The Physics
Opus in profectus

Heat and Work

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historical development

~1798 Benjamin Thompson, Count Rumford (1753–1814)

Taking a cannon (a brass six-pounder) cast solid, and rough as it came from the foundry, and fixing it (horizontally) in the machine used for boring, and at the same time finishing the outside of the cannon by turning, I caused its extremity to be cut off; and, by turning down the metal in that part, a solid cylinder was formed, 734 inches in diameter, and 9810 inches long.

This short cylinder, which was supported in its horizontal position, and turned round its axis, by means of the neck by which it remained united to the cannon, was now bored with the horizontal borer used in boring cannon….

Count Rumford's cannon boring apparatus

The cylinder, revolving at the rate of about thirty-two times in a minute, had been in motion but a short time when I perceived, by putting my hand into the water and touching the outside of the cylinder, that heat was generated; and it was not long before the water which surrounded the cylinder began to be sensibly warm.

At the end of one hour I found, by plunging a thermometer into the water in the box (the quantity of which fluid amounted to 18.77 pounds avoirdupois, or 2¼ wine gallons) that its temperature had been raised no less than 47 degrees; being now 107° of Fahrenheit's scale…. At the end of two hours, reckoning from the beginning of the experiment, the temperature of the water was found to be raised to 178 °F.

At two hours twenty minutes it was 200 °F; and at two hours thirty minutes it actually boiled!

It would be difficult to describe the surprise and astonishment expressed in the countenances of the bystanders, on seeing so large a quantity of cold water heated and actually made to boil without any fire…

By meditating on the results of all these experiments we are naturally brought to that great question which has so often been the subject of speculation among philosophers; namely.

What is heat? Is there any such thing as an igneous fluid? Is there anything that can with propriety be called caloric?

It is in hardly necessary to add that anything which any insulated body, or system of bodies, can continue to furnish without limitation cannot possibly be a material substance: and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything, capable of being excited and communicated, in the manner the heat was excited and communication in these, except it be motion.

Count Rumford, 1798

~1824 Sadi Carnot (1796–1832).

Heat is nothing other than motive power, or perhaps motive power that has had a change of form. If there is a destruction in the particles of a body, there is at the same time heat production in a quantity precisely proportional to the quantity of motive power that is destroyed; reciprocally, in every configuration, if there is destruction of heat, there is production of motive power.

[T]he quantity of motive power in nature is invariable, that it is never properly speaking produced nor destroyed, Truly it changes for, sometimes manifesting itself as one kind of movement, sometimes another, but it is never annihilated.

Sadi Carnot

~1842 Julius von Mayer (1814–1878)

If two bodies find themselves in a given difference, then they could remain in a state of rest after the annihilation of that difference if the forces that were communicated to them as a result of the leveling of the difference could cease to exist; but if they are assumed to be indestructible, then the still persisting forces, as causes of changes in relationship, will again reestablish the original present difference.

