The Interdisciplinary
Laboratory
Pre-Lab Assignment
for Experiment #1:
Thermal Properties
of an Ectothermic Animal
In the first week of this laboratory
exercise you will be measuring the cooling rates of aluminum cylinders
of varying sizes to determine how rates of heat loss scale with the size
and shape of an object. The dimensions of some of the cylinders with
which you will be working are given below:
| Set #1 (Proportionately scaled (= isometric)) |
| cylinder |
length (cm) |
diameter (cm) |
| 1-1 |
3 |
1 |
| 1-2 |
6 |
2 |
| 1-3 |
9 |
3 |
| 1-4 |
12 |
4 |
| |
| Set #2 (Constant length, variable diameter) |
| cylinder |
length (cm) |
diameter (cm) |
| 2-1 |
6 |
1 |
| 2-2 |
6 |
2 |
| 2-3 |
6 |
3 |
| 2-4 |
6 |
4 |
| |
| Set #3 (Constant diameter, variable length) |
| cylinder |
length (cm) |
diameter (cm) |
| 3-1 |
3 |
2 |
| 3-2 |
6 |
2 |
| 3-3 |
9 |
2 |
| 3-4 |
12 |
2 |
-
Calculate the volume (V), surface area
(A) and surface area: volume ratio (A/V) of each cylinder.
-
The cylinders in set #1 increase in
size isometrically – that is, as their volume increases they
maintain a constant shape (length:diameter ratio). For this set of
cylinders plot ln(A) (= y-axis) as a function of ln(V) (= x-axis) and fit
a straight line to the points. The slope, a, of this line is the
exponent in an equation of the form y = bxa that describes the
mathematical relationship between volume and surface area.
What is the value of this exponent?
-
As you can see from equations (3) and
(4) in the lab manual, an object's rate of temperature change via heat
loss is a direct function of its surface area:volume ratio. In the
isometric cylinders, would you expect the rate of temperature change to
increase or decrease with increasing cylinder size? Explain.
-
In contrast to set #1, the cylinders
in sets #2 and #3 increase in size allometrically – their shape
changes with increasing volume. The cylinders in set #2 increase
in volume by getting fatter, while those in set #3 increase in volume by
getting longer. Plot ln(A) vs. ln(V) for both of these sets of cylinders
and calculate the value of the exponent, a, as in question (2).
-
Now consider all three sets of cylinders.
In which set of cylinders would you expect the rate of temperature change
to vary the least with increasing volume? In which set should
it vary the most with increasing volume? Explain.
-
After having read through the laboratory manual for this experiment in
its entirety, what remaining questions do you have on either the background
material or the experimental protocol?
(Note: Your answers to questions 3 and
5 are the hypotheses you will test in lab this week!)
Please e-mail your answers to questions
1-6 to Stephen_Adolph@hmc.edu
by no later than 8 pm Monday 9 September or 8 pm Monday 7 October (depending
on your rotation). Turn in hardcopies of your graphs for questions
2 and 4 at the beginning of class on Wednesday 11 September or Wednesday
9 October.