-83, to investigate Joseph Black’s prior discovery of latent heat[4]

Joseph Black was a physician (MD), and professor of Medicine at University of Glasgow (where he also served as lecturer in Chemistry). Before Dr. Black's work, it was widely believed that melting ice required very little heat (or energy), since there was no discernable temperature change during the process.

The original work conveys the meaning of heat of fusion very well. Examples have been embedded in the work to show how calculations would be done nowadays. The ice calorimeter is used to determine how much heat is released by a chemical change by measuring the mass of ice that it melts, and using Joseph Black's prior discovery of latent heat.

## Excerpts from Joseph Black's Lectures on the Elements of Chemistry

Delivered in the University of Edinburgh by the Late Joseph Black, M.D. ... published from his manuscripts by John Robison (1803)[5]

"... 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;[italics added] 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."

[Note: As heat is removed from liquid water, its temperature changes in proportion to the heat removed until it reaches the freezing point, where we now know that there is nofurther temperature change until all the liquid has frozen. Then the temperature again begins to fall as heat is removed]

"This was the universal opinion on this subject, so far as I know, when I began to read my lectures in the University of Glasgow, in the year 1757. But I soon found reason to object to it, as inconsistent with many remarkable facts, when attentively considered; and I endeavoured to shew, that these facts are convincing proofs that fluidity is produced by heat in a very different manner."

"I shall now describe the manner in which fluidity appeared to me to be produced by heat, and we shall then compare the former and my view of the subject with the phenomena."

"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."

"And, 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 perceive the foundation of this opinion, and the inconsistency of the former with many obvious facts, we must consider, in the first place, the appearances observable in the melting of ice, and the freezing of water."

"If we attend to the manner in which ice and snow melt, when exposed to the air of a warm room, or when a thaw succeeds to frost, we can easily perceive, that however cold they might be at the first, they are soon heated up to their melting point, or begin soon at their surface to be changed into water. And if the common opinion had been well founded, if the complete change of them into water required only the further addition of a very small quantity of heat, the mass, though of considerable size, ought all to be melted in a very few minutes or seconds more, the heat continuing incessantly to be communicated from the air around. Were this really the case, the consequences of it would be dreadful in many cases; for, even as things are at present, the melting of great quantities of snow and ice occasions violent torrents, and great inundations in the cold countries, or in the rivers that come from them. But, were the ice and snow to melt as suddenly as they must necessarily do, were the former opinion of the action of heat in melting them well founded, the torrents and inundations would be incomparably more irresistible and dreadful.[italics added] They would tear up and sweep away every thing, and that so suddenly, that mankind should have great difficulty to escape from their ravages. This sudden liquefaction does not actually happen; the masses of ice or snow melt with a very slow progress, and require a long time, especially if they be of a large size, such as are the collections of ice, and wreaths of snow, formed in some places during the winter. These, after they begin to melt, often require many weeks of warm weather, before they are totally dissolved into water. This remarkable slowness with which ice is melted, enables us to preserve it easily during the summer, in the structures called Ice-houses. It begins to melt in these, as soon as it is put into them; but, as the building exposes only a small surface to the air, and has a very thick covering of thatch, and the access of the external air to the inside of it is prevented as much as possible, the heat penetrates the ice-house with a slow progress, and this, added to the slowness with which the ice itself is disposed to melt, protracts the total liquefaction of it so long, that some of it remains to the end of summer. In the same manner does snow continue on many mountains during the whole summer, in a melting state, but melting so slowly, that the whole of that season is not a sufficient time for its complete liquefaction."

[Note: This macroscopic behavior demonstrates quite clearly that energy must be supplied to a solid in order to melt it. On a microscopic level melting involves separating molecules which attract each other. This requires an increase in the potential energy of the molecules, and the necessary energy is supplied by the surroundings. The kinetic energy of the molecules (rotation, vibration, and limited translation) remains constant during phase changes, because the temperature does not change.]

"This remarkable slowness with which ice and snow melt, struck me as quite inconsistent with the common opinion of the modification of heat, in the liquefaction of bodies."

"And this very phenomenon is partly the foundation of the opinion I have proposed; for if we examine what happens, we may perceive that a great quantity of heat enters the melting ice, to form the water into which it is changed, and that the length of time necessary for the collection of so much heat from the surrounding bodies, is the reason of the slowness with which the ice is liquefied. If any person entertain doubts of the entrance and absorption of heat in the melting ice, he needs only to touch it; he will instantly feel that it rapidly draws heat from his warm hand. He may also examine the bodies that surround it, or are in contact with it, all of which he will find deprived by it of a great part of their heat; or if he suspend it by a thread, in the air of a warm room, he may perceive with his hand, or by a thermometer, a stream of cold air descending constantly from the ice; for the air in contact is derived of a part of its heat, and thereby condensed and made heavier than the warmer air of the rest of the room; it therefore falls downwards, and its place round the ice is immediately supplied by some of the warmer air; but this, in turn, is soon deprived of some heat, and prepared to descend in like manner; and thus there is a constant flow of warm air from around, to the sides of the ice, and a descent of the same in a cold state, from the lower part of the mass, during which operation the ice must necessarily receive a great quantity of heat.

