A 4.774-cm-diameter aluminum cylinder is mounted horizontally, so that you can rotate it about its central axis with a crank. A flat nylon rope is wrapped around the cylinder a little more than five turns. A rubber band anchors the top end of the rope to the base plate of the apparatus, and provides light tension. Hanging from the bottom portion of the rope is a large mass. (An 11-kg mass is shown above.) When you turn the crank (clockwise), friction between the cylinder and the rope produces tension in the bottom portion of the rope, and lifts the mass a small distance above the floor. As you crank, this friction heats the cylinder. A thermistor embedded in the cylinder is connected via slip rings and brushes to two banana jacks, to which an ohmmeter is connected. The large display allows the class to see the resistance of the thermistor during the demonstration. A table of temperature vs. the thermistor’s resistance allows you to determine the initial temperature of the cylinder, and the temperature after you have finished cranking. A counter next to the crank keeps track of the number of turns you have given the cylinder. By calculating the mechanical work you have done in turning the crank, and the amount of heat deposited in the aluminum cylinder in the process, and then dividing, you can determine the mechanical equivalent of heat.
At least as early as the times of the ancient Greeks and Romans, people began to wonder about the nature of heat. The prevailing view then was that heat was some sort of material, and that it had mass (or weight; it was ponderable). Eventually, people began to think of heat as an invisible massless (or weightless, imponderable) fluid. In 1789, in his Traité élémentaire de chimie, Antoine Lavoisier gave this fluid the name caloric. During the period of roughly a century before then, others had proposed that heat was some kind of vibration. For example, in 1690 John Locke, in his Essay Concerning Human Understanding (Book II, Chapter VIII, § 21), proposed that the sensation of heat and cold might be due to the increase or diminution, respectively, of the motion of minute particles in our hands, caused by the greater or lesser motion of minute particles in whatever body with which our hands were in contact. In 1788, in a letter to David Rittenhouse, titled A New and Curious Theory of Light and Heat (Transactions of the American Physical Society, Vol. 3 (1793), pp. 5-8), Benjamin Franklin opens with the statement, “Universal space, as far as we know of it, seems to be filled with a subtil fluid, whose motion, or vibration, is called light.” He then goes on to develop the idea that heat is due to the influence of these vibrations on the matter with which this fluid interacts. Still, caloric theory, according to which heat was itself a fluid, prevailed.
Toward the end of the 18th century, Count Rumford of Bavaria (Benjamin Thompson, born in Woburn, Massachusetts), while supervising the boring of cannon for the Bavarian government, was impressed with how much heat was generated in the process. To prevent overheating of the cannon, workers filled the bore with water, which they had to replenish as it boiled away. People explained the continuous production of caloric necessary to do this, by proposing that as a material became more finely subdivided, its capacity for retaining caloric decreased. Thus, as chip formed during the boring process, this should release caloric. Rumford noticed, however, that the chip itself was hotter than boiling water, and further, that a quantity of chip had the same capacity for heat as a plate of the same mass. These observations compelled him to perform a series of experiments, for which he modified the neck of a cannon blank for turning against a blunt boring tool. In contact with the rotating cannon blank, this tool produced only a fine scale, whose mass was negligible in comparison to that of the cannon blank. In these experiments, Rumford found that he could generate considerable heat from friction alone. When he enclosed the neck and boring tool with a water-tight box and filled the box with water, he also found that the longer he turned the cannon blank against the tool, the greater the increase in the temperature of the water and cannon. He described his experiments in a paper that he read before the Royal Society (Philosophical Transactions of the Royal Society of London, Vol. 88, (1798), pp. 80-102). In his conclusion, after considering various possible sources for this heat, he wrote:
And, in reasoning on this subject, we must not forget to consider that most remarkable circumstance, that the source of the heat generated by friction, in these experiments, appeared evidently to be inexhaustible.
It is hardly necessary to add, that any thing 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 any thing, capable of being excited, and communicated, in the manner the heat was excited and communicated in these experiments, except it be MOTION.
Rumford thus showed that heat could be produced by mechanical work.
In the late 1840s, James Joule performed a set of careful experiments to make a quantitative determination of what is now known as the mechanical equivalent of heat. These constitute his now-famous “paddle wheel experiment.” In these experiments, Joule used an apparatus in which two hanging masses were attached to a mechanism by which as they fell, they turned a shaft that rotated a set of paddle wheels. The paddle wheels sat between sets of stationary vanes inside a copper vessel, which was filled with either water or mercury. Friction in the fluid heated it as the masses fell. By means of a thermometer inserted into the vessel before and after each run, Joule measured the change in temperature due to the frictional heating. In 1849, Joule presented his results to the Royal Society in a paper titled, On the Mechanical Equivalent of Heat (Philosophical Transactions of the Royal Society of London, Vol. 140 (1850), pp. 61-82). He concluded that the quantity of heat produced by friction is always proportional to the mechanical work done, and that the quantity of heat necessary to raise the temperature of a pound of water (between 55° F and 60° F) by 1° F requires mechanical work of 772 foot-pounds. He gives as his most correct figure 772.692 ft-lb. Between 55 and 60 degrees F, the heat capacity of water is about 0.99992 cal/g·°C, so the heat capacity of one pound of water is about 252.2 cal/g·°F. One foot-pound equals 1.36 N-m, so 772.692 ft-lb equals 1,051 J, which gives a value of 4.167 J/cal. The thermochemical calorie is now defined as being equal to 4.184 J (as opposed to the International Table calorie, which is defined as 4.1868 J; see NIST Special Publication 811, footnotes nine and ten).
