EXPERIMENT 7 VARIATION OF THERMO-EMF WITH TEMPERATURE Thermo-EMF Structure 7.1 Introduction Objectives 7.2 Working Principle of a Potentiometer 7.3 Measurement of Thermo-EMF and its Variation with Temperature Setting up the Apparatus Procedure 15
Experiments with Electrical and Electronic Circuits 7.1 INTRODUCTION You are familiar with the principle of conservation of energy, which states that energy can neither be created nor destroyed; it can only change from one form to another. For example, in a battery/cell, the chemical energy is converted into electrical energy. In a hydro-power plant, potential energy (of water) is converted into electrical energy by a turbine. In an electric heater, the electrical energy is converted into heat energy. In a steam engine, heat energy is converted into mechanical (kinetic) energy. You may like to know: Can we reconvert heat energy into electrical energy? Answer to this question was provided by T.J. Seebeck in 1821. He observed that if wires of two different metals, such as copper and iron, are joined together to form a closed loop and if two junctions are kept at different temperatures, an electric current begins to flow in the loop. This phenomenon is called thermoelectric effect, and generation of current in the loop due to difference in temperatures is called Seebeck effect. The loop comprising the two metals is referred to as a thermocouple. The existence of current implies that there is an electromotive force (emf) acting in the circuit. This is known as thermo-electromotive force and the electric current produced in this way is called thermo-electric current. Do you know the factors on which the direction of current and the magnitude of thermo-emf depend? These are seen to depend on the nature of materials used and the difference of temperature between the two junctions, respectively. Table 7.1: Thermo-emf generated by some typical thermocouples Thermocouple Iron-Copper Iron-Constantan (J) Cromel-Alumel (K) Thermoemf 10 6 VK 1 13.9 50.2 39.4 Do you know that conversion of heat energy into electrical energy by a thermocouple can not be considered an efficient process because the emf produced is of the order of a few millivolts? We can however improve efficiency by using better thermocouples, based on alloys. Typical values of thermo-emf per degree rise in temperature for some thermocouples are given in Table 7.1. On account of their reliability and low cost, thermocouples are suitable as small power supply units in space satellites, ships etc. Thermocouples are extensively used as thermometers, particularly for measuring high temperatures. You will learn some of these details in PHE-06 Course on Thermodynamics and Statistical Mechanics. In this experiment, you will learn to use a thermocouple as thermometer and study how thermo-emf varies with temperature. Objectives Copper-Constantan (T) Chromel-Constantan (E) Source: ASTM data 16 39 58.5 After performing this experiment, you should be able to: arrange experimental set up for measurement of thermo-emf; measure potential difference of the order of a few microvolts; plot a graph between the thermo-emf and temperature; and determine unknown temperature using the graph.
7.2 WORKING PRINCIPLE OF A POTENTIOMETER In your 10+2 school physics, you have learnt that a voltmeter is used to measure potential difference (p.d.) in a circuit. But such measurements may not be very accurate particularly when we are dealing with small values. You may still argue that in such a case, we should use a sensitive voltmeter. To understand the reason, refer to Fig. 7.1. It shows a voltmeter connected to the cell whose emf is to be measured. Suppose that the internal resistance of the cell is r and that of voltmeter is R. The current in the circuit is given by E i =. R + r The potential difference V R across the terminals of the voltmeter will be E V R = R R + r E =. r 1+ R Thermo-EMF Fig.7.1: EMF measurement using a voltmeter Ideally, we should have V R = E but that is never possible as r 0 and R. We hope that now you can appreciate that finite resistances of the cell and the voltmeter are responsible for inexact measurement of potential difference by a voltmeter. To avoid such problems as encountered with a voltmeter, we look for a device which allows no current to flow at the time of actual measurement. In the previous experiment, you learnt to use Carey Foster s Bridge for null detection. In this experiment, you will learn to use a potentiometer. Potentiometer gives a measure of an unknown potential difference by comparing it with a known one. This is explained below: Suppose that we wish to measure an unknown potential difference V ab between the terminals A and B, as shown in Fig. 7.2a. To do so, we take a source of variable potential difference V cd, which can be varied from zero to V max, where V max V ab. Connect a circuit as shown in Fig. 7.2b. Change the value of V cd. If V ab > V cd, the current through the galvanometer, i G will be anticlockwise. But when V cd exceeds V ab, the direction of current will be reversed. And for V ab = V cd, we will get i G = 0. Thus, if we know V cd, V ab can be easily determined. In its simplest form, a potentiometer consists of a long piece of uniform wire (a few metre in length) of fairly high resistance. The wire is stretched over a wooden base and its ends are connected to two terminals of potentiometer. The base carries a metre scale with equal divisions. A jockey C, which can slide above the potentiometer wire, makes a contact with the wire when pressed. An accumulator (called the driver cell), which can maintain a steady p.d. between the ends of the wire, is connected to two terminals of the potentiometer through a key. Note that p.d. of the accumulator should always be greater than the p.d. to be measured. What do you think will Fig.7.2: a) Potential difference between terminals A and B; and b) a circuit containing variable potential difference V cd 17
