Thermoelectric Effects
Class 12 Physics Notes • NEB Syllabus 2083
Syllabus, 10 solved multiple choice questions, step-by-step numericals and derivations, handwritten and typed PDF notes and frequently asked questions on the Seebeck effect, thermocouples, the Peltier effect and the thermopile.
1. Syllabus
Unit: Electricity and Magnetism
Chapter 15: Thermoelectric Effects (2 hours)
These notes follow the NEB Class 12 Physics syllabus (+2 Physics, Nepal). Practise the multiple choice questions first, then work through the numericals, and finish with the PDF notes for quick revision.
2. Multiple Choice Questions
Question 1. Which of the following statements correctly defines the Seebeck effect?
- a) The conversion of heat energy into electrical energy due to a temperature difference.
- b) The emission of electrons from a heated metal surface.
- c) The production of heat due to the passage of electric current.
- d) The generation of a magnetic field in a coil due to current flow.
Correct Answer: a) The conversion of heat energy into electrical energy due to a temperature difference.
Reason: The Seebeck effect occurs when two dissimilar metals are joined to form a closed loop and their two junctions are kept at different temperatures. A thermoelectric e.m.f. is produced, which converts heat directly into electrical energy.
Question 2. In a thermocouple, the thermoelectric e.m.f. is generated due to:
- a) the difference in electrical resistance of the metals.
- b) the difference in temperature between two junctions of dissimilar metals.
- c) the application of an external magnetic field.
- d) the flow of current from high potential to low potential.
Correct Answer: b) the difference in temperature between two junctions of dissimilar metals.
Reason: The basic requirement for a thermocouple to operate (through the Seebeck effect) is a temperature difference \(\Delta\theta\) between its hot and cold junctions.
Question 3. Why does the thermoelectric e.m.f. vary non-linearly with temperature in a thermocouple?
- a) Because the resistance of metals varies with temperature.
- b) Due to the dependence of the energy distribution of electrons on temperature.
- c) Because the temperature difference between the junctions remains constant.
- d) Due to the direct proportionality between e.m.f. and temperature.
Correct Answer: b) Due to the dependence of the energy distribution of electrons on temperature.
Reason: The diffusion of electrons across a junction depends on the energy distribution of the electrons, which changes with temperature. As a result the e.m.f. varies approximately as a parabola:
Question 4. What is the main function of a thermocouple?
- a) To generate a magnetic field.
- b) To convert electrical energy into mechanical energy.
- c) To measure temperature using the thermoelectric e.m.f.
- d) To store electrical energy.
Correct Answer: c) To measure temperature using the thermoelectric e.m.f.
Reason: Although a thermocouple generates a small e.m.f., its main use is as a sensitive thermometer. The e.m.f. is calibrated against known temperatures, and the unknown temperature is read from it.
Question 5. A thermocouple made of iron and constantan is used in an industrial furnace. The hot junction is at \(800^\circ\mathrm{C}\) and the cold junction is at room temperature (\(25^\circ\mathrm{C}\)). What behaviour of the e.m.f. is expected?
- a) The e.m.f. remains constant whatever the temperature change.
- b) The e.m.f. increases with the temperature difference.
- c) The e.m.f. decreases with the temperature difference.
- d) The e.m.f. oscillates randomly.
Correct Answer: b) The e.m.f. increases with the temperature difference.
Reason: The neutral temperature of an iron-constantan thermocouple is well above the temperatures at which it is normally used. In its working range, therefore, the e.m.f. increases steadily as the temperature difference between the hot and cold junctions increases.
Question 6. A Peltier device is used for cooling an electronic circuit. What happens when the direction of the current is reversed?
- a) The cooling effect remains unchanged.
- b) The cooling and heating junctions switch roles.
- c) The entire device stops working.
- d) The thermoelectric e.m.f. becomes zero.
Correct Answer: b) The cooling and heating junctions switch roles.
Reason: The Peltier effect is reversible. When the direction of the current is reversed, the junction that was absorbing heat (cooling) starts evolving heat, and the junction that was evolving heat starts cooling.
Question 7. The efficiency of a thermoelectric generator depends on:
- a) the material used and the temperature difference between the junctions.
- b) only the material used.
- c) only the temperature difference.
- d) the external electric field applied.
Correct Answer: a) the material used and the temperature difference between the junctions.
