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

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?