Energy Balance Modeling Project
For Summer 1997 Envision-It! Workshop
Heating/Cooling of Water in Identical Cans
The following experiment (which I have used in the classroom on several
occasions) illustrates the flow of energy into and out of a system. We
will develop a Matlab model
of this experiment and explore the strengths and limitations of the model.
- Get pairs of identical cans (I use 16 ounce soup cans)
and remove labels.
Spray paint one can black and leave the other silver
- Fill with about 100 ml of room temperature water
and place a thermometer in each can
- Place the two cans each about 3 cm from a 100W light bulb
-
Record the temperature as a function of time (it will rise quickly
at first and then reach an equilibrium after a few hours).
If available, this is a good use of an electronic thermometer which can
be monitored by the computer.
If doing it manually, record the temperature every few minutes for
about an hour, and then less often for later times. You should also
record the final temperature of the cans (for example, after letting it
sit overnight).
- Note that the black can heats up faster than silver.
The energy absorbed is in the form of visible & infrared radiation
which depends on the "color" of the surface
- Now fill each can with hot tap water (about 45 degrees C), and
again record temperature versus time.
- Note that cans cool at nearly the same rate. Heat loss is due to
convection, conduction and radiation (to some extent). These
depend primarily on the temperature difference between
an object and its surroundings and are much less sensitive to the color
of the cans.
This simple experiment illustrates several important points
- In a real physical situation, there are often several
mechanisms that are competing in the energy gain/loss. Each of these
may depend of different physical properties of the system
- We can develop a
mathematical model
which describes the experiment
(in this case, the energy flow into & out of the cans and its
temperature dependence)
- Using the model, we can develop a program which allows
us to extract quantitative results and to make physical predictions.
- The simple model, however, may fail to fit the data perfectly
and thus we would need to refine the model
- This experiment has applications in the real world -
passive solar energy storage system for a home which is
55 gallon drums (painted black) filled with water exposed to the sun during
the day and radiating heat at night.
Electronic Copy:
http://physics.gac.edu/~huber/envision/canexpt/canexpt1.html
Revised: 18-JUN-97
by Tom Huber,
Physics Department,
Gustavus Adolphus College.
Develop the Mathematical
Model
