Physics 103: Fall 2005

Joule’s Experiment

This experiment is a rough version of Joule’s original experiment. Although it is simple in principle, it shows that energy added to a system may show up in a consistent way as an increase in temperature. This in turn leads to the notion of internal energy, and the idea that energy is conserved, the First Law of Thermodynamics. It is actually not simple to do the experiment well! We have not attempted to control the flow of heat from the apparatus into the room, so in fact the energy we add to the apparatus will not all be represented as a change in temperature. If some small energy appears to be “lost,” we believe it has not genuinely disappeared, but rather it has only been added to the internal energy of the surrounding air, etc.

We expect to see a proportionality , where is the change in internal energy of the system and is the change in temperature.

In this case we call the constant of proportionality C the heat capacity. The “system” will be a little cylindrical can of copper with some water in it. In order to make numerical sense of the measured heat capacity of the system, we will need to know the mass of water and the mass of copper. Since copper is a good conductor of heat, it will be very nearly all at the same temperature even as it warms up, and the turning can will also keep the water constantly mixing and in thermal equilibrium with the copper, even if both together are slightly out of equilibrium with the rest of the room.

A cord with a weight hanging from it can be wound several times around the can. The other end of the cord is tied to a spring scale.

When you turn the can by the crank handle, the friction force that the cord exerts on the can is the difference between the weight and the reading on the spring scale. The simplest thing is just to turn the can fast enough that the spring scale reads zero: then the can exerts a force on the cord equal to the weight, and by Newton’s Third law, the cord exerts the same force on the can (in the opposite direction). If you don’t have a spring scale, just turn fast enough that the cords go slack on the side opposite the weight. The work you are doing in turning the crank must be increasing the energy of the system, but the mechanical energy of the system doesn’t change. It must be that the INTERNAL energy increases.

The work you do, which presumably becomes internal energy of the system, is , where is the total distance the can slips on the cord. This is simply , where R is the radius of the can, and N is the number of turns. Thus you have many different ways to add the same energy, by adjusting the friction force and the number of turns you crank. See experimentally whether the change in internal energy and the change in temperature are proportional. Graph your data in such a way that they should lie on a straight line, and interpret the slope as the heat capacity C.

Finally, make quantitative sense of C. The specific heat of water is 1, by definition, and that of copper is 0.092 (much less than 1!), as we will find, roughly, in a lecture demonstration, so we can compute what the heat capacity of the system should be. Is your thermally measured value of C for this system close to this expected value? What systematic error can we expect, and what would be its effect?