Quality of MeasurementCalibrating a Digital Thermometer Circuit

Lawrence JonesPhysics Coursework 2 • Peter Symonds College • 9 February 2011

Lawrence Jones • Peter Symonds College 1

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Quality of MeasurementDIAGRAMS

Picture and diagram of equipment setup

Below is a simple picture of the setup of the first experiment as it was when the first set of

results were taken. This is followed by a diagram of this setup with labelled objects.

Lawrence Jones • Peter Symonds College 2

Quality of MeasurementMETHOD

The method I will use on the first experiment

The first experiment I carry out will measure the voltage over the fixed resistor while

temperature changes occur over the thermistor. The voltage will be read from the fixed

resistor as opposed to the thermistor because I will be using an inverse thermistor. These

resistors experience an increase in resistance as temperature decreases, and measuring over

the fixed resistor would produce more coherent results- as temperature rises, voltage rises.

1. Measure resistance of the thermistor at the highest temperature that will be used in the

experiment and the lowest

2. Find the average of these two readings and set the fixed to resister to the nearest value

3. Link up a circuit so that from the 6V battery pack, the components in clockwise

direction go fixed resistor then thermistor then 0V terminal of battery. Hook up

voltmeter in parallel to the fixed resistor

4. Start the kettle boiling

5. Pour boiling water in a beaker along with a digital thermometer and place the

thermistor in the beaker

6. When the temperature of the water reaches 90 degrees, connect the circuit, record a

reading on the voltmeter into a table, and unplug the circuit

7. Wait for the beakers temperature to drop by 5 degrees

8. Repeat steps 6 & 7 until you get down to 20 degrees, at which point take a reading and

proceed to step 9

9. Repeat 6, 7 & 8 two more times

10. Plot readings into a graph

Quality of MeasurementSAFETY

The safety considerations of this experiment are mainly in using heated water and the kettle.

The main priority is to use gloves to prevent scalding of the hands whilst pouring water.

Another is to consider the proximity of the water to a plug point.

Gloves should be worn at all times throughout the experiment to prevent exposure to heated

elements.

Another consideration to make is short circuiting the battery. When a battery is short

circuited it not only destroys the accuracy of the measurements but the battery will heat up

rapidly, presenting a potential danger to anyone coming in contact with the pack. To avoid

this, I will just ensure that the battery is not short circuited and gloves are worn.

Quality of MeasurementPRELIM

The prelim experiment

Prior to each experiment, a preliminary is required to judge the optimum resistance for the

fixed resister. This is necessary as otherwise the sensitivity of the sensor circuit could be

severely impaired.

It is possible to complete the preliminary in two ways. You could take a reading of the voltages

at the maximum and minimum inputs, at every value possible of the fixed resistor. You would

choose the best value by the biggest range produced, as this would suggest that it would

produce a graph with the highest highs and the lowest lows. The steeper the gradient, the

more sensitive the graph would be.

However it is also possible to determine the optimum resistance mathematically using the

potential divider equation.

The greatest difference in Vout between the lower and higher resistance values will be

reached when the Z1 is going to be half the sum of the lowest and highest resistance of the

sensor.

At 90 degrees the thermistor is at 200Ohms

At 20 degrees the thermistor is at 1408Ohms

Therefore the optimum fixed resistor value will be 1608/2 = 804R and the closest fixed

resistor value for this will be 1K.

As there is only a slightly different reading for the second experiment, there is no need to

repeat the prelim.

Quality of MeasurementFIRST SET OF RESULTS

First set of results, with unregulated uncertainties

Temp (C) Voltage (V)Voltage (V)Voltage (V) Voltage Average (V)

Uncertainty (V)

20 3.33 3.30 3.24 3.290 0.04

25 3.57 3.59 3.49 3.550 0.05

30 3.76 3.70 3.73 3.730 0.03

35 4.04 4.02 3.98 4.013 0.03

40 4.26 4.29 4.17 4.240 0.06

45 4.38 4.38 4.39 4.383 0.005

50 4.59 4.64 4.69 4.640 0.05

55 4.83 4.92 4.87 4.873 0.045

60 5.01 5.04 4.97 5.007 0.035

65 5.13 5.14 5.18 5.150 0.025

70 5.28 5.32 5.27 5.290 0.025

75 5.40 5.44 5.44 5.427 0.02

80 5.47 5.40 5.43 5.433 0.035

85 5.50 5.52 5.49 5.503 0.015

90 5.61 5.59 5.58 5.593 0.015

Average uncertainty is 0.032’33’ recurring, or 0.04 to the next significant figure for the

voltage

There is constant uncertainty of the temperature of 0.1 degrees

Quality of Measurement1ST EVALUATION

Going over the experiment and choosing changes

Causes of uncertainty

After thinking over the experiment, I have determined a few causes of uncertainty.

The first, temperature fluctuations- within the beaker there are bound to be certain currents

of hotter water. As the thermometer cannot ever be in the same place as the thermistor, we

cannot ever know with one thermometer whether the thermistor is being hit by a localized

warm current. As such, the thermistor could be exposed to a different temperature than that I

will be taking the reading as. This would cause uncertainty in the results.

