Preliminary work:
Certain pieces of preliminary work have to be completed before the actual investigation can begin. This is to check that the things that I plan to do are possible, and to find out what control variables to use (values).
For the preliminary work of this investigation, I need to find 6 test tubes that have surface area / volume ratios that are sufficiently well spread. I intend to find all of the different test tubes that are available, and find the surface area and volume of each. I will then work out the surface area / volume ratio of each, and select 6 different test tubes that have sufficiently well spread surface area / volume ratios. This will help with the fairness of the investigation.
To work out the surface area of a test tube, I will first find the diameter of the test tube, and halve it to find the radius. The radius will be squared, and multiplied by Pi
(π). From this, I will be able to find the surface area of the top and bottom of the effective cylinder. To find the area of the remainder of the test tube, I will take the original diameter, and multiply it by Pi (π), to find the circumference. The circumference should then be multiplied by the length of the test tube (from the top of the test tube to the middle of the spherical bottom), to find the overall area of the rest of the test tube. (RESOURCE 4 PAGE 115) The actual overall surface area of a test tube is therefore =
To work out the volume of a test tube, I will fill the test tube with water, and pour this water into a measuring cylinder of an appropriate capacity, as shown:
The surface area / volume ratio of a test tube is therefore found by dividing the surface area by the volume.
The second piece of preliminary work that I will complete will be to find an appropriate temperature from which each experiment for the actual investigation should begin. This temperature should be easy to obtain in every test tube (using a kettle or Bunsen burner), and should take an appropriate amount of time to reduce to the end temperature (i.e.: not too long), for test tubes that have even the smallest surface area / volume ratio.
Also, I should find suitable intervals for taking results in the actual experiment, by finding how long it takes for the test tube with the largest surface area / volume ratio to lose heat (from 70˚C).
Preliminary work RESULTS:
I found that the controlled temperature from which every reading should begin should be 70°C, and that each measurements of temperature should be taken every 15 seconds.
Apparatus list:
The following apparatus will be required, to be used in the experiment:
- Supply of heated water
- Six different test tubes of sufficiently varying ‘surface area / volume’ ratios.
- Test tube rack
- Stopwatch
- Thermometer
Plan:
Firstly, all apparatus required will be organised and arranged in the area in which the experiment will take place. The six test tubes will be taken one at a time, starting with the test tube numbered ‘1’, and finishing with test tube ‘6’. Test tube ‘1’ will be taken, a thermometer placed in it, and filled with boiling water taken directly from a kettle. The test tube will be placed in a test tube rack, and the stopwatch switched on when the temperature of the water reduces to 70°C. Continuous measurements of temperature of the water will be taken every 15 seconds, until 150 seconds (10 measurements) have been completed. The test tube will be thoroughly cleaned and dried, and the procedure repeated twice more for test tube ‘1’. The entire experiment will be repeated for test tubes ‘2’, ‘3’, ‘4’, ‘5’ and ‘6’, taking 3 results for each different test tube.
Resources Used:
Results:
Below shows the averages taken for temperature of the test tubes at the given time intervals:
FOR RAW DATA TAKEN FROM THE EXPERIMENT, please see ‘attached sheet 1’.
Graphical Results:
Firstly, ‘time’ (secs.) was plotted against ‘temperature’ (°C), in order to get a basic graphical result of the temperature of each test tube at every time interval. Then, in order to find how the shape and size (SA / Volume ratio) of a test tube affects the rate of temperature loss away from the test tube, a second graph was plotted (showing ‘SA / Volume ratio’ against ‘rate of heat loss’). The rate of heat loss away from the model was found by drawing a tangent to the midpoint (75 seconds) of each line on the first graph. Then, the rate was calculated by dividing the change in temperature by the time taken for the change.
FOR BOTH OF THE GRAPHS DRAWN, please see ‘attached sheet 2’.
Conclusion:
From the results shown above, and the graphs, I conclude that the initial prediction, that ‘the larger the surface area / volume ratio of a ‘model’, the greater the rate of heat loss away from the simulation will be’ is correct. The predicted graphs are very similar to those produced from the actual experiment, and this shows that the prediction was very precise. From the graphs, it is clear that as the surface area / volume ratio of a model increases, so too does the average rate of heat loss away from the model (the amount of heat that can be lost every second). This is because the graph produced was linear, proving that:
‘Surface area / volume ratio’ ‘average rate of heat loss’
The graph is almost certainly a straight line, because there is no indication that it may be a curve of any form. Although this may be true for the range of surface area / volume ratios used, there is no evidence to suggest that the direct proportionality between the input and output variables will continue forever. One would think logically, that there must be a limit to the amount of heat that can be lost from a ‘model’ / a real mammal or bird at one given time. Therefore, the rate of heat loss away from the test tube must come to a maximum at one point. This would suggest that however large the surface area, and however small the volume of any model or organism, the amount of heat that can be lost at any given time (the rate) has a limit.
