energy put in by heater – energy lost to heat water = running 'true' energy
= (voltage x current x time) – (change in water's temperature x mass x specific heat capacity)
The specific heat capacity assumed for water will be taken to be 4192.5 J kg-1 K-1 as this is its specific heat capacity at about 11.5°C which is the roughly the average temperature of the distilled water during the copper's period of linear temperature increase.
Thus, when the temperature of the copper is plotted against heat energy supplied for the linear section of the graph, a straight line of best fit can be drawn for each repeat of the experiment. By comparing the lines, it is possibly to check that the two experiments give consistent data. The gradient of the line of best fit will give the reciprocal of the specific heat capacity multiplied by the mass. This is because ∆E = ∆Θ x c x m
Hence, as the graph plots ∆Θ against ∆E the gradient will give ∆Θ/∆E which equals 1/c x m. Therefore, the inverse of the gradient gives ∆E/∆Θ which equals specific heat capacity times mass. Dividing both sides by the mass will give the specific heat capacity (mass/gradient). These calculations will be carried out for both the lines and the average will give the resultant, most accurate value for the specific heat capacity.
The following apparatus will be used:
- copper block
- electric balance
- data book
- bubble wrap
- cotton wool
- 12V, 8.5A DC power supply
- wiring
- various sized polythene beakers
- masking tape
- oil
- stop clock
- ammeter
- voltmeter
- two temperature probes and displays
- alcohol thermometer
- heat-proof mat
- distilled water
- 200ml measuring cylinder
- immersion heater
Sensitivity:
Electric balance ± 0.5 g
Ammeter ± 0.005 A
Voltmeter ± 0.005 V
Temperature probe ± 0.05°C
Alcohol thermometer ± 0.5°C
Stop clock ~+1 s (± 0.005 s)
Measuring cylinder ± 0.5 ml
The electric balance is suitably accurate especially for the calculations that would be made. When measuring in kilograms, it is sensitive to four decimal places. The ammeter and voltmeter are highly sensitive digital electronic devices that offer a high degree of sensitivity unparalleled by other lab. equipment. It was decided upon to use the temperature probes to measure temperatures due to their very high sensitivity. It is also much easier to read their digital displays at a glance and, unlike traditional alcohol thermometers, there is no danger of parallax error with the digital probes. However, after the experiment was carried out and the temperature probes were calibrated with by boiling water, they were found to be very inaccurate. When the water boiled an alcohol thermometer showed the temperature to be around 99°C, but the two temperature probes measured about 94°C. It is reasonable to expect this difference to be consistent throughout the temperature range so that the error is still only about –5-6°C in the temperature range in which the experiment was conducted. In addition, the variable that must be measured is temperature change, so an error such as this should have a negligible effect on results and the following conclusions. As such, it was decided that, on balance, the temperature probes' higher sensitivity would be of greater use in the experiment anyway. The stop clock measures accurately to 0.01 s giving a potential error of ± 0.005 s but, as it has to be read by a human and the reading on the display noted down by hand, this can be extended up to almost plus 1 s. However, as the temperature changes at a fairly slow rate and readings are only taken every thirty seconds, this could not have a significant effect on the quality of the results garnered.
Accuracy:
The power supply can be set to various voltage settings – for this experiment, 12V was chosen. However, due to various factors such as internal resistance, this stated value is often different to the true voltage in the circuit and the voltage across the heater. Because of this, a voltmeter was used to measure the actual voltage and this has the advantage of being far more accurate than the value claimed by the power supply. An electric heat supply is very accurate as, due to the E = IVt formula, the amount of energy put into the copper can be measured very precisely – it is far superior than other methods of heating the substances such as with a Bunsen or hot water. Also, the copper block was cylindrical because this is a similar shape to the shape of the cylindrical electric heating element and this will mean that the heat is spread fairly evenly through the metal. The amount of energy can be measured digitally and the number of joules transferred at any given time can be calculated.
Variables:
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Energy put into the copper block – This is the independent variable that will be controlled to see how the other variables are affected.
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Room temperature – Any change in room temperature between the two lessons will be very small and any effect this may have on the results will be negligible.
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Room pressure - The experiments will take place at the same altitude and roughly the same air pressure. There will be very little difference between the two repeats.
