The readings obtained are as follows and the graph is attached.
The volume of water used for this experiment was kept at 250cm³
The experiment was completed over two days.
On the first day 15th October 2004, the temperature in the physics laboratory (P1) where the experiment took place was 19.8°C
On the second day 19th October 2004, the temperature in P1 was 20.1°C.
The results of this experiment are reasonably accurate because there are few factors that affect it and they tend to remain fairly constant throughout the experiment for example the impurities present in the water and the prevailing atmospheric pressure could affect the boiling point of the water though this is relatively insignificant.
The readings in this experiment are accurate to one decimal point and readings are repeated to reduce the effect of random error and to eliminate erratic error. It is always better to take the average of two or more readings because then we increase the degree of accuracy and precision and what we get is closer to the truth.
There is no constant value for the sensitivity of the thermistor in this experiment because the graph produced is a curve rather than a straight line. This means that the gradient is constantly changing and as the gradient changes, sensitivity is altered. The result is that different points on the graph have different values for sensitivity.
I do not know precisely the percentage error present in the readings but I would guess that the error should not be more than + or – 1.2%.
The instruments used limit the accuracy. We only know what the Multimeter tells us and this is to 1 decimal place and is most probably an approximation of the actual value. For example a reading of 4.14236567555 would be rounded up to 4.1 to one decimal place and the percentage error in this is about 1%, which is within the limits of experimental error.
SAFETY
The issue of safety is very important in any experiment. In this experiment there is no really serious risk. However even minor concerns cannot be overlooked.
The major safety points considered include
- Avoiding the use of wet hands to handle electrical apparatus so as to reduce/eliminate the risk of electric shocks.
- Being careful and conscientious with the hot water as hot water is potentially dangerous.
- Ensuring proper electrical wiring (avoid using faulty equipment, use insulated wires etc.) so as to reduce/eliminate the risk of electrical injury and damage to electrical equipment.
Apart from these few points there is nothing serious to be considered. However one should generally be careful and conscientious when handling any experiment.
DIFFICULTIES/SETBACKS ENCOUNTERED.
The major problem dealt with was the lack of linearity. I originally assumed that the scale would be linear but the experiment rendered this assumption invalid so I had to deal with this by creating a look up table and graph which are attached to this report to facilitate easy conversion of voltage to temperature and vice versa. This solved the problem of non-linearity effectively.
Another problem was the problem of obtaining a wide range. I had to vary the input voltage and resistance to determine which voltage and resistance would give the most suitable range and eventually an input voltage of 8V D.C coupled with a resistance of 10 kilo ohms produced a reasonable range that was suitable for the experiment. I anticipated that this would be an issue because different combinations of voltage and resistance produce different effects in the circuit. The calculations I made before starting the experiment helped me to limit the combinations that I tested. They pointed in the direction of an input voltage of about 5-10V and resistance of about 10 kilo ohms. This helped me to save a lot of time and unnecessary hassle.
I also realized that sticking to the same equipment throughout the entire experiment was a good idea (to reduce the effect of systematic error) and so I made sure that I used the same equipment throughout. This was necessary because any factor that was present at the beginning of the experiment will remain that way throughout the entire experiment and so the effect of systematic error is reduced.
APPLICATIONS OF THIS SYSTEM
This system has a wide range of applications. It could be use to detect atmospheric temperature, to detect the temperature of liquids, as a clinical thermometer to detect the temperature of people. I could also be used to effectively compare a range of temperatures.
It could also be used to determine resistance since temperature is proportional to resistance. However for this function it is necessary to produce another conversion table to convert the readings in volts to resistance in ohms.
There are many other applications of this system and many more to be thought of by the person applying it.
REFERENCES
Advancing Physics AS textbook
Advancing Physics website
Stonyhurst College Pupils resources
APPRECIATION
Mr. J Blore
Stonyhurst College,
Department of Physics.
HOW DOES THE CIRCUIT WORK?
The circuit is a simple potential divider circuit. It operates on the potential divider formula
VA/VSUPPLY= RA/RA+B
Where A is the variable resistor in this case the thermistor and B is the fixed resistor.
I have found that there is a direct relationship between the log of the resistance and the temperature of the thermistor. Therefore, I have plotted a graph which is linear to show this relationship. It can be used as an alternative to the voltage-temperature conversion graph and table but the current used must be 5 amperes. The equation relating the resistance of a thermistor to the temperature is:
As we can see, this is unnecessarily complicated and so using the simple logarithmic graph eliminates the necessity to use this equation for every value of R obtained.
The Voltage-Temperature graph can be used as well. This is better to use and is the basis of my sensor.
This is for I=3A
NOTE: This only works when I=5A because that is the value of current used to obtain the resistance.
HOW GOOD IS MY SENSOR
For a sensor to be efficient, it must have the properties of a good sensor. These are high resolution, sensitivity, low systematic error, creativity, adequate data handling, minimal noise, random error and fluctuations.
These have been defined at the beginning of this project. I will now look at these properties individually and relate them to my sensor.
Resolution: My sensor has a high resolution. However this is limited by the reading accuracy of the instruments used. In this case, my sensor detected changes as small as 0.1 milli Volts. This is a reasonably good sensitivity for this sensor. The relationship between the temperature and voltage is not a direct one as the graph is not a straight-line graph. However, the maximum difference between any two values is about 67mV and the minimum is about 11mV. Therefore
Maximum error = 0.1/11 = 0.9%
Minimum error = 0.1/67 = 0.15%
These are below 1% so they are accurate enough.
Sensitivity: The sensitivity of my sensor is reasonable. However it decreases as progressive measurements are taken. This is because the relationship is not direct. The Voltage/Temperature graph is a decreasing negatively sloped one. Initially, a temperature change of 10 degrees Celsius produces a corresponding change in voltage of about 67mV. This decreases as the temperature increases and eventually, a temperature change of 10 degrees Celsius is followed by a change of about 11mV. This is about a one to one ratio. This is admittedly not a very high ratio but it does not really affect the results as the instruments used are digital and resolve to a high degree. The sensitivity is compromised by the resolution in this case.
Noise, Random error and Fluctuations: A good sensor reduces this to a bare minimum. I took a series of repeated readings and determined the average to make sure that these were very small in the final result. I also ensured that the conditions were kept constant and so the voltage-temperature conversion graph I obtained at the end is pretty accurate and reliable.
Systematic error: This does not really affect the final result but should be kept minimal or at least constant. In my sensing project, I used the same instruments throughout. This gives consistency so even if one of the instruments had a systematic error, it would be irrelevant since it affects all the readings to the same degree. However, as far as I could observe, there was no systematic error. There was no zero error in the voltmeter or anything of that nature.
Data handling: I tried to handle the data I obtained as effectively as possible. I used graphs and tables to present the result and how to read and interpret the graph are explained adequately so it is generally comprehensible and easy to use.
Creativity: My sensor falls short in this respect because it is a rather basic potential divider circuit and measures temperature, which is not uncommon. However, it is very useful and that is what is really important from my point of view. Temperature measurement has a wide variety of applications. It can be used to determine the optimum temperature of a baby’s bath, baby’s food, minimum and maximum temperatures reached in a day and many other useful applications.
IMPROVEMENTS THAT COULD BE MADE TO MY SENSOR.
My sensor could be improved in a number of ways. Firstly, I could have measured the change in resistance with temperature and not voltage. This is because using resistance as my variable would have given me a much clearer linear logarithmic graph making deducing values much easier and reliable.
Also, most textbooks relate the change in resistance of thermistors with temperature and not the change in voltage that occurs as a consequence of the change in resistance. Therefore, I would have had more formulae at my disposal.