CALIBRATION OF A THERMISTOR THERMOMETER (version = fall 2001) I. Introduction Calibration experiments or procedures are fairly common in laboratory work which involves any type of instrumentation. Calibration procedures always require a standard substance or device against which the instrument to be calibrated is checked. For example ph meters are calibrated with standard buffer solutions and spectrophotometer are calibrated with standard solutions or mechanical devices of known absorbencies. In physical measurement laboratories the purpose of most calibrations is to provide a means to convert from one measurement unit to another unit. The calibration of a ph meter converts a voltage measurement to a measure of hydrogen ion concentration. The calibration of a spectrophotometer converts an electrical measurement to a measure of light absorption. II. Thermometers Any property which changes with temperature can be used to make a thermometer. You are familiar with liquid in glass devices which use the expansion of a liquid to indicate temperature change. Other thermometers utilize the expansion of a gas or the resistance change of a wire or other resistance material. In this experiment your calibration work will allow the measured electrical resistance of a thermistor to be converted to a temperature. Thermistors are semiconductors whose electrical resistance changes with temperature. The standard device will be a platinum resistance thermometer. III. Platinum Thermometers For the temperature range from about 60 K to 500 K the platinum resistance thermometer is the primary standard thermometer. Platinum thermometers consist of a small coil of platinum wire incased in a protective sheath. Platinum thermometers must themselves be calibrated. Platinum thermometers can be purchased from several manufacturers, some of these companies have the facilities to calibrate them but the best place to have them calibrated is at the National Bureau of Standards. Ours was purchased from and calibrated by the Leeds and Northrop Company. The calibration report (attachment 1) contains information about the method of calibration and the calibration constants and fitting equations which can be used to calculate the temperature of our platinum thermometer at any point within its calibrated range. With this information, the platinum thermometer can be used either as a stand alone temperature measuring device or as the temperature standard against which other thermometers are calibrated. Remember, the platinum thermometer does not read out in degrees. You measure its resistance at the correct electrical current flow and then calculate the corresponding temperature using the calibration constants and equations provided in the calibration report. If all has gone as planned, you have already written a computer program which will convert the resistance of the platinum
thermometer to the Celsius temperature. Because of the expensive nature of a platinum thermometer, most labs have only one and use it to calibrate other, less expensive, thermometers. That is what we will do in this experiment. IV. Thermistor Thermometers The thermometers that you will calibrate are made from tiny beads of a semiconductor material. The electrical resistance of this material is very sensitive to temperature (thermal resistor = thermistor) and is stable over time. These characteristics make thermistors a good material for the construction of thermometers. For our purposes the thermistor bead has been mounted in copper tubing to protect the bead and to generally make the thermistor thermometer more durable and easier to use. V. Calibration Information The actual calibration process is really very simple. The platinum thermometer and the thermistor thermometer will be placed in the same constant temperature environment (a computer controlled water bath). The electrical resistance of both devices will be determined. The resistance of the platinum thermometer will be used to calculate the water bath temperature. This temperature will then be coupled with the electrical resistance of the thermistor thermometer to give you a temperature, resistance data pair for the thermistor. The temperature of the calibrating bath is then changed and the process is repeated. This is continued until the entire temperature range you which to cover has been completed. During this experiment you will actually calibrate your thermistor twice. The first calibration will cover the temperature range from 0 to 60(C in about 5( intervals. The second calibration will cover the temperature range from 20 to 30(C in about 1.3( intervals. Both sets of calibration data can be plotted on the same large graph. Most students plot thermistor resistance on the y-axis and the centigrade temperature on the x-axis. For most students, this will be the first time you will use the large graph paper. This graph paper can be purchased by the foot at the back counter in the UNO bookstore. For this experiment, you will need at least six feet of graph paper and be sure to bring it to the first lab period of this experiment. VI. Generation of the Calibration Equations Based on information (attachment 2) provided by the Yellow Springs Instrument Company ( a major manufacturer of bead thermistors), you will use an empirical equation developed by Steinhardt and Hart to fit your thermistor data (eq. 1). 1/T = A + B*ln(R) + C*(ln(R)) 3 (Eq. 1) Where: T = Kelvin temperature R = electrical resistance of your thermistor
