Analysis of the “Coffee Cooling” Data
Part I. Procedure
In this period you will be modeling your observed values of temperature vs. time for a cooling cup of coffee
with the following equation:
(Ti - Troom ) = (T0 - Troom )e -ti / K
where K=mcx/kA
To do this in MS Excel™, follow the “recipe” given below.
Step 1. Enter Ti and ti in two adjacent columns in Excel. Start three columns over to the right and three rows down.
Label each column at the top (e.g., “T i”) and add a title for the entire spreadsheet in the upper leftmost cell. Save
the file!
Step 2. Input the observed value of (T i–Troom) in the next column. Put Troom as a constant in the second column with a
label for it in the first column.
Step 3. Calculate a theoretical value for (T i–Troom) in the next column using your theoretical decay constant. Put the
decay constant below Troom as a constant in the second column with a label for it in the first column.
Step 4. Calculate the squared difference between the theoretical and observed (T i–Troom). Put a sum of the squared
differences below the decay constant in the second column.
Step 5. Graph the observed and theoretical values for (T i–Troom) vs ti. Put the graph in a permanently visible part of
your window. To do this, first select simultaneously all the data and headings corresponding to ti and the
observed and theoretical values of (T i–Troom). Then select the chart wizard tool. Then draw a box with the mouse
outlining the desired location of your plot. Select the scatter plot option and, then, the data symbol-plus-line
option.
Step 6. Use the Solver analysis tool to provide an improved theoretical version of the decay constant. Solver does
this by changing the decay constant to minimize the sum of the squared differences. It will ask you which cell
you want changed (i.e., the decay constant) and which cell is the “Target Cell” (aka, the summed difference cell
which you want minimized).
Part II. “Write-up” Guide
Statement of the Problem
Succinctly explain why you’re doing the experiment. Start by explaining that you’re investigating how the laws
of physics can be used to explain simple, everyday phenomena, in this case the transfer of heat from a “coffee cup”
to the surrounding environment. Add an example of how this otherwise simple physics might be used in a significant
way by professionals (e.g., engineers, geologists, biologists, chemists, etc.) Possible mechanisms of heat transfer and
the associated equations should be included in your discussion. End this section with a specific proposal of a test
(that is, in as few words as possible, a sentence or two, state what you did in the experiment to test your theory).
Methods
Describe the physical setup of your experiment. Be compulsive here. Scientific experiments are useless unless
they are reproducible. They are not reproducible unless another scientist knows what equipment you’ve used.
Include a list of equipment and materials and a sketch of the apparatus after it is set up. Specify important quantities
such as mass of water, width of cylinder, etc.
Describe the procedure used. Include a step by step “instruction” manual. Include all the details such as stirring
the “coffee” with the thermometer and explain why this was done.
Presentation of Data
Clearly present the data in tabular and graphical form. Describe the results (e.g., amount of scatter, range of
values) without referring to theory. Note how the appearance of the data might reflect experimental error. For
example, if there’s a significant gap in the data that correponds to a missing data point, explain why the data was
missed.
Analysis of Data
Analyze the data to test your theory. In this section you might have to develop your theory a little more than you
did in the first section of the report. For example, equations may have to be manipulated and additional versions of
the raw data might have to be calculated. Refer to your data table if you describe new versions of the data that were
presented in the table but not previously explained.
Describe the curve-fitting technique in some detail. Don’t include every menu call but rather describe the
“philosophy” behind your use of the Solver tool in Excel™. Include for each case a printout of the actual data, the
synthetic data, and the difference after it’s been minimized by the Solver. Include also a graph of the data vs the
theoretical fit. The theoretical equation, including the actual values of the constants you determined using Solver,
should be labeled on the graph.
Conclusions
Here is where you conclude whether or not the theory fit the data, whether or not you can “blame” any misfit on
experimental technique, inadequate manipulation of theoretical equations to allow comparison with data, etc.
If appropriate, include suggestions for future work. Don’t simply suggest something, though. Justify your
suggestions.
References Cited
Any ideas presented in the report that are not your own (e.g., your textbook or some advice from another
student) must be included in a bibliographical list at the end of your lab report. See Rob for details on citation and
reference format.