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Temperature of copper block – The starting temperature of the copper block will depend on the room temperature and hence, should be almost the same in both experiments. This is also the dependent variable and the change in temperature will be measured throughout the experiment.
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Temperature of distilled water – This is another dependent variable. The change in temperature of the water will also be measured during the experiment and combined with the other results taken in order to find the specific heat capacity. Similarly to the copper block, the starting temperature of the water should not change much and affect the results.
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Temperature range – For both experiments roughly the same amount of heat energy will be supplied for the same length of time to make sure that the temperature range is kept fairly constant. This is because specific heat capacities of copper and water vary slightly according to temperature, as does the rate of heat loss. In addition, at higher temperatures the resistance of the circuit will increase and the water could evaporate.
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Insulation - for the repeat of the experiment, the same insulation will be used to ensure that minimal heat loss is set at a constant rate for each test and will not vary.
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Measuring devices – The same measuring devices (including, among others, temperature probes and displays, ammeters, voltmeters) will be used for all repeats to ensure that the readings obtained are consistent and do not affect the results or introduce anomalies.
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Material – throughout the experiment, the same copper block of the same mass will be used. This is to ensure no error is introduced due to a different material with a different density and other properties or the mass being different resulting in more energy being required to raise the temperature for each degree centigrade.
Safety:
Because of the hazardous nature of the experiment, special care must be take to adhere to safety guidelines and avoid accidents. When the heater is turned on, the hot element must never be touched unprotected, as it gets very hot indeed. It should also be remembered that the element stays very hot for a period after the power has been switched off. Due to the insulation, the copper will be much hotter to the touch than the outside of the flask and allowances must be made for this. The ammeter and voltmeter must always be set to the correct settings before they are turned on so as to avoid dangerously fusing them due to current surges. Water is also dangerous as, when spilled, it can get very slippery. In addition, when calibrating temperature sensors by boiling water, special care must be taken due to the hazardous nature of boiling water and especially steam. Finally, care must always be taken will electrical apparatus particularly when water is nearby.
Skill C
Results:
Turning points/anomalies:
The first graph to follow shows how the temperature of the metal rises during and after heating and then begins to cool. This is because the heater is turned off and, as the copper's surroundings are colder, heat energy is dissipated. The temperature of the copper continues to rise after the heater has been switched off because the heater is still giving out heat energy as the element itself cools off. Similarly, the temperature of the water continues to rise even though the copper is already cooling because, as the copper cools, it gives out energy which heats the water. As seen in the graph, the copper cools slightly faster in the first experiment. This was probably because there was a slight difference in the efficiency of the insulation due to a human error and thus, the cooling rate was slightly higher. Also, it is possible that the room temperature could have been lower producing a greater temperature difference and same effect of faster cooling.
In the second experiment, the water started off 1°C warmer than in the first experiment even though the copper block was at the same temperature. This difference is insignificant because only the temperature change is important but, nevertheless, could be attributed to the very inaccurate temperature probes. However, there are no real anomalies and the two experiments give such similar results that no further repeats were needed.
Procedures adapted:
In addition to what had been planned, the temperature probes were calibrated with boiling water as described above. The inaccuracy this exposed helps to explain some systematic errors in the procedure. Also, because the water took so long to begin to cool, each experiment took much longer to perform than had been expected. Because of this, there was only enough time for two experiments to be carried out. This is because the copper had to cool in between so that roughly the same temperature range could be tested. In addition, much care was taken to ensure that the insulation was suitably loose around the copper and the beakers. Cotton wool and bubblewrap are good insulators because they have many air pockets which have a very low heat conductivity. This helps to significantly slow down conduction and convection through the medium. It was made certain that the insulation was not wrapped too tightly around the beaker with the masking tape as this would compress the insulating materials too much and squash the air pockets which provide such good insulating properties. Finally, extra insulation was added to the top of the beaker because the heat loss from the top was underestimated. This is especially important considering that water was being heated and could evaporate and that hot air expands and becomes less dense which causes it to rise.
Skill D
Processing:
The specific heat capacity is found from the formula ∆E = ∆Θ x c x m. The gradients of the linear lines in the second graph give the temperature change per joule of energy supplied (∆Θ/∆E). This is measured in °C J-1. The inverse of the gradients is the energy per degree centigrade of temperature change (∆E/∆Θ) measured in J °C-1. The measurement in J °C-1 simply has to be divided by the mass of the metal to find the specific heat capacity measured in J kg-1 °C-1.
