On Joule’s paddle wheel experiment in textbooks

Authors of university and secondary school textbooks have resorted to Joule’s famous paddle wheel experiment when introducing the topic ‘energy’. The explanations provided are misleading. In this study, Joule’s original article was used to address this problem.

Figure 1 shows the schematic of the Joule apparatus [38].Figure 2 illustrates the inside of the calorimeter.Figure 3 shows the paddle wheel being introduced into the water container, where Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. the paddles rotate.At the start of the experiment, the bodies suspended by the string were at a certain height from the ground (figure 1), which represents the initial energy.When released, they rotate the central axis, which sets the paddles in motion and, consequently, the water.At the end of the experiment, the bodies were on the ground and the temperature of the water was higher than the initial temperature.The heat developed was calculated based on the temperature difference.From this summary description, we realise that the initial energy gives rise to the falling motion of the bodies and the heat in the calorimeter.Let us now proceed to present Joule's experiments in modern textbooks.
Bergmann and Schaffer wrote: 'If the object M has fallen, the potential energy m'gh has been transferred to the water in the form of heat' [3, p 1032].The illustration of Joule's experiment used by these authors does not have two bodies (figure 1) but only one, so the authors are referring to a falling body.However, it is not this difference that is at issue, but the potential energy transferred to the water in the form of heat.This is important because if the potential energy has been   In summary, according to current textbooks, potential energy is used to give rise to heat.Therefore, the question is: where does the energy of the moving bodies originate?If we consider the kinetic energy of these bodies, only a part of the potential energy is transformed into heat or transferred to water in the form of heat.Let us now examine what Joule did.

Joule (1850)
Joule does not refer to the energy.This term was only introduced into the heat theory in 1851 [41].Thus, what I am going to use comes from the corrections he made to what we now call potential energy in order to arrive at the value of this energy that he used to calculate the mechanical equivalent of heat.
Joule determined the height of the bodies and used the magnitude weight × height to calculate the mechanical equivalent of heat.However, the height used in this calculation was not that at which the bodies started.From this height, he subtracted the distance, which depends on the velocity of the falling bodies.Let us see.
He says, bodies fall with a constant velocity v = 0.061 468 m s −1 and adds, the velocity corresponds to a distance of 0.003 86 m.The relationship between this velocity and the distance can be justified by the relationship between the velocity acquired and the height of the fall Indeed, h v = v 2 2g = 0.000 193 m (h v is used to represent the height corresponding to the velocity of the bodies, to distinguish it from the height of the bodies, to be represented by h).As the falling motion of the bodies was performed 20 times, the total distance was as 20 × 0.0193 m.This value is subtracted from the total height of the bodies (32.0103 m): In conclusion, Joule takes as the quantity that is converted into heat.Now As he takes Therefore, Joule divided the initial value mgh between the falling motion of the bodies and the heat that appeared in the calorimeter.

Conclusion
According to Joule, the potential energy, mgh justifies the kinetic energy of the falling bodies and the thermal energy in the calorimeter.One might think that the value of the kinetic energy of the falling bodies is very low and can therefore be neglected.However, Joule used it.Moreover, it is not neglected in textbooks because of its low value.It is simply ignored.Thus, students were left without an explanation for the origin of the kinetic energy of the falling bodies because they had learned that the potential energy was used to produce heat.This problem can be overcome.

Figure 1 .
Figure 1.Scheme of the Joule apparatus.

Figure 2 .
Figure 2. Detail of the inside of the container, where the paddle wheel rotates.

Figure 3 .
Figure 3.The paddle wheel is introduced into the container, which has plates firmly fixed inside it.
32.0103 − 0.003 86 = 32.0064m.It is the latter value-and not the measured value of the height of the bodies-that Joule used to calculate the mechanical equivalent of heat [38, p 70].