The second, the calibration of the thermometer. When I finished the experiment, I put three

more thermometers in the same beaker of water. All four thermometers read different

temperatures, with a range of 1.3degrees between them. This is obviously quite a serious issue

when it comes to taking an accurate reading of the temperature, and could cause serious

systematic error.

The third is the drainage of the battery. As I take each reading, some more of the batteries

power will be depleted. Eventually, the reduction in EMF will start to affect the readings

taken, causing uncertainties to appear.

What action to take

Out of the three above, the first two are the most important in my eyes. To combat this

problem, I will use four digital thermometers in the same beaker. The points of the sensor will

meet forming a square around the thermistor, and the voltage reading will be taken only when

the average of all four thermometers reaches the desired temperature.

This will reduce systematic error by taking the average of the readings into consideration. Any

big systematic errors should be relatively balanced out, resulting in more accurate readings. It

will also help reduce uncertainty as the temperature that the thermistor will be exposed to will

be much more accurately read- with four thermometers taking an average, this should account

for any localized differences in the water around the thermistor.

Quality of MeasurementMETHOD - AMENDED

The method I will use to account for uncertainties

This method explains how to carry out the experiment while reducing uncertainties (this

assumes prelim settings are already in place from previous experiment)

1. Link up a circuit so that from the 6V battery pack, the components in clockwise

direction go fixed resistor then thermistor then 0V terminal of battery. Hook up

voltmeter in parallel to the fixed resistor

2. Start the kettle boiling

3. Set up four digital thermometers in a beaker, all with the points of the sensors aimed at

the middle of the beaker. Use bluetack or similar adhesive to fix the thermometers in

place and then secure thermistor so that the bulb is directly in the centre of all the

thermometers

4. Pour the water from the kettle into the beaker

5. When the temperature of the water reaches 90 degrees, connect the circuit, record a

reading on the voltmeter into a table, and unplug the circuit

6. Wait for the beakers temperature to drop by 5 degrees

7. Repeat steps 6 & 7 until you get down to 20 degrees, at which point take a reading and

proceed to step 9

8. Repeat 6, 7 & 8 two more times

9. Plot readings into a graph

Quality of MeasurementSECOND SET OF RESULTS WITH 4 THERMOMETER AVERAGE

Second set of results, with regulated uncertainties

Temp (C) Voltage (V)Voltage (V)Voltage (V) Voltage Average (V)

Uncertainty (V)

20 3.29 3.27 3.24 3.267 0.02

25 3.49 3.50 3.47 3.487 0.015

30 3.72 3.72 3.69 3.710 0.015

35 3.92 3.94 3.89 3.917 0.025

40 4.16 4.17 4.17 4.167 0.005

45 4.37 4.38 4.40 4.383 0.015

50 4.65 4.63 4.62 4.633 0.015

55 4.87 4.87 4.87 4.870 0

60 4.96 4.97 4.96 4.963 0.005

65 5.16 5.16 5.17 5.163 0.005

70 5.27 5.26 5.26 5.263 0.005

75 5.38 5.37 5.37 5.373 0.005

80 5.47 5.47 5.46 5.467 0.005

85 5.57 5.58 5.56 5.570 0.01

90 5.62 5.63 5.64 5.630 0.01

Average uncertainty is 0.010’66’ recurring, or 0.02 rounded to the next significant figure

There is constant uncertainty of the temperature of 0.1 degrees

Quality of MeasurementFINAL EVALUATION

After completing both the experiments, it is clear that there is a limitation to the amount of

uncertainty I can reduce. There are flaws with the equipment used that prevent this, flaws

from me being the person to read them, and flaws in the entire setup as a whole.

One of these flaws is that a temperature of the water can never be fully gauged. A much more

reliable way of doing things would be to use a water bath in a sealed environment. As the

edges of the beaker will grow cooler faster (having been exposed to the air) this will mean

different parts of the water will be at different temperatures. A water bath kept at exactly the

same temperature for about 10 minutes will have settled, and the majority of temperature

eddies will have diminished. This would ensure a much greater chance that the thermistor

would be exposed to the correct temperature rather than just what was expected of the correct

temperature.

Another flaw is that the battery will grow weaker after a certain amount of use. If a system is

relying on the output of voltage to remain the same at a regular temperature, then the

readings are going to go very astray if the EMF of the battery drops significantly. A way of

avoiding this would be to use a constant power source, supplied from the mains but converted

to DC current and run through a capacitor. The capacitor would even out the fluctuations

from the power plant, and therefore the supply would be steady and without risk of running

out or decreasing in power. This would be the ideal situation, but obviously is much too in

depth for this experiment. Another idea is to put the resistance in the circuit ridiculously

high, and this reduces the amount of power required for the circuit to operate. However this is

only delaying the problem of the batteries EMF running down, not removing it entirely.

Another concern that was present with the second experiment is that it did not account for the

differences in the digital temperature readings totally. Whilst an average was much preferable

to a single reading, it still isn't a guarantee that the actual temperature is even within that

range. To fix this we would need to find a thermometer that registered a zero reading just as

water started freezing and a 100 degree reading just as water started boiling. The we would’ve

got a thermometer that would really work.