Its percentage error is equal to the percentage error of the temperature change plus that of the 'true' energy plus that of the mass.
Experiment one: (2 x ± 0.21%) + (± 1.10%) + (± 0.50%) = ± 2.01%
Experiment two: (2 x ± 0.21%) + (± 0.98%) + (± 0.50%) =
The process for finding the specific heat capacity of copper is shown below:
Experiment one: (0.0025)-1 ÷ 1.0035 = 398.60 J kg-1 °C-1 ± 2.01%
Experiment two: (0.0027)-1 ÷ 1.0035 = 396.07 J kg-1 °C-1 ± 1.90%
∴ Average specific heat capacity: 383.84 J kg-1 °C-1 ± 1.96%
It is also possible to extrapolate the cooling of the curve back to find the maximum temperature that would have been reached allowing for the constant cooling of the copper and then calculate the specific heat capacity. This is possible because the rate of cooling as the copper is heated is proportional to the average temperature during the linear temperature increase. By finding the rate of cooling after the maximum temperature has been reached and using a cooling formula, it is possible to find what the maximum temperature change would have been if all cooling had been eliminated. Then, putting this value into the formula ∆E = ∆Θ x c x m, the specific heat capacity, c, could have been found. However, by its nature, this method is less accurate than finding the gradient of the linear section as described above. This preferential method allows for much greater precision.
Conclusion:
Is has now been found that the specific heat capacity of copper is about 384 J kg-1 °C-1 in the range of 10°C to 30°C. However, allowing for the ~-5°C offset of the temperature probes, this is probably closer to the range between 15°C and 35°C. The specific heat capacity definitely cannot be quoted to any decimal places as it already has a ~± 2.0% error due to equipment sensitivity, as well as experimental errors. Also, because a difference of 0.001 in the gradient of the second graph will result in a change of about ± 16 J kg-1 °C-1, a greater degree of accuracy is misleading. According to a physics data book, the specific heat capacity of copper is 385 J kg-1 °C-1. This is very close to the result achieved, showing that the experiment was very successful and that the results are particularly reliable. The result procured from the two experiments was only 0.26% below the recognised value for copper's specific heat capacity. Also, the R2 values for the lines of best fit are both 0.99 which is very close to the optimum of 1.00 showing that the results are very accurate.
Qualitative discussion of limitations, errors and conclusion:
The experiment was limited by the inability to completely remove any heat loss at all. This probably accounted for most of the errors in the results. Even though the purpose of the distilled water was to measure the heat loss, this is very hard with the equipment provided and is also very imprecise. The insulation itself is heated up slightly by the hot metal and only a small percentage of the lost energy heats up the water. It is very hard to completely insulate the copper block and reduce heat loss any further. Also, copper was chosen as it has a relatively low heat capacity. This is because it is a solid at room temperature and has a high density. The metallic copper atoms are closely packed and, when heated, begin to vibrate vigorously. As the atoms are so close to the neighbouring atoms, these vibrations easily travel through the material and hence, heat is conducted easily resulting in a low specific heat capacity. Copper has a high heat conductivity and hence, requires little energy to raise its temperature. Conversely, if the material has a very high specific heat, lots of power is required which would greatly increase the rate of heat loss and it would also take a large length of time to provide enough energy to sufficiently heat the object, during which it will have cooled a lot.
The inaccuracy of the temperature probes was only discovered after the experiments had been carried out and could have contributed to any errors in the results. However, as the data value being measured was temperature change, assuming the temperature offset was fairly constant over a large range, this should not have affected the results so far as to make them unreliable.
The heating element and the conduction oil each have their own specific heat capacity and require energy to heat up and transfer energy into the copper block. As specific heat capacities change slightly with temperature, more minor errors could have been included in the calculated results. Despite this, the temperature range tested was quite small and, as such, any effect should be negligible. In experiments of this type, human errors in making measurements always factor in. Also, many assumptions were made, including the current and voltage changing regularly, no water evaporating, the block being pure copper and that the voltmeters and ammeters were accurate as well as sensitive.