Source? 1841

Der Zweck folgender Zeiten ist, die Beantwortung der Frage zu versuchen was wir unter „Kräften‟ zu verstehen haben, und wie sich solche untereinander verhalten. Während mit der Benennung Materie einem Objecte sehr bestimmte Eigenschaften, als die der Schwere, der Raumerfüllung, zugetheilt werden, knüpft sich an die Benennung Kraft vorzugsweise der Begriff des unbekannten, unerforschlichen, hypothetischen. Ein Versuch, den Begriff von Kraft ebenso präcis als den von Materie aufzufassen und damit nur Objecte wirklicher Forschung zu bezeichnen, dürfte mit den daraus fliefsenden Consequenzen, Freunden klarer hypothesenl reier Naturanschauung nicht unwillkommen seyn.   The following pages are designed as an attempt to answer the questions, What are we to understand by "Forces"? and how are different forces related to each other? Whereas the term matter implies the possession, by the object to which it is applied, of very definite properties, such as weight and extension; the term force conveys for the most part the idea of something unknown, unsearchable, and hypothetical. An attempt to render the notion of force equally exact with that of matter, and so to denote by it only objects of actual investigation, is one which, with the consequences that flow from it, ought not to be unwelcome to those who desire that their views of nature may be clear and unencumbered by hypotheses in relation.
Kräfte sind Ursachen, mithin fmdet auf dieselbe volle Anwendung der Grundsatz: causa æquat effectum. Hat die Ursache c die Wirkung e, so ist c = e; ist e wieder die Ursache einer andern Wirkung f, so ist e = f, u.s.f. c = e = f… = c. In einer Kette von Ursachen und Wirkungen kann, wie aus der Natur einer Gleichung erhellt, nie ein Glied oder ein Theil eines Gliedes zu Null werden. Diese erste Eigenschaft aller Ursachen nennen wir ihre Unzerslörlichkeit.   Forces are causes: accordingly, we may in relation to them make full application of the principle— causa æquat effectum. If the cause c has the effect e, then c = e; if in its turn e is the cause of a second effect f, we have e = f, and so on; c = e = f… = c. In a chain of causes and effects, a term or a part of a term can never, as plainly appears from the nature of an equation, become equal to nothing. This first property of all causes we call their indestructibility.
Hat die gegebene Ursache c eine ihr gleiche Wirkung e hervorgebracht, so hat eben damit c zu seyn aulgehört; c ist zu e geworden; wäre nach der Hervorbringung von e, c ganz oder einem Theile nach noch übrig, so müßte dieser rückbleibenden Ursache noch weitere Wirkung entsprechen, die Wirkung von c überhaupt also e ausfallen, was gegen die Voraussetzung c = e. Da mithin c in c, e in f, u.s.w. übergeht, so müssen wir diese Größen als verschiedene. Erscheinungsformen eine und desselben Objectes betrachten. Die Fähigkeit, verschiedene Formen annehmen zu können, ist die zweite wesentliche Eigenschaft aller Ursachen. Beide Eigenschaften zusammengefaßt sagen wir: Ursachen sind (quantitativ) unzerstörliche und (qualitativ) wandelbare Objecte.   If the given cause c has produced an effect e equal to itself, it has in that very act ceased to be: c has become e; if after the production of e, c still remained in whole or in part ,there must be still further effects corresponding to this remaining cause: the total effect of c would thus be e, which would be contrary to the supposition c = e. Accordingly, since c becomes e, and e becomes f, &c., we must regard these various magnitudes as different forms under which one and the same object makes its appearance. This capability of assuming various forms is the second essential property of all causes. Taking both properties together, we may say, causes are (quantitatively) indestructible and (qualitatively) convertible objects.
Zwei Abiheilungen von Ursachen fmden sich in der Natur vor, zwischen denen erfahrungsmäßig keine Uebergange stattfinden. Die eine Abtheilung bilden die Ursachen denen die Eigenschaft der Ponderabilitat und Impenctrabilität zukommt, — Materien; die andere die Ursachen, denen letztere Eigenschaften fehlen, — Kräfte, von der bezeichnenden negativen Eigenschaft auch Imponderabilien genannt. Kräfte sind also: unzerstörliche, wandelbare, imponderable Objecte   Two classes of causes occur in nature, which so far as experience goes, never pass one into another. The first class consists of such causes as possess the properties of weight and impenetrability; these are kinds of Matter: the other class is made up of causes which are wanting in the properties just mentioned, namely Forces, called also Imponderables, from the negative that has been indicated. Forces are therefore indestructible, convertible, imponderable objects.
Es ist der Gegenstand der Mechanik, die zwischen Fallkraft und Bewegung, Bewegung und Fallkraft, und die zwischen den Bewegungen unter sich bestehenden. Gleichungen zu entwickeln; wir erinnern hier nur an einen Punkt. Die Größe der Fallkraft v steht — den Erdhalbmesser = ∞ — gesetzt mit der Größe der Masse m und mit der ihrer Erhebung d, in geradem Verhältnisse; v  = md. Geht die Erhebung d = 1 in der Masse m in Bewegung dieser Masse von der Endgeschwindigkeit c = 1 über, so wird auch v = mc; aus den bekannten zwischen d und c stattfindenden Relationen ergiebt sich aber für andere Werthe von d oder c, mc2 als das Maß der Kraft v; also v = md = mc2; das Gesetz der Erhaltung lebendiger Kräfte finden wir in dem allgemeinen Gesetze der Uuzerstörbarkeit der Ursachen begründet.   It is the problem of Mechanics to develop the equations which between falling force and motion, motion and falling, and between different motions: here we will call to mind one point. The magnitude of the falling force v is directly proportional (Earth's radius being assumed = ∞) to the magnitude of the mass m and the height d to which it is raised; that is, v  = md. If the height d = 1 to which the mass m is raised, is transformed into the final velocity c = l of this mass, have also v = mc; but from the known relations existing between d and c, it results that, for other values of d or of c, the measure of the force v is mc2; accordingly v = md = mc2: the law of the conservation of vis viva is thus found to be based on the law of the indestructibility of causes.
Unter Anwendung der aufgestellten Sätze auf die Wärme und Volumenverhältnisse der Gasarten findet man… daß dem Herabsinken eines Gewichtsteiles von einer Höhe von circa 365 m die Erwärmung eines gleichen Gewichtsteiles Wasser von 0° auf 1° entspreche.   By applying the principles that have been set forth to the relations subsisting between the temperature and the volume of gases, we find… that the fall of a given weight from the height of about 365 metres corresponds to the warming of an equal weight of water from 0° to 1° C.
Julius von Mayer, 1842 Translated by G.C. Foster, 1862