Evaluation:
Overall, I believe that the results obtained were fairly inaccurate in the experiment conducted. This is because the problems brought about in such an experiment that would have led to inaccuracies of results were found to be vast:
- Firstly, the temperature of the water measured at each point was relatively inaccurate. This was due to the fact that the temperature recorded was limited by the accuracy of the thermometer used (accurate to 1°C on the scale), and by the accuracy of the person conducting the experiment (in this case, myself). Furthermore, the temperature of the water in each test tube was not constant throughout, and any movement of the thermometer (or the whole test tube) would have shown an inaccurate measurement on the thermometer. Also, the accuracy of the recordings obtained was hindered by the fact that the thermometers were not digital, but were analogue, and prone to inaccuracies.
- Furthermore, each test tube was held upright in a test tube rack. This was in order to measure the temperature of the water at the specified time intervals, but would have caused inaccuracies with the amount of the test tube in contact with another object (affecting the heat loss away from the test tube). This was consistent throughout the experiment, however, except when larger test tube racks were used to support the bigger test tubes that could not fit into the same rack as the other test tubes.
- Also, a thermometer was submerged in each test tube, to measure the temperature of the water. This may have brought about minor inaccuracies in the results, as the presence of the thermometer displaced water that would have been in the test tube without the thermometer being present. Again, this was consistent throughout the experiment, so it would not have affected the reliability of the experiment (if it were to be repeated).
Furthermore, the procedure had a few problematic areas, mainly concerning the controlled variables:
- The temperature of the situation was not kept constant throughout the experiment, and could not feasibly be kept constant. The temperature of the heated laboratory is unlikely to have changed drastically enough to affect the results on ONE occasion, but the experiment took approximately 2 hours to complete – over 3 different sittings. Therefore, it may be possible that the temperature of the laboratory was different on these occasions, and the results would have been affected.
- The thermometer used was again, different on each of these three sittings, and this fact may have affected the results, but to what extent is difficult to define. The type of thermometer used was the same on each occasion, but the actual one was different.
- The movement of the thermometer / test tube proved also to be difficult to control. With 26 other people trying to conduct their experiments at the same time, movement of the bench would have inevitably occurred. However, it is unlikely that such movement would have affected the results drastically.
The line of best fit found on the second graph produced, indicates that some results were not as expected. This can be investigated by calculating the percentage discrepancy of the points that were not on the line of best fit, as follows:
% Discrepancy = [(value plotted - value on line) / value on line] x 100
The percentage discrepancy of each point was found, from the line of best fit:
This indicates that all of the results are within 10.2% agreement with the line of best fit, suggesting that the data obtained is relatively inaccurate. The discrepancies, as stated previously, could have come from the inaccuracies of human error, the inaccuracies of the thermometer, or the inaccuracies of the ‘controlled variables’ problems.
Although the readings have been found to be relatively inaccurate, I believe that the evidence collected was quite reliable. Obtaining 3 results for each SA / volume ratio of test tube made it possible to identify anomalous results, of which there seem to be 4 (highlighted grey on the above table). These anomalous results can be attributed to human error, movement of the test tube, and inaccuracies of the thermometers used. These anomalous results were averages of each of the 3 readings for every test tube, and were plotted on the first graph. The fact that the rates plotted on the second graph were up to 10.2% away from the line of best fit indicates that these anomalies may have contributed to the inaccuracies.
Therefore, I believe that although inaccuracies found were vast, the evidence obtained is reliable enough to support a firm conclusion. This is because even though the results were inaccurate, the inaccuracies were consistent throughout, meaning that the overall outcome of the experiment was correct (although the actual readings may not have been).
In order to improve the accuracy of the evidence further, the following changes could be made to the overall experiment:
- Electronic temperature sensors, and precise data logging could have been used to measure the exact temperature at the given time intervals.
- Electronic measuring devices could also have been used to measure the exact rate of heat loss away from the ‘model’ in each case. This is instead of drawing a tangent to each line on the first graph (to find the rate), which is a relatively inaccurate method.
- The experiment could have been completed in an isolated area (where the movements of others would not have affected the results).
To extend the experiment with new lines of enquiry, I could investigate how the volume of used water in one test tube affects the heat loss away from the model. Furthermore, I could experiment with real organisms, to investigate how heat loss away from their bodies is affected by different factors (such as external temperature etc.).