The Interdisciplinary Laboratory
Pre-Lab
Assignment
for Experiment #1:
Thermal
Properties
of an Ectothermic Animal
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) |
mass (g) |
|
1-1 |
3.0 |
1.0 |
6.3 |
|
1-2 |
6.0 |
2.0 |
50.9 |
|
1-3 |
9.0 |
3.0 |
172.4 |
|
1-4 |
12.0 |
4.0 |
408.0 |
Set #2 (Constant length, variable diameter)
|
cylinder |
length (cm) |
diameter (cm) |
mass (g) |
|
2-1 |
6.0 |
1.0 |
12.7 |
|
2-2 |
6.0 |
2.0 |
50.9 |
|
2-3 |
6.0 |
3.0 |
114.8 |
|
2-4 |
6.0 |
4.0 |
204.0 |
Set
#3 (Constant diameter, variable length)
|
cylinder |
length (cm) |
diameter (cm) |
mass (g) |
|
3-1 |
3.0 |
2.0 |
25.3 |
|
3-2 |
6.0 |
2.0 |
50.9 |
|
3-3 |
9.0 |
2.0 |
76.5 |
|
3-4 |
12.0 |
2.0 |
102.1 |
(1)
Calculate the volume (V), surface area (A) and surface area: volume
ratio (A/V)
of each cylinder. (Use real numbers;
please do not leave answers in terms of pi
or as fractions.)
(2)
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/V) (= y-axis) as a function of ln(mass) (=
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 surface area:volume ratio and mass.
What is the value of this exponent? As
cylinder size (mass) increases, does the
surface area:volume ratio stay the same, increase or decrease?
(3)
As you can see from equations (3) and (4) in the lab manual, an
object’s
cooling rate is a direct function of its surface area:volume ratio. Would you expect the cooling rate of a
cylinder to increase or decrease with increasing cylinder size? Explain.
(4)
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/V)
vs ln(mass) for all 3 sets of cylinders on the same graph, and fit a
straight
line to the points. What is the value of the exponent for this
relationship?
(5)
Think about your results for (2) (all cylinders the same shape) and (4)
(cylinders of very different shapes). From
these results, what do you think will be the more important predictor
of a cylinder's
cooling rate: its shape or its mass?
Explain your reasoning.
(6)
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 mcfadden@hmc.edu
by no later than 7 pm Monday 8 September or Monday 6 October. Turn in hardcopies of your graphs for
questions 2 and 4 at the beginning of class on Wednesday 10 September
or 8 October.
Please DO NOT send graphs via
e-mail.