Warming, Cooling,
and Urban Ozone Pollution
Part 3: The Warming Curve
Next we study the temperature
curve from the warning phase of the student experiment: Starting from ambient
room temperature, the probe is warmed by grasping it in a fist.
- Use the data in your worksheet
to plot the warming curve.
- This time you don't have
a clear indication of "ambient" temperature. Make a guess at
an appropriate ambient temperature, and scale your data accordingly. Note
that you cannot use the largest temperature value as ambient, because you're
going to take logs of the differences. Be careful with signs -- again,
because you're going to take logs. Plot the scaled data.
- Make a semilog plot of
the scaled data. Is the result linear? If not, describe the nonlinearity.
- Even if the semilog plot
is not linear, estimate an "average" slope k for a line
that would match the trend of the data. Then construct a function of the
form
T = a + (T0 - a) e-kt
that should approximate the data. Superimpose the graph of this
function on a plot of the data. How good a fit is it?
- Can you think of a reason
why the Newton model would not fit as well in this case? (Hint: This is
not a question about semantics. The fact that "cooling" is in
the name is not a reason for the law to fail to describe warming.)
Send comments to the
authors <modules at math.duke.edu>
Last modified: October 21,
1997