Experiments with Electrical and Electronic Circuits happen if this condition is not met? In such a situation, you will not be able to obtain the null point. The potential difference per unit length of the potentiometer wire is called the potential gradient and you can calculate it by dividing the potential drop across the wire by the total length of the wire. For example, if the emf of the battery/potential across the wire is 1.3 V and the potentiometer has 10 wires, each of length 1 m, the potential gradient will be 1.3 mv cm 1. To understand the working principle of a potentiometer, refer to Fig. 7.3 and consider the flow of electric current along the wire AB. The current in the wire is driven by the accumulator (cell). The unknown potential difference to be measured is connected between the terminals x and y. Terminal y is connected to a galvanometer G, which is further connected to the jockey C. Fig. 7.3: Working principle of a potentiometer If the positive terminal of the cell is connected to A (as shown), then x must be connected to the positive side of the potential difference being measured. The potentiometer is said to be balanced when the jockey is at such a position on the wire AB that on pressing it, no current flows through the galvanometer. This is denoted by the point, say C, and is referred to as the null point. The currents through various parts of the potentiometer circuit are shown in Fig. 7.3. At the null point, the current through the galvanometer is zero, i.e. i G = 0. Therefore, by applying Kirchhoff s first rule at C we can write i = i 1 Kirchhoff s First Rule: The algebraic sum of currents meeting at a junction is zero. The currents approaching the junction are taken as positive, while those leaving it are taken as negative. and by applying Kirchhoff s first rule at A, we have i 1 i 2 i = 0 which implies that i 2 = 0 That is, the potential at x is equal to that at A (since i 2 = 0) and the potential at y equals the potential at C (since i G = 0). Therefore, p.d between x and y = p.d. between A and C 18 = irl
where r is resistance per unit length of the wire AB. The product ir signifies potential gradient or the drop of potential per unit length of the potentiometer wire. Thus, knowing the potential gradient in the potentiometer wire and the length at which the balance point is obtained, the unknown potential between x and y can be easily determined. Thermo-EMF 7.3 MEASUREMENT OF THERMO-EMF AND ITS VARIATION WITH TEMPERATURE You now know that wires of two different materials joined at their ends to form a closed loop constitute a thermocouple. On heating one of the junctions, a current begins to flow in the loop, as shown in Fig. 7.4. In the physics laboratory, you may be given a thermocouple. But even if you are asked to fabricate a thermocouple, you should be able to easily solder the wires at their ends. The choice of the materials of the wires depends on the nature of use of the thermocouple. For ordinary purposes, copper-iron or copper-constantan thermocouples are used. For copper-iron thermocouple, the current flows from copper to iron through the hot junction, and the thermo-emf generated is about 13.9 10 6 V for each degree rise of temperature between the two junctions. For copper-constantan thermocouple, the current flows from constantan to copper at the hot junction and the emf generated is about 39 10 6 V for each degree rise of temperature between the two junctions. Fig.7.4: Direction of flow of current in a typical thermo-couple Since the magnitude of thermo-emf is quite small, so shall be the drop of potential required across the potentiometer wire; of the order of a few hundred millivolt. Further, for accuracy of measurement, the potential gradient along the length of the potentiometer wire should be as small as possible. For this, you will require either a very high resistor (R) in the battery circuit (Fig. 7.5a) or use a potential divider arrangement (Fig.7.5b). Note that the only difference between the two circuits is in the way the battery is connected. In Fig. 7.5b we are using a rheostat as potential divider. Fig.7.5: Experimental arrangement to measure thermo-emf when a) a very high resistance; and b) a potential divider arrangement is used 19