Reason: The efficiency is limited by the temperatures of the hot and cold junctions (as in the Carnot principle), and it also depends on the figure of merit of the thermoelectric materials, which involves their Seebeck coefficient, electrical conductivity and thermal conductivity.
Question 8. A thermocouple generates an e.m.f. of \(5\ \mathrm{mV}\) when the temperature difference between its junctions is \(100^\circ\mathrm{C}\). What e.m.f. is generated when the temperature difference is \(500^\circ\mathrm{C}\)? (Assume a linear relation.)
- a) \(10\ \mathrm{mV}\)
- b) \(20\ \mathrm{mV}\)
- c) \(25\ \mathrm{mV}\)
- d) \(50\ \mathrm{mV}\)
Correct Answer: c) \(25\ \mathrm{mV}\)
Reason: For a linear relation the Seebeck coefficient is
Question 9. A Peltier module has a coefficient of performance (COP) of \(0.5\). If the input power is \(10\ \mathrm{W}\), how much heat is absorbed at the cold junction per second?
- a) \(2\ \mathrm{W}\)
- b) \(5\ \mathrm{W}\)
- c) \(10\ \mathrm{W}\)
- d) \(20\ \mathrm{W}\)
Correct Answer: b) \(5\ \mathrm{W}\)
Reason: The coefficient of performance of a cooling device is the ratio of the heat absorbed to the input power:
Question 10. A copper-constantan thermocouple develops a thermoelectric e.m.f. of \(1\ \mathrm{mV}\) for a temperature difference of \(10^\circ\mathrm{C}\). If the hot junction is at \(300^\circ\mathrm{C}\) and the cold junction is at \(20^\circ\mathrm{C}\), the expected e.m.f. is:
- a) \(20\ \mathrm{mV}\)
- b) \(25\ \mathrm{mV}\)
- c) \(28\ \mathrm{mV}\)
- d) \(30\ \mathrm{mV}\)
Correct Answer: c) \(28\ \mathrm{mV}\)
Reason: The sensitivity is \(S=\dfrac{1}{10}=0.1\ \mathrm{mV/^\circ C}\), and the temperature difference is \(\Delta\theta=300-20=280^\circ\mathrm{C}\):
3. Numerical and Subjective Questions
a) What is the Seebeck effect?
The phenomenon of production of an electric current (and hence an e.m.f.) in a closed circuit of two dissimilar metals, when their two junctions are kept at different temperatures, is called the Seebeck effect. The e.m.f. produced is called the thermo e.m.f.
b) Discuss the cause of the thermo e.m.f. Explain its mechanism with the help of a diagram.
Figure: Seebeck effect in a thermocouple of two dissimilar metals A and B
Cause: the fundamental cause of the thermo e.m.f. is that different metals have different densities of free electrons.
Mechanism: consider a loop of two metals (for example copper and iron) forming two junctions. When one junction is heated, the free electrons at that junction gain kinetic energy and diffuse from the hot junction towards the cold junction. Because the density of free electrons, and so the rate of diffusion, is different in the two metals, there is a net accumulation of electrons at one end, which produces a potential difference between the junctions. This potential difference is the thermo e.m.f., and it drives a continuous current through the closed loop.
c) List the factors on which the thermo e.m.f. produced in a thermocouple depends.
d) In a copper-iron thermocouple the e.m.f. is related to the temperature \(\theta\) of the hot junction (the cold junction being at \(0^\circ\mathrm{C}\)) as \(E=a\theta+b\theta^2\), with \(a=14\ \mu\mathrm{V/^\circ C}\) and \(b=-0.04\ \mu\mathrm{V/^\circ C^2}\). Find the neutral temperature and the temperature at which the thermo e.m.f. changes its sign.
Neutral temperature \(\theta_n\): the e.m.f. is maximum when \(\dfrac{dE}{d\theta}=0\):
Temperature of inversion \(\theta_i\): the e.m.f. becomes zero (and then changes sign) when \(E=\theta_i(a+b\theta_i)=0\). Since \(\theta_i\neq0\):
a) What is thermoelectric e.m.f.?
The thermoelectric e.m.f. is the e.m.f. produced in a circuit of two different conductors when there is a temperature difference between their two junctions.
b) Describe the origin of the thermo e.m.f. and explain the variation of the thermo e.m.f. with the temperature of the hot junction.