VI. Electrical Measurements During the calibration of your thermistor thermometer you will use a potentiometer, a computer interfaced digital ohm meter (data acquisition system), and a computer controlled water bath. Potentiometers are used to measure voltage. They are relatively inexpensive but very accurate instruments. Ohm meters are used to measure electrical resistance. The computer controlled bath will provide stable calibrating temperatures between 0(C and 60(C. Platinum resistance thermometers have one major disadvantage. Their resistance change per degree is very small. The typical platinum thermometer has a resistance of 25 ohms at 0(C and 30 ohms at 60(C. For this reason, accurate temperature measurements require that you must be able to measure small resistance changes very accurately. Most resistance measuring equipment cannot provide the required precision at a reasonable cost. In this experiment we will use a potentiometer and Ohm's law to calculate the resistance of the platinum thermometers. The circuit shown in figure 1 will be used for this purpose. Variable DC Pow er Supply Pt Thermometer 100.000 Ohm Standard Resistor Potentiometer 2 Potentiometer 1 Figure 1 Potentiometer 1 is preset to.100000 volts and the power supply adjusted until this voltage drop is obtained across the standard resistor. Once this is accomplished the voltage drop across the platinum thermometer is measured with potentiometer 2 and the resistance of the platinum thermometer calculated using Ohm's law. Question: What is the current in this circuit? Resistance changes in the thermistor thermometer are much larger than those in the platinum thermometer. The thermistor used in your thermometer will have a resistance of about 10,000 ohms at 25(C and will change from about 30,000 ohms at 0(C to about 2,000 ohms at
60(C. This large change will allow us to use achieve sufficient accuracy using a good quality ohmmeter to measure the resistance of the thermistor thermometers. VII. Procedure The water bath will be under computer control. It is much faster to warm the bath up than it is to cool it down so we will generally work from lower to higher temperatures. You will be assigned a thermistor thermometer to calibrate. Each thermometer is identified by its unique set of lead colors. The thermistor thermometers will be suspended in the computer controlled water bath along with the standard platinum thermometer. The thermistor thermometers will be connected to data acquisition systems which will read, and save in memory, the resistance of each thermometer about every 15 seconds. The standard platinum thermometer will be connected to a high precision potentiometer. Although the resistance readings of the thermistor thermometers can be done with computer hardware and software, the potentiometer readings must be done manually. Fortunately, only two or three potentiometer readings are needed at each temperature. Once you have decided that the temperature is constant and that you have enough temperature and resistance data to calculate good average values for both variables, your thermistor thermometer resistance data will be transferred to your p-chem computer disk. Due to the large number of resistance readings, a spreadsheet will be used to calculate the average resistance of your thermistor thermometer at this temperature. Once you have a good temperature - resistance data pair, the temperature of the water bath will be changed (this will take 20-30 minutes) and the whole process will be repeated. This will continue until the temperature range of 0 to 60(C has been covered at about 5( intervals and the temperature range of 20 to 30(C has been covered at about 1.3( intervals. VII. Calculations 1. Using your Pt thermometer temperature calculation program, calculate the average centigrade temperature at each calibration point. 2. Using a spreadsheet, determine the average thermistor resistance at each calibration temperature. 3. On large graph paper, plot thermistor resistance ( y axis) versus centigrade temperature. Both the 0-60(C data and the 20-30(C data can go on the same sheet of graph paper. 4. Draw your best fit line through the experimental points for each data set. 5. Determine the least squares values for A, B & C (equation 1) for both data sets. 6. Using Q-BASIC or a spreadsheet and you re a, B & C s, calculate the centigrade temperatures at several resistance values. Do this for both data sets. Plot each calculated
data set on the appropriate large scale graph. 7. Using a spreadsheet, construct a publication quality graph which contains your experimental 0-60(C data and the least squares line for this data. 8. Repeat step 7 for your 20-30(C calibration. IX. Suggested Reading 1. Journal of Chemical Education, Volume 44, page A935 (1967). X. Report Your report on this work must include at least the following information. 1. Data tables of all experimental data. Do separate tables for the two temperature ranges. 2. A table of you re a, B and C values for both temperature ranges. 3. Your large graph ( 2 plots on one graph). Each plot should contain all experimental points used in least squares fit, all calculated points and your hand drawn line. 4. Copies of both small graphs. 5. Copies of all computer programs and /or spreadsheets that you wrote and used in this experiment.