Joule's Paddle-Wheel Experiment (1845): Heat as Energy

Joule’s paddle-wheel experiment was a series of measurements by the English physicist James Prescott Joule, first reported in 1845, which showed that mechanical work can be turned into heat at a fixed rate. Falling weights turned a paddle wheel in a container of water, and the tiny rise in the water’s temperature revealed how much work was needed to produce a given amount of heat. The result, known as the mechanical equivalent of heat, became one of the experimental foundations of the law of conservation of energy.

Background: what is heat?

In the early nineteenth century most scientists explained heat with the caloric theory. Heat was thought to be an invisible, weightless fluid, called caloric, that flowed from hot bodies to cold ones and could be neither created nor destroyed. The theory had been given its name in the chemical revolution of Antoine Lavoisier.

Some observations did not fit. In the 1790s Count Rumford noticed that boring cannon produced an apparently endless supply of heat from friction. However, his arguments did not overturn caloric theory, which also worked well in Sadi Carnot’s influential 1824 study of steam engines.

Joule’s early work

James Prescott Joule (1818–1889) was born in Salford, near Manchester, into a brewing family. Brewing required careful temperature measurement, and Joule had the money and skill to build precise apparatus. He was interested at first in electric motors and wondered whether they could replace steam engines.

In 1840–1841 he found that the heat produced by an electric current in a wire is proportional to the resistance multiplied by the square of the current, now called Joule’s first law. In 1843, at the British Association meeting in Cork, he reported experiments in which a hand-turned electromagnetic machine generated current and heat, and gave a first figure for the work needed to produce a unit of heat. The audience showed little interest.

The paddle-wheel apparatus

To avoid electrical complications, Joule turned to a direct mechanical method. In his best-known apparatus, two weights hung on cords wound around a drum. As the weights fell a measured distance, they turned a brass paddle wheel inside an insulated vessel of water. Fixed vanes inside the vessel stopped the water from simply rotating, so the paddles churned it and friction warmed it.

The temperature rise was extremely small, a fraction of a degree Fahrenheit, so Joule used thermometers that he believed could be read to about 1/200 of a degree. He repeated the fall of the weights many times, corrected for heat lost to the surroundings and for the energy of the weights when they hit the floor, and compared the work done with the heat gained.

He presented the paddle-wheel method to the British Association meeting in Cambridge in June 1845. His first paddle-wheel figure, published in 1845, was about 890 foot-pounds of work per British thermal unit (the heat needed to warm one pound of water by one degree Fahrenheit).

Refinement and recognition

Joule continued to refine the experiment, using water, sperm-whale oil and mercury. At the British Association meeting in Oxford in 1847 the young physicist William Thomson, later Lord Kelvin, heard Joule speak and became interested, though he took several years to accept fully that heat was a form of motion. Thomson later recalled meeting Joule in the Alps that summer, when Joule was on his honeymoon and planned to measure the temperature difference between the top and bottom of a waterfall.

Joule’s paper “On the Mechanical Equivalent of Heat”, read to the Royal Society in 1849 and published in 1850, gave about 772 foot-pounds per British thermal unit. This is within about 1 per cent of the modern value of about 778.

Rival claims

Joule was not alone. In 1842 the German physician Julius Robert von Mayer published an estimate of the mechanical equivalent of heat, based on the properties of gases rather than direct experiment. The Danish engineer Ludwig Colding also reached similar conclusions. In 1847 Hermann von Helmholtz set out a general principle of the conservation of energy. Priority disputes followed, especially between supporters of Joule and of Mayer.

Consequences

Around 1850 Rudolf Clausius and William Thomson combined Joule’s equivalence with Carnot’s analysis of heat engines. The result was thermodynamics, with its first law (energy is conserved, and heat and work are two forms of energy transfer) and second law (heat flows spontaneously from hot to cold). Caloric theory was abandoned. The new science shaped engineering, chemistry and later electromagnetic theory.

Timeline

• 1841: Joule publishes his law on heating by electric current.
• 1842: Julius Robert von Mayer publishes an estimate of the mechanical equivalent of heat.
• 1843, August: Joule reports a value from electromagnetic experiments at Cork.
• 1845, June: Joule presents the paddle-wheel method at Cambridge.
• 1847, June: Joule speaks at the British Association in Oxford; William Thomson takes notice.
• 1850: Joule’s refined value of about 772 foot-pounds is published by the Royal Society.
• 1889, 11 October: Joule dies at Sale, near Manchester.

Why it matters

Joule’s patient measurements turned the idea that heat is a form of energy into a precise, testable number. That number linked mechanics, electricity and heat in a single accounting system and underpins the law of conservation of energy. The SI unit of energy, the joule, carries his name.