Origin: the thermo e.m.f. arises from the diffusion of charge carriers (electrons) from the hot to the cold region. It has two parts: the contact (Peltier-type) potential difference at each junction, which depends on the temperature of the junction, and the potential difference set up along each conductor because of the temperature gradient (Thomson effect).
Variation: keep the cold junction at a constant temperature (say \(0^\circ\mathrm{C}\)) and raise the temperature \(\theta\) of the hot junction. The e.m.f. increases along a parabola, becomes maximum at the neutral temperature \(\theta_n\), then decreases, becomes zero at the temperature of inversion \(\theta_i\), and reverses its direction beyond it.
Figure: Variation of the thermo e.m.f. E with the temperature θ of the hot junction (cold junction at 0 °C)
c) The two junctions of a thermocouple are kept at \(0^\circ\mathrm{C}\) and \(\theta^\circ\mathrm{C}\). The thermo e.m.f. is \(E=10^{-5}\theta-0.01\times10^{-5}\theta^2\) volt. Find the neutral temperature and the maximum value of the thermo e.m.f.
The maximum e.m.f. occurs at \(\theta=\theta_n=50^\circ\mathrm{C}\):
a) Explain the Peltier effect. How is it different from the Seebeck effect?
Figure: Peltier effect (the heated and cooled junctions interchange when the current is reversed)
When a steady current is passed through a circuit of two dissimilar metals, heat is evolved at one junction and absorbed at the other. This reversible heating and cooling at the junctions is the Peltier effect.
Difference: in the Seebeck effect a temperature difference produces a current (an e.m.f.), while in the Peltier effect a current produces a temperature difference.
b) How can you say that the Peltier effect is the converse of the Seebeck effect?
In the Seebeck effect, heat energy is converted into electrical energy (a temperature difference produces an e.m.f. and current). In the Peltier effect the process is reversed: electrical energy is converted into heat energy (a current produces a hot and a cold junction). So the Peltier effect is the converse of the Seebeck effect.
c) Compare and contrast the Seebeck and Peltier effects with examples and applications.
| Seebeck effect | Peltier effect | |
|---|---|---|
| Input | A temperature difference between the junctions. | A current through the junctions. |
| Output | A voltage (e.m.f.) and current. | A temperature difference (heating and cooling). |
| Applications | Thermocouples for measuring temperature; thermoelectric generators, for example those that power spacecraft. | Thermoelectric coolers, portable mini-refrigerators and cooling of computer processors. |
| Common feature | Both need two dissimilar conductors joined at two junctions. | |
d) The e.m.f. produced by a thermocouple is \(E=aT+bT^2\), where \(a=25\ \mu\mathrm{V/^\circ C}\) and \(b=0.01\ \mu\mathrm{V/^\circ C^2}\). Calculate the e.m.f. when \(T=100^\circ\mathrm{C}\).
a) Define the neutral temperature and the temperature of inversion of a thermocouple. How are they determined?
Neutral temperature \(\theta_n\): the temperature of the hot junction at which the thermo e.m.f. is maximum (the cold junction being kept at a fixed temperature, usually \(0^\circ\mathrm{C}\)).
Temperature of inversion \(\theta_i\): the temperature of the hot junction at which the thermo e.m.f. becomes zero and then reverses its direction.
Determination: they can be found experimentally from the graph of \(E\) against \(\theta\) (the peak gives \(\theta_n\) and the point where the curve crosses the axis gives \(\theta_i\)), or from the equation \(E=a\theta+b\theta^2\) by calculus:
b) On what factors does the temperature of inversion depend?
The temperature of inversion depends on (i) the nature of the two metals forming the thermocouple and (ii) the temperature \(\theta_c\) of the cold junction. The parabola is symmetrical about \(\theta_n\), so
c) The junctions of a nickel-copper thermocouple are kept at \(0^\circ\mathrm{C}\) and \(100^\circ\mathrm{C}\). Find the Seebeck e.m.f. produced. For nickel, \(a=16.3\times10^{-6}\ \mathrm{V/^\circ C}\) and \(\beta=-0.042\times10^{-6}\ \mathrm{V/^\circ C^2}\).
In this notation the e.m.f. is \(E=at+\dfrac12\beta t^2\):
a) Discuss the principle and construction of a thermocouple.
Principle: a thermocouple works on the Seebeck effect. A thermo e.m.f. is produced in a circuit of two dissimilar metals when its two junctions are at different temperatures.