Operating the demonstration:
You may operate the apparatus with either the 11-kg mass shown above, or a six-kilogram mass (with one of the five-kilogram masses sitting on the hanger, instead of both); the manual for the apparatus specifies a 10-kg mass. As noted above, the diameter of the aluminum cylinder (between the flanges, where the rope sits) is 4.774 cm. The mass of the cylinder is 200.4 g, and the specific heat of aluminum is 0.220 cal/g·°C.
Before you start, note the temperature of the cylinder. The page set out with the apparatus gives a table of temperature vs. resistance. You can either interpolate between resistance values, or use the equation printed below the table. This equation is the result of a logarithmic fit of temperature vs. resistance over the range 4 °C to 35 °C.
Rotate the crank in the clockwise direction, keeping a steady speed. The mass should rise a small distance above the floor when you start cranking. As you turn the crank, the counter will keep track of how many times you have turned it. Stop at the desired number of turns, and note the temperature of the cylinder. (Take the minimum resistance that the thermistor reaches.) Again, you can interpolate or use the equation.
In raising the mass above the floor by turning the crank N turns, you will have performed mechanical work equivalent to lifting the mass through a distance of Nπ(4.774 cm)(1 m/100 cm), or N(0.150 m). (Put another way, friction will have acted over a distance of N(0.150 m) to hold the mass slightly above the floor while you turned the crank.) This work is N(0.150 m)mg. For the 11-kg and 5-kg masses, respectively, mg equals 107.8 N and 58.86 N (taking g = 9.81 m/s2). For 100 turns, the distance is 15.0 m, and the work is 1,618 N-m for the 11-kg mass, and 882.8 N-m for the 6-kg mass.
The heat generated in the aluminum cylinder is mCΔT, where m, the mass of the cylinder, is 200.4 g, C, the heat capacity of the cylinder, is 0.220 cal/g·°C, and ΔT is the change in temperature of the cylinder. If you crank for 100 turns, with the 11-kg mass the temperature will rise roughly nine degrees, and with the 6-kg mass, it will rise about five degrees. The heat deposited in the cylinder is thus (200.4 g)(0.220 cal/g·°C)(9 °C) = 396.8 calories for 100 turns with the 11-kg mass, and about 220.4 calories for 100 turns with the 6-kg mass. Dividing the mechanical work by the heat gives 4.079 joules/calorie with the values for the 11-kg mass, and 4.005 joules/calorie with those for the six-kilogram mass.
Ideally, to make a proper measurement, you would cool the cylinder below room temperature, let it warm up to half the expected temperature rise below room temperature, and begin turning the cylinder then. For example, for the 11-kg mass, you would start cranking when the cylinder had warmed to 4.5 degrees below room temperature, and with the six-kilogram mass, you would let the cylinder warm to 2.5 degrees below room temperature before starting. This way, the heat absorbed by the cylinder from the room air during the first half of the measurement would equal the heat lost to the room air during the second half, and the errors would cancel. With the measurement performed as described above, once you start cranking, the cylinder begins losing heat to the surrounding air. Also, the temperature changes given in the examples here are rough estimates. In the heat capacity of the cylinder, we are also ignoring the fact that some of the mass is in the small board with the rotating contacts, a small plastic drive ring and the thermistor, and we are also neglecting the small heat capacity of the turns of rope in contact with the cylinder. The error thus introduced, however, is probably small compared to the error in the estimates of the temperature change. Still, the values calculated above are about 2.5 and 4.3 percent low, so fairly close for a quick demonstration.
References:
1) Cajori, Florian. Isis, Vol. 4, No. 3 (Apr., 1922), pp. 483-492 (On the History of Caloric).
2) Barnett, Martin K. The Scientific Monthly, Vol. 62, No. 2 (Feb., 1946), pp. 165-172 (The Development of the Concept of Heat -- I).
3) Barnett, Martin K. The Scientific Monthly, Vol. 62, No. 3 (Mar., 1946), pp. 247-257 (The Development of the Concept of Heat -- II).
4) Mott-Smith, Morton, Ph.D. The Concept of Heat and Its Workings Simply Explained (New York: Dover Publications, Inc., 1962), pp. 3, 38.
5) Sears, Francis Weston, and Zemansky, Mark W. College Physics, Third Edition (Reading, Massachusetts: Addison-Wesley Publishing Company, Inc., 1960), pp. 305-308.
6) Resnick, Robert and Halliday, David. Physics, Part One, Third Edition (New York: John Wiley and Sons, 1977), pp. 475-477.