"It is, therefore, evident, that the melting ice receives heat very fast, but the only effect of this heat is to change it into water, which is not in the least sensibly warmer than the ice was before. A thermometer, applied to the drops or small streams of water, immediately as it comes from the melting ice, will point to the same degree as when it is applied to the ice itself, or if there is any difference, it is too small to deserve notice. A great quantity, therefore, of the heat, or of the matter of heat, which enters into the melting ice, produces no other effect but to give it fluidity, without augmenting its sensible heat; it appears to be absorbed and concealed within the water, so as not to be discoverable by the application of a thermometer.''[italics added] "

## Experiments

"... In order to understand better this absorption of heat by the melting ice, and concealment of it in water, I made the following experiments:"

"I chose two thin globular glasses 4 inches in diameter, and very nearly the same weight. I poured 5 ounces of pure water into one of them, and then set it in a mixture of snow and salt until the water was frozen into a small mass of ice. It was then carried into a large empty hall, in which the air was not disturbed or varied in temperature during the progress of the experiment..."

"I now set up the other globular glass precisely in the same way, and at the distance of 18 inches to one side, and into this I poured 5 ounces of water, previously cooled almost to the freezing point--actually to 33°F. Suspended in it was a very delicate thermometer when its bulb in the center of the water, and its stem so placed that I could read it without touching the thermometer. I then began to observe the ascent of this thermometer, at suitable intervals, in order to learn with what celerity the water received heat; I stirred the water gently with the end of a feather about a minute before each observation. The temperature of the air, examined at a little distance from the glasses, was 47°F."

"The thermometer assumed the temperature of the water is less than half a minute, after which, the rise of it was observed every 5 to 10 minutes, during half an hour. At the end of that time, the water was 7 degrees warmer than at first; that is, its temperature had risen to 40°F." (Dr. Black next explains that the time to warm the ice-containing glass to 40°F was 10.5 hours)

"It appears that the ice-glass had to receive heat from the air of the room during 21 half-hours in order to melt the ice and then warm the resulting water to 40°F. During all this time it was receiving heat with the same celerity (very nearly) as had the water-glass during the single half-hour in the first part of the experiment... Therefore, the quantity of heat received the ice-glass during the 21 half-hours was 21 times the quantity received by the water-glass during the single half hour. It was, therefore, a quantity of heat, which, had it been added to liquid water, would have made it warmer by (40-33) X 21, or 147 degrees. No part of this heat, however, appeared in the ice water, except that which produced the temperature rise of 8 degrees; the remaining part, corresponding to 138 to 140 degrees, had been absorbed by the melting ice and was concealed in the water into which it was changed."

## Modern Analysis of the Experiments

Example $$\PageIndex{1}$$: Heat of Fusion

Estimate the Heat of fusion of water from Joseph Black's Data. Solution We can use the heat capacity of water determined by James Joule to determine how much heat was absorbed by each goblet:

The 5 oz of liquid water rose in temperature from 33 to 40 oF in 30 minutes. 1 US fluid ounce = 29.5735296 milliliters

$\text{V} = \text{5 oz} \times \text{29.57 mL/oz} = \text{148 mL m} = \text{V} \times \text{D} = \text{148 g 33}^{\circ} \text{F} = \text{0.6}^{\circ} \text{C} \nonumber$

The heat it absorbed was:

$\text{q} = \text{4.18} \frac{\text{J}}{\text{g}^{\circ}\text{C}} \times \text{148 g} \times \text{(4.4 - 0.6)} = \text{4.3} \times \text{10}^3 \text{or 2.4 kJ}\nonumber$

The other goblet contained ice, and was of the same size and shape, but it took 10 hours 30 minutes to rise from 32 to 40 oF. so it absorbed close to the same amount of heat per minute:

$\frac{\text{2.4 kJ}}{\text{30 min}} = \text{0.08} \frac{}{}\nonumber$

As before, 30 minutes must have been required to raise the temperature of liquid water from the freezing point to 40 oF, so it must have taken 10 hours to melt the ice. The amount of heat would be:

$\text{q} = \text{0.08} \frac{kJ}{min} \times \text{10 hrs} \times \text{60} \frac{min}{hr} = \text{48 kJ}\nonumber$

On a per mole basis, since we have 148 g of ice:

$\text{148 g} \times \frac{\text{1 mol}}{\text{18 g}} = \text{8.2 mol}\nonumber$

$\Delta \text{H}_M = \frac{\text{q}}{\text{n}} = \frac{\text{48 kJ}}{\text{8.2 mol}} = \text{5.8} \frac{\text{kJ}}{\text{mol}}\nonumber$

This is the "Enthalpy of Fusion" of water. The currently accepted value is 6.01 kJ/mol (see the table below)!!