Construction: it consists of two wires of different metals (for example chromel and alumel). The wires are welded or twisted together at one end to form the hot (measuring) junction. The other ends, which are connected to a voltmeter or other measuring instrument, form the cold (reference) junction.
b) How is it used to measure temperature? How can thermocouples be used for temperature measurement in industries? List the advantages and limitations.
Measurement: the cold junction is kept at a known reference temperature (for example in melting ice). The hot junction is placed where the temperature is to be measured. The e.m.f. produced is measured and converted into a temperature with a calibration chart.
Industrial use: thermocouples are used in furnaces, gas-turbine exhausts and diesel engines because they are rugged and can work at very high temperatures.
c) A thermocouple has its neutral temperature at \(270^\circ\mathrm{C}\). If the cold junction is at \(30^\circ\mathrm{C}\), at what temperature will the e.m.f. become zero again?
The neutral temperature lies midway between the cold-junction temperature and the temperature of inversion:
a) Discuss the materials used in common thermocouples and explain why they are chosen.
Common pairs are Type K (chromel-alumel), Type J (iron-constantan) and Type T (copper-constantan). Platinum and platinum-rhodium alloys are used for very high temperatures.
The materials are chosen for their melting points, their resistance to oxidation in industrial surroundings, a high Seebeck coefficient (so that a measurable voltage is obtained) and a nearly linear e.m.f.-temperature curve over the working range.
b) Two metals A and B form a thermocouple. The e.m.f. generated is \(2.8\ \mathrm{mV}\) when the hot junction is at \(150^\circ\mathrm{C}\) and the cold junction is at \(30^\circ\mathrm{C}\). Find the average Seebeck coefficient.
The average Seebeck coefficient is the e.m.f. per unit temperature difference:
a) Describe the working of a thermopile and its use in detecting radiation.
Figure: Thermopile for detecting heat radiation
A thermopile is a number of thermocouples connected in series. Connecting them in series adds the small e.m.f.s of the individual thermocouples, which makes the instrument very sensitive.
Detection of radiation: one set of junctions (the hot junctions) is blackened so that it absorbs the incident heat (infrared) radiation, and its temperature rises. The alternate junctions are shielded and stay at the room temperature. The temperature difference produces an e.m.f., which is directly proportional to the intensity of the radiation and is measured with a sensitive galvanometer.
b) A thermocouple gives a reading of \(5\ \mathrm{mV}\) when the hot junction is at \(200^\circ\mathrm{C}\). Find the e.m.f. when the hot junction is at \(150^\circ\mathrm{C}\), assuming a linear relation.
The cold junction is taken to be at \(0^\circ\mathrm{C}\), and for a linear relation \(E\propto\theta\):
a) Explain the construction and calibration of a thermocouple using standard reference junctions.
Construction: two pure wires of dissimilar metals are cleaned and welded tightly at one tip (the hot junction). The other ends are connected to copper leads that go to a high-resistance voltmeter.
Calibration: the cold (reference) junctions, where the metals of the thermocouple meet the copper leads, are placed in an ice-water bath so that their temperature is exactly \(0^\circ\mathrm{C}\). The hot junction is then placed at known fixed temperatures (for example boiling water at \(100^\circ\mathrm{C}\), and the freezing points of tin and zinc). The e.m.f. is recorded at each fixed point to make a calibration curve or table, from which an unknown temperature can be read.
b) A thermocouple produces a thermoelectric e.m.f. of \(4.5\ \mathrm{mV}\) when the hot junction is at \(100^\circ\mathrm{C}\) and the cold junction is at \(0^\circ\mathrm{C}\). Calculate the Seebeck coefficient.
4. View PDF Notes
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5. Frequently Asked Questions
What is the thermoelectric effect? (meaning in physics)
What topics are included in Chapter 15 Thermoelectric Effects of NEB Class 12 Physics?
What is the Seebeck effect?
What is the difference between the thermoelectric effect and the Seebeck effect?
What is the Peltier effect?
What is a thermocouple and what is it used for?
What factors does the thermo e.m.f. depend on?
What is the formula for thermoelectric e.m.f.?
What are the neutral temperature and the temperature of inversion?
What is a thermopile?
Why is the Peltier effect called the converse of the Seebeck effect?
What are the advantages and limitations of thermocouples?
What are the applications of the Seebeck and Peltier effects?
Where can I find a thermoelectric effect PDF and PPT for Class 12?
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