~1843 James Joule (1818–1889) England. In a series of experiments, Joule establishes what is now known as the mechanical equivalent of heat.

First by electrical means…

By a dynamometrical apparatus attached to his machine, the author has ascertained that, in all the above cases, a quantity of heat, capable of increasing the temperature of a pound of water by one degree of Fahrenheit's scale, is equal to the mechanical force capable of raising a weight of about eight hundred and thirty pounds to the height of one foot.

James Joule, 1843

And later by mechanical means…

The apparatus exhibited before the Association consisted of a brass paddle-wheel working horizontally in a can of water. Motion could be communicated to this paddle by means of weights, pulleys, &c., exactly in the matter described in a previous paper.

The paddle moved with great resistance in the can of water, so that the weights (each of four pounds) descended at the slow rate of about one foot per second. The height of the pulleys from the ground was twelve yards, and consequently, when the weights had descended through that distance, they had to be wound up again in order to renew the motion of the paddle. After this operation had been repeated sixteen times, the increase of the temperature of the water was ascertained by means of a very sensible and accurate thermometer.

A series of nine experiments was performed in the above manner, and nine experiments were made in order to eliminate the cooling or heating effects of the atmosphere. After reducing the result to the capacity for heat of a pound of water, it appeared that for each degree of heat evolved by the friction of water a mechanical power equal to that which can raise a weight of 890 lb. to the height of one foot had been expended.

James Joule, 1845

and finally in 1850…

I will therefore conclude by considering it as demonstrated by the experiments contained in this paper,—

1st. That the quantity of heat produced by the friction of bodies, whether solid or liquid, is always proportional to the quantity of force expended. And,

2nd. That the quantity of heat capable of increasing the temperature of a pound of water (weighed in vacuo, and taken at between 55° and 60°) by 1° Fahr., requires for its evolution the expenditure of a mechanical force represented by the fall of 772 lbs through the space of 1 foot.


~ When? William Thomson, Lord Kelvin (1824–1907) Ireland–Scotland. Heat, electricity, magnetism, light were all forms of energy that were convertible

Nothing can be lost in the operations of nature — no energy can be destroyed.

~1847 Hermann Helmholtz (1821–1894) Germany, final statement of the First Law of Thermodynamics. "Über die Erhaltung der Kraft [On the Conservation of Force]" 1847.

From a similar investigation of all other known physical and chemical processes, we arrive at the conclusion that nature as a whole possesses a store of [energy], which cannot in any way be either increased or diminished; and that, therefore, the quantity of [energy] in nature is just as eternal and unalterable as the quantity of matter. Expressed in this form, I have named the general law "the principle of conservation of [energy]".

"Über die Erhaltung der Kraft." Hermann L.F. von Helmholtz, Scientific Memoirs, Natural Philosophy, 1853; trans. John Tyndall

~1850 Rudolf Clausius (1822–1888) Germany

Die Energie der Welt ist Konstant. 1850

mathematical discussion

Conservation of energy as it was first written. Heat is a form of energy. Heat can do work.

U = Q + W

Q > 0 system absorbs heat from the environment
Q < 0 system releases heat to the environment
W > 0 work done on the system by the environment
W < 0 work done by the system on the environment

Work is a macroscopic energy energy transfer. Heat is a microscopic energy transfer.