```EXPERIMENTAL: AN INVESTIGATION INTO THE RELATIONSHIP BETWEEN THE
TEMPERATURE CHANGES OF A BLACK-BULB THERMOMETER AS ITS DISTANCE VARIES
FROM A HEAT SOURCE
Introduction
Radiant heat energy, in the form of electromagnetic waves, is emitted
from hot bodies (e.g., the Sun, light bulbs, and living organisms).  A
detailed knowledge of the variables which affect the absorption of this
energy is necessary to understand a variety of phenomena, including
'the use of (renewable) solar energy to heat buildings', 'homeostasis
in ectotherms', 'photochemical reactions', and 'the detection of prey
by certain predators (e.g., snakes)'.
The amount of radiant energy absorbed by a surface is well known to be
affected by a number of independent variables; these include the total
and type of energy emitted from the heat source, the distance of the
surface from the source, the colour of the surface, and its lustre
(i.e., whether the surface is shiny or dull).  However, to investigate
quantitatively the effect of any one of these independent variables,
all of the others must be both measured and held constant.
Consider, as a specific example, the following qualitative hypothesis:
As the distance of a thermometer decreases from a heat source, so does
its temperature rise.  A quantitative investigation of this hypothesis
requires that only the independent variable of interest is changed
(i.e., distance): all other independent variables must be both measured
and held constant (i.e., room temperature, heat source, time, and type
of thermometer).```
 ```Using a 0-50°C black-bulb thermometer heated by a 100 W light bulb for 180 s, you are required to investigate two related hypotheses. Hypothesis 1: As the distance (D) increases, within the range 0.060- 0.140 m, the temperature rise (DT) decreases in linear proportion; i.e., DT = k × D + c. Hypothesis 2: As the inverse-square of the distance (D-²) increases, within a distance range of 0.060-0.140 m, the temperature rise (DT) increases in linear proportion; i.e., DT = k × D-² + c.```
```Method
1.  Using a reference thermometer, measure room temperature.
2.  Carefully clamp a 0-50°C black-bulb thermometer at a measured
height from the bench.
3.  Place a 100 W light bulb, fitted in a holder, 0.060 m from this
thermometer; this distance (D) is measured, using a pair of dividers,
from the light bulb side-surface to the bulb of the thermometer.
4.  Measure the starting temperature of the black-bulb thermometer to
the nearest 0.1°C.
5.  Simultaneously, switch on the light bulb and start the clock.
6.  After exactly 180 seconds, measure the final temperature (again to
the nearest 0.1°C); you will need to keep one eye on the thermometer
and one eye on the clock.
7.  Repeat steps 2 to 6 for the other distances suggested in the Table,
using the same starting temperature; thus, cool the thermometer to
below this value, clamp it in position, and then allow it to reach the
required starting temperature.
8.  Repeat steps 2 to 6 twice more for the distance D = 0.100 m, again
using the same starting temperature.
9.  Finally, to determine whether the temperature gradient has changed,
use the reference temperature to re-measure room temperature.
Table of Results and Calculations```
 ```Constants: __________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ ``` ``` Distance (D) / m``` ``` Distance-² (D-²) / m-²``` ``` Starting Temp. / °C``` ``` Final Temp. / °C``` ``` Temp. rise DT / °C``` ` 0.060` ` ` ` ` ` ` ` ` ` 0.080` ` ` ` ` ` ` ` ` ` 0.100` ` ` ` ` ` ` ` ` ` 0.100` ` ` ` ` ` ` ` ` ` 0.100` ` ` ` ` ` ` ` ` ` 0.120` ` ` ` ` ` ` ` ` ` 0.140` ` ` ` ` ` ` ` `
```Graphs
1.  Plot all seven points of a first graph, with the dependent variable
(DT) on the vertical axis.  Draw a best line through as many points as
is sensible; here, you should obtain a smooth curve.
2.  The tabulated data and this first graph should provide the evidence
for this conclusion: "At room temperature (_____), the temperature rise
(DT) of a dull-black bulb thermometer, heated for ______ by a ______
light bulb, decreased as the distance (D) increased (within the range
of _________).  The curve indicates that these two variables are not in
in linear proportion to each other; i.e., DT ‡ k × D + c."
3.  A curve is, however, less mathematically convenient than a straight
line; to generate the latter, it is often necessary to consider other
forms of an independent variable x: for example, x², x³, x-¹, x-², ...
4.  Calculate the data for a different form of the independent variable
(D-²), and then use these values to plot a second graph; draw a best
line through as many points as is sensible.  As here you should obtain
a straight line, determine its gradient (units are °C m²); this value,
'k', is the proportionality constant in the inverse-square relationship
DT = k × D-² + c.
Sources of Error and Calculations
Broadly speaking, experimental work can be considered to include three
types of error: systematic (e.g., those arising from inaccuracies in
each instrument used); random or observational (e.g., those arising
from inaccuracies in reading each instrument); and design (i.e., those
introduced by assumptions inherent in the experimental method).
1.  The clock, ruler, and thermometer are all sources of systematic
error.  Estimate reasonable values for the probable errors in your
reading of each of these instruments. _________________________________
2.  Remembering that the thermometer is read twice in obtaining DT,
calculate and then compare the percentage errors for the measurement of
time, D, and DT when D = 0.140 m. _____________________________________
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3.  Suggest one or more possible errors inherent in the experimental
method. _______________________________________________________________
_______________________________________________________________________
4.  Use both the Table and the second graph to form a precisely worded
conclusion in respect of Hypothesis 2. ________________________________
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Dr. R. Peters                  Next                      Contents' List```