The value achieved from the experiment was slightly lower than the 'official' specific heat capacity of copper. Because it is so hard to measure all the heat lost, it was expected that the value achieved from the experiment would be higher than the recognised measurement. This is because the energy change recorded would have been higher than the true amount of energy transferred (∆E) to the copper. Hence, as the mass and temperature change were the same, the specific heat capacity would be measured as being higher too (∆E = ∆Θ x c x m). The reason why the value found from this experiment was actually lower was probably mainly due to human error and the temperature probes. Perhaps more importantly, the heater was not hot when it was first turned on and needed some power to heat up the element at the beginning of each experiment as well as having to heat the oil. In addition, there may have been a small difference in ambient room temperature which could have had an effect. All these small factors in combination may have been enough to reduce the measured specific heat capacity enough so that it was slightly lower than the recognised value.
The results are also limited due to the very low gradients of the second graph caused by the large amount of energy that was required to increase the temperature by a small amount. As explained above, this meant that a small change in the gradient would affect the specific heat capacity calculated by a quite a large amount. By using a spreadsheet program to precisely calculate the gradient, any human error in accurately finding the gradient was eliminated. However, as the lines of best fit do not pass through the origin by quite a large intercept, this indicates that there was quite a large systematic error. Again, this is likely to have been caused by the inaccuracy of the temperature probes. Also, there is a little deviation of points and their error boxes from the lines of best fit as correlation is not perfect. This is probably due to human error and the limited sensitivities of the measuring instruments and apparatus and only has a small effect. Taking averages helps to even out any small errors such as these in each of the experiments.
Despite a seemingly large number of limitations to the reliability of the conclusion, ample consideration was made for many of the errors. The high quality of the graphs that were procured shows that the experiment was very successful and the small difference between the accepted value and the one calculated is evidence of this. As any inaccuracies were minimised, the conclusion is dependable and likely to be correct. The most was made of the equipment provided and heat loss was controlled as well as possible, meaning that the results achieved were the best they could be under such conditions.
Modifications:
Should the experiment be carried out again with fewer restrictions on the apparatus allowed, greater control over the heat loss could have been achieved. Research could be conducted into the insulating properties of different materials to discover the best insulators. A much better was of measuring heat loss could be developed and also, vacuums could be utilised. A simple piece of vacuum apparatus, even something similar to a simple Thermos flask, would be sufficient to cut out the vast majority of heat loss. This is because conduction and convection as modes of energy transfer require a medium and hence, cannot occur through a vacuum. This would mean that the only heat loss to account for would be the heating of excess air within the vacuum container and electromagnetic infrared radiation. Even this can be limited by the use of silvering to reflect radiation that is escaping.
Special equipment could be used to keep the power constant so that the energy transferred can be measure more accurately. Also, the heater and any conduction medium such as oil would be warmed up first so that energy is not wasted heating up the element used to transfer energy into the copper block. More accurate and more sensitive measuring devices could be used and the tests would be carried out over exactly the same temperature range. Also, this range would be made smaller to reduce to possibility of changing specific heat capacities affecting results.
Should more time be available, many more repeats could be carried out so that the average would give even more accurate results. In addition, the temperature probes would be calibrated before performing the experiment to ensure they were suitably accurate and sensitive. This combined with much more sensitive measuring instruments would help in reducing in-built errors.
Finally, all measuring devices could be linked up to a computer which would record all the variables and draw a graph of the results of the experiment as it took place. This would have numerous advantages. Firstly, any human error in making readings at certain times would be eliminated as a computer can perform several high-level tasks simultaneously – all the readings could be taken at precisely the same time and recorded with no delays. All of this would be automated and could occur at much more regular intervals, meaning that smoother graphs could be constructed. Human intervention need not even be required and repeats could be carried out without user commands. The power could be constantly monitored, kept constant and any fluctuations noted and regarded in calculations. Another advantage is that the data could be plotted while the experiment went on meaning that any anomalies could instantly be spotted and the appropriate repeats be organised. Furthermore, the apparatus would not have to be touched in between repeats so that there would be very no difference between the conditions and no errors introduced because of humans.
Notes:
Should choose specific heat capacities of water for each temperature -> look in data book.
Time at which the heater was switched off.
Denotes maximum temperature of copper block reached.
Denotes maximum temperature of water reached.
Time at which the heater was switched off.
Denotes maximum temperature of copper block reached.
Denotes maximum temperature of water reached.