Heat & Work


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, 7¾ inches in diameter, and 98/10 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….

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 ℉.

At two hours twenty minutes it was 200 ℉; 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.

Benjamin Thompson (Count Rumford)

~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

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 0š auf 1š [C] entspreche.

[T]he warming of a given weight of water from 0 to 1 ℃ corresponds to the fall of an equal weight from the height of about 365 meters.

Julius von Mayer

~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 Prescott Joule. "On the Caloric Effect of Magneto-Electricity, and on the Mechanical Value of Heat." Report of the British Association for the Advancement of Science., Vol. 12 (1843) 33.

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 Prescott Joule. "On the Existence of an Equivalent Relation between Heat and the ordinary Forms of Mechanical Power." Philosophical Magazine. Ser. 3,, Vol. 27 (1845) 205.

~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

~ 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.

~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.

ΔU = 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

more …