"... I have, in the same manner, put a lump of ice into an equal quantity of water, heated to the temperature 176, and the result was, that the fluid was no hotter than water just ready to freeze. Nay, if a little sea salt be added to the water, and it be heated only to 166 or 170, we shall produce a fluid sensibly colder than the ice was in the beginning, which has appeared a curious and puzzling thing to those unacquainted with the general fact.'

"It is, therefore, proved that the phenomena which attended the melting of ice in different circumstances, are inconsistent with the common opinion which was established upon the subject, and that they support the one which I have proposed."

[In the original, Dr. Black goes on to describe "supercooling" of very pure water, where it remains liquid 6 or 7 degrees below its freezing point, until it is disturbed.]

## Modern Summary

The heat energy which a solid absorbs when it melts is called the enthalpy of fusion or heat of fusion and is usually quoted on a molar basis. (The word fusion means the same thing as “melting.”) When 1 mol of ice, for example, is melted, we find from experiment that 6.01 kJ are needed. The molar enthalpy of fusion of ice is thus +6.01 kJ mol–1, and we can write

$\ce{H2O (s) -> H2O (l)}\nonumber$
(0°C) ΔHM = 6.01 kJ mol–1

Selected molar enthalpies of fusion are tabulated below. Solids like ice which have strong intermolecular forces have much higher values than those like CH4 with weak ones.

### Heat of Vaporization

When a liquid is boiled, the variation of temperature with the heat energy supplied is similar to that found for melting. When heat is supplied at a steady rate to a liquid at atmospheric pressure, the temperature rises until the boiling point is attained. After this the temperature remains constant until the enthalpy of vaporization has been supplied. Once all the liquid has been converted to vapor, the temperature again rises. In the case of water the molar enthalpy of vaporization is 40.67 kJ mol–1. In other words

$\ce{H2O (l) -> H2O (g)}\nonumber$
(100°C) ΔHm = 40.67 kJ mol–1

Table $$\PageIndex{1}$$ Molar Enthalpies of Fusion and Vaporization of Selected Substances.

 Substance Formula ΔH(fusion) / kJ mol1 Melting Point / K ΔH(vaporization) / kJ mol-1 Boiling Point / K (ΔHv/Tb) / JK-1 mol-1 Neon Ne 0.33 24 1.80 27 67 Oxygen O2 0.44 54 6.82 90.2 76 Methane CH4 0.94 90.7 8.18 112 73 Ethane C2H6 2.85 90.0 14.72 184 80 Chlorine Cl2 6.40 172.2 20.41 239 85 Carbon tetrachloride CCl4 2.67 250.0 30.00 350 86 Water* H2O 6.00678 at 0°C, 101kPa 6.354 at 81.6 °C, 2.50 MPa 273.1 40.657 at 100 °C, 45.051 at 0 °C, 46.567 at -33 °C 373.1 109 n-Nonane C9H20 19.3 353 40.5 491 82 Mercury Hg 2.30 234 58.6 630 91 Sodium Na 2.60 371 98 1158 85 Aluminum Al 10.9 933 284 2600 109 Lead Pb 4.77 601 178 2022 88

Heat energy is absorbed when a liquid boils because molecules which are held together by mutual attraction in the liquid are jostled free of each other as the gas is formed. Such a separation requires energy. In general the energy needed differs from one liquid to another depending on the magnitude of the intermolecular forces. We can thus expect liquids with strong intermolecular forces to have larger enthalpies of vaporization. The list of enthalpies of vaporization given in the table bears this out.

Two other features of the table deserve mention. One is the fact that the enthalpy of vaporization of a substance is always higher than its enthalpy of fusion. When a solid melts, the molecules are not separated from each other to nearly the same extent as when a liquid boils. Second, there is a close correlation between the enthalpy of vaporization and the boiling point measured on the thermodynamic scale of temperature. Periodic trends in boiling point closely follow periodic trends in heat of vaporiation. If we divide the one by the other, we find that the result is often in the range of 75 to 90 J K–1 mol–1. To a first approximation therefore the enthalpy of vaporization of a liquid is proportional to the thermodynamic temperature at which the liquid boils. This interesting result is called Trouton’s rule. An equivalent rule does not hold for fusion. The energy required to melt a solid and the temperature at which this occurs depend on the structure of the crystal as well as on the magnitude of the intermolecular forces.

From ChemPRIME: 10.9: Enthalpy of Fusion and Enthalpy of Vaporization

## References

1. http://web.lemoyne.edu/~giunta/blackheat.html
2. The original manuscripts of Joseph Black (1728-1799)are available in the Harvard Cases Histories in Experimental Science, Vol. I, James B. Conant, ed., 1957.fckLR
3. http://en.Wikipedia.org/wiki/Joseph_Black
4. en.Wikipedia.org/wiki/Calorimetry
5. as excerpted by William Francis Magie, A Source Book in Physics (New York: McGraw-Hill, 1935)