Poking at small effects you can’t explain can be a way of unraveling a much bigger piece of physics – Professor Carl Carlson, theoretical physicist [1]

Forging a law around the concept of energy and its conservation demanded many observations, many experiences, and many measurements.  The long history involved traveled through the works of the two individuals who independently quantified the mechanical equivalent of heat, namely Robert Mayer, discussed in a previous post, and now James Joule.  While Mayer’s rather stunning achievement was based on one “eureka’ moment followed by one calculation—okay, it wasn’t as fast and easy as I’m portraying, but it’s amazing how far he went with so little—Joule travelled a different path involving the painstaking collection of an unassailable trove of data.  Their respective approaches couldn’t have been more different.

Weight falls –>  paddle spins –>  water warms

While a discovery requires but a single observation, a law requires a body of supporting data.  Joule knew this.  He sensed the existence of a single exact exchange rate between work and heat and realized that the best way to capture it and display it to the world was through the use of a definitive, clean, and simple experimental set-up.  So, in the true spirit of Occam’s Razor, he eliminated his original interest, the electric motor, and stripped down his apparatus to the bare essentials:  a falling weight connected by a string to a spinning paddle inside a water-bath calorimeter. [2] The design of this simple set-up was remarkable in and of itself, as it offered a direct measure of the conversion of work into heat.  And then he worked to make these measurements perfect.  And how he worked!  Over and over and over, eliminating all sources of error, all sources of heat loss, all sources of friction save the one that mattered:  the paddle moving through the water.

Who remembers learning about significant figures?

The amazing aspect of this whole endeavor was that the actual measurement Joule sought to capture was very, very tiny.  By the time he completed the main thrust of his work in 1848, [3] he was attempting to accurately measure a total increase in temperature of only about a half a degree Fahrenheit!  To achieve even this small temperature rise required him, in one set of experiments, to carefully let a pair of 29-pound lead weights slowly fall 63 inches, over and over again, 20 times in all, rewinding the weights back to the starting point after each fall, all to obtain a single data point.  And then starting the whole process all over again to get more single data points.  The mean figure he reported for his first 40 tests was 0.575250 (!!!) degrees Fahrenheit.  Talk about significant figures.  Such claimed accuracy naturally invites questions.  But the fact is that he employed extremely accurate thermometers from the famed Mr. Dancer of Manchester [4] and claimed that he could, with much practice, read off with the naked eye to 1/20th the division, which translated into the detection of temperature changes as small as 1/200th of a degree![5]  On top of this, he felt that his use of statistical averages allowed him to use so many significant figures in his numbers, an assumption that may not stand up to rigorous statistical analysis but one we won’t argue here.  A truly amazing piece of experimental work. [6]

The inscription on Joule’s tombstone

Obsessed, Joule sought increasing accuracy until he arrived at a final number in 1849:  772 pounds falling through a one foot distance raises one pound of water one degree Fahrenheit. This published result, which was to be inscribed on his tombstone along with a wonderfully relevant and inspiring quote from the Gospel of John (9:4), “I must work the works of him that sent me, while it is day: the night cometh when no man can work”, will be regarded as the historical occasion on which the mechanical equivalent of heat was fixed to within a few figures.  Later work eventually brought this number up slightly to 778.  We use a variation of this number (1 calorie = 4.18 Joules, one Joule being defined as a unit of energy equal to the work done by the movement of one Newton of force through one meter of distance) to convert thermal energy to the same energy units as mechanical work, such units naturally being named in Joule’s honor.

No matter the approach, the answer remains the same

Note that this result was about the same as that which Joule determined in his original design with the dynamo. Like the board game of Mouse Trap, the weights fell, the crank turned, electricity flowed, the wires heated, and water temperature rose.  Each cause in this chain exactly equaled the resulting effect.  Nothing was lost.  You could remove pieces or switch their order, heat-to-work or work-to-heat; it didn’t matter.  Joule realized that each step was linked to the others by an abstract exactness such that a negative change in one reappeared as a positive change in the other.

The lone voice

Joule’s was a lone voice operating in the wilderness outside the establishment.  There was little pull at that time from a physics community that even questioned the premise that one could heat up water merely by shaking it.  The caloric theory said nothing to this effect.  Indeed, the conversion of abstract work into tangible heat, a fundamental aspect of the mechanical theory of heat, was an unacceptable concept to many, made all the more so by the fact that the effect was so small that only the most trained of experimentalists could detect it.  Detection required someone of great skill and persistent patience.  It required Joule.  He was second to none.

Learn more about Joule’s life and accomplishments!

To appreciate more about Joule’s accomplishments, check out Chapter 21 in my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics. Thank you for listening!

References

[1] Carlson quote cited in Grant, Andrew. 2013. “Atom & Cosmos: Proton’s Radius Revised Downward: Surprise Measurement Could Lead to New Physics,” Science News, 183(4), 23 February, p. 8.

[2] One could consider the spinning paddle as having a similar effect as a moving piston.  Molecules that strike either moving structure rebound with higher energy, thus resulting in an increase in temperature.

[3] Chalmers, Thomas Wightman. 1952. Historic Researches.  Chapters in the History of Physical and Chemical Discovery. Charles Scribner’s Sons. Chapter II-3.

[4] The brewers in Manchester demanded such accurate measurements to guide their brewing processes.

[5] Chalmers, p. 37.

[6] To truly appreciate how amazing Joule’s experimental work was, see Sibum, Heinz Otto. 1995. “Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England.” Studies in History and Philosophy of Science Part A 26 (1): 73–106. The challenges that Sibum encountered in attempting to replicate the precision and accuracy of Joule’s experiments were many, including, for example, the challenge of dealing with the radiative heating effect that his body had on the apparatus upon entering the room.

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