Tong Research Paper

... the mechanical power exerted in turning a magneto-electric machine is converted into the heat evolved by the passage of the currents of induction through its coils; and, on the other hand, that the motive power of the electro-magnetic engine is obtained at the expense of the heat due to the chemical reactions of the battery by which it is worked.^[9]

Joule here adopts the language of vis viva (energy), possibly because Hodgkinson had read a review of Ewart's On the measure of moving force to the Literary and Philosophical Society in April 1844.
Further experiments and measurements by Joule led him to estimate the mechanical equivalent of heat as 838 ft·lbf of work to raise the temperature of a pound of water by one degree Fahrenheit.^[10] He announced his results at a meeting of the chemical section of the British Association for the Advancement of Science in Cork in 1843 and was met by silence.
Joule was undaunted and started to seek a purely mechanical demonstration of the conversion of work into heat. By forcing water through a perforated cylinder, he was able to measure the slight viscous heating of the fluid. He obtained a mechanical equivalent of 770 ft·lbf/Btu (4.14 J/cal). The fact that the values obtained both by electrical and purely mechanical means were in agreement to at least one order of magnitude was, to Joule, compelling evidence of the reality of the convertibility of work into heat.
Joule now tried a third route. He measured the heat generated against the work done in compressing a gas. He obtained a mechanical equivalent of 823 ft·lbf/Btu (4.43 J/cal).^[11]

James Joules believed that energy does not disappear. Rather it is conserved and it goes to surrounding objects in the form of heat. The independent variable in Joule’s experiment was the stirring of the water with energy. The dependent variable was the water’s temperature. James Joules, along with assistants, built an apparatus to test his hypothesis. He built the apparatus out of four revolving blades that was surrounded by stationary vanes that are connected to a stick that is connected to the bottom of a spinning drum. The revolving blades and stationary vanes are inside a container of metal framework, which is covered by a copper jacket. A rope is tied around the spinning drum. The other end of the rope goes though a pulley and is tied to a weight. There is also a slit to put a thermometer though so the water’s temperature can be measured. Finally a ruler is used to measure how low the weight dropped when it was lowered.

Joules believed that energy is always conserved. To prove this theory, he lowered the weight down by a measured amount. Then he multiplied the acceleration due to gravity with the height that the weight that got dropped is from the ground with the mass of the weight. This gave him the amount of potential energy that got converted to kinetic energy after the weight was lowered. Joules first measured the temperature of the water using a very precise thermometer. Joules lowered the weight, which caused the rope to be pulled on and therefore the spinning drum was spun. This caused the system of paddles to spin the water. Joules then measured the temperature of the water after the paddles stopped turning. The amount of temperature degrees that the water was raised by was approximately the same as the amount of kinetic energy that the lowered weight used on the water. This confirmed Joule’s hypothesis about energy being conserved. This allowed Joule to come up with the equation: CΔT=mgh. Henceforth, Joule was able to determine the specific heat (C) of water too. He was to estimate a mechanical equivalent of 4.41 J/cal. In 1845, Joule read his paper that contained the paddle-wheel experiment, On the mechanical equivalent of heat to the British Association meeting in Cambridge. In 1850, Joule published a refined measurement of 4.159 J/cal. Today the accepted specific heat of water is 4.186 J/cal.

In 1798 Benjamin Thompson, an Englishman who spent his early years in pre-revolutionary America, was minister for war and police in the German state of Bavaria. One of his jobs was to oversee the boring of cannons in the state arsenal. Thompson was struck by the enormous, and seemingly inexhaustible, amount of heat generated in this process. He simply could not understand where all this heat was coming from. According to Lavoisier's calorific theory, the heat must flow into the cannon from its immediate surroundings, which should, therefore, become colder. The flow should also eventually cease when all of the available heat has been extracted. In fact, Thompson observed that the surroundings of the cannon got hotter, not colder, and that the heating process continued unabated as long as the boring machine was operating. Thompson postulated that some of the mechanical work done on the cannon by the boring machine was being converted into heat. At the time, this was quite a revolutionary concept, and most people were not ready to accept it. This is somewhat surprising, since by the end of the eighteenth century the conversion of heat into work, by steam engines, was quite commonplace.