Experiments with Electrical and Electronic Circuits Let us first list the apparatus with which you will work to measure the thermoemf for different values of the hot junction temperature using the experimental arrangement shown in Fig. 7.5. Apparatus A potentiometer preferably with 10 m long wire, a battery of constant emf, a rheostat, a copper-iron or a copper-constantan thermocouple, a millivoltmeter or digital multimeter, a sensitive galvanometer, a one-way plug key, a mercury thermometer graduated upto 350 C, two beakers, two tripod stands, two wire gauges, Bunsen burner, mustard oil or glycerol, connecting wires, sand paper and a clamp stand. 7.3.1 Setting up the Apparatus 1. Take a potentiometer, preferably with a 10 m long wire (AB), and place it on the table. 2. Take some connecting wires and clean their ends with a sand paper. 3. Take a battery and connect its positive terminal to one of the lower terminals of the rheostat Rh. Connect its negative terminal through the key K to the other lower terminal of the rheostat Rh. In this way, entire emf of the battery is made available across the rheostat. 4. Connect the terminal of the rheostat, connected to the positive terminal of the battery to end A of the potentiometer wire AB. 5. Connect the upper terminal on the other side of the rheostat to end B of the potentiometer wire. The rheostat will act as a potential divider. 6. Cut the copper wire of the copper-iron thermocouple in the middle. Connect one of its free ends to end A of the potentiometer wire and the other free end to the galvanometer G. 7. Connect the other terminal of the galvanometer to the jockey (C) which slides over the potentiometer wire. 8. Place the beakers on the tripod stands with wire gauges, as shown in Fig. 7.5b. Now pour water in one beaker and mustard oil/glycerol in the other and fill it up to the two-third. Place the Bunsen burner underneath the beaker containing the mustard oil/glycerol. 9. Insert the two junctions of the copper-iron thermocouple in the beakers such that they are dipping well in the liquids. 20 10. Insert the bulb of the thermometer in the mustard oil and clamp it with a clamp stand. You must ensure that the bulb of the thermometer neither touches the junction of the thermocouple, nor the sides of the beaker.
11. Check that the junction whose copper wire is connected to end A of the potentiometer wire is dipped in water. Thermo-EMF 12. Move the slider of the rheostat very close to that end whose lower terminal is connected to the positive terminal of the battery. Make sure that all the connections are tight. Loose connections can increase resistance in the circuit. 7.3.2 Procedure 1. Insert the plug in key K so that the current starts flowing through the potentiometer wire. 2. Adjust the slider of the rheostat such that the fall of potential along the potentiometer wire is only a few hundred mv. Measure this with the help of millivoltmeter or a multimeter and record it in Observation Table 7.2. 3. Measure the length of the potentiometer wire and record it. 4. Divide the fall of potential with the total length of the wire. This gives potential gradient along the potentiometer wire. 5. Record the temperature of the cold junction, i.e. water. You must shield the cold water beaker from the hot junction beaker. 6. Light the burner and heat the oil/glycerol. 7. While the heating is in progress, check the connections by tapping the jockey at the two extreme ends of potentiometer wire. Note the directions of deflections in the galvanometer on pressing the jockey. If the two deflections are on opposite sides of the zero, the circuit is in order. 8. Heat the oil, say, up to 350 C, and then let it cool. The temperature at which thermo-emf is maximum and begins to decrease on raising the temperature of hot junction is known as neutral temperature. The nature of the curve is as shown below: 9. After every 10 minutes, measure the balancing length by identifying the null point, i.e., observing zero deflection position in the galvanometer. This is done by pressing the jockey at different points on the potentiometer wire. For convenience you should begin location of null point a few seconds before the 10 minute limit each time. Record the temperature of the hot junction in Observation Table 7.2 at the time you locate the null position (zero deflection position). You should not press the jockey on the potentiometer wire with large force. 10. The product of the balancing length and the potential gradient gives the magnitude of thermo-emf for a given temperature difference between the hot and the cold junctions. 11. Plot the temperature difference along x-axis and the thermo-emf along y-axis and draw a smooth curve. What is the nature of your graph? Theoretically, we expect it to be a part of a parabola. Discuss your result with your counsellor. 21
Experiments with Electrical and Electronic Circuits 12. Note the value of neutral temperature from the graph and record it. Observation Table 7.2: Temprature dependence of thermo-emf Total length of the potentiometer wire (L) =... cm Potential drop across the ends of potentiometer wire (V) =... mv Potential gradient along the potentiometer wire V = =.... mv cm 1 L Temperature of the cold junction =... C S.No. Temperature of hot junction ( C) Difference between hot junction and cold junction temperatures ( C) Balancing length l (cm) Thermo-emf (mv) V l L 1. 2. 3. 4... Result: The neutral temperature of the given thermocouple =... C 22