Thermoelectricity | CEE Academy

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THERMOELECTRICITY

▢ Seebeck Effect:

❖ Definition: Production of emf by maintaining temperature difference between two junctions of two different metals

❖ Nature: Reversible effect

❖ Reversibility: If hot and cold junctions are interchanged, direction of thermoelectric current reverses

❖ Thermoelectric Current: Current induced due to Seebeck effect

❖ Thermocouple: Arrangement of two different metals used to convert heat energy into electrical energy

Table 1: Thermoemf Depends On

Factor	Effect
Nature of metals	Different metals produce different thermoemf
Temperature difference of junctions	Thermoemf depends on temperature difference

▢ Seebeck Series:

❖ Series:

•
Bi
•
Ni
•
Co
•
Pt
•
Cu
•
Mn
•
Hg
•
Pb
•
Sn
•
Cr
•
Al
•
Ag
•
Zn
•
W
•
Cd
•
Fe
•
As
•
Sb

❖ Current Direction Rule: In thermocouple of any two metals, current flows from metal appearing first in series to metal appearing later in series through hot junction

Table 1: Examples of Current Direction

Thermocouple	Direction of current
Cu-Fe	Cu to Fe through hot junction
Sb-Bi	Sb to Bi through cold junction

❖ Separation Rule: For given temperature difference, thermoemf increases with separation between metals in Seebeck series

❖ Maximum Thermoemf Pair: Sb-Bi produces maximum thermoemf for given temperature difference

▢ Thermoemf Variation:

❖ Statement: For a given thermocouple, as hot junction temperature increases, thermoemf first increases, becomes maximum, then decreases and finally becomes zero at inversion temperature

Table 1: Thermoemf vs Hot Junction Temperature

Temperature region	Thermoemf behaviour
Below neutral temperature	Thermoemf increases
At neutral temperature	Thermoemf maximum
Between neutral and inversion temperature	Thermoemf decreases
At inversion temperature	Thermoemf zero
Beyond inversion temperature	Thermoemf reverses direction

▢ Neutral Temperature:

❖ Symbol: \(\theta_n\)

❖ Definition: Temperature of hot junction at which thermoemf produced in thermocouple is maximum

Table 1: Neutral Temperature

Point	Answer
Depends on	Nature of thermocouple metals
Independent of	Temperature of cold junction
For given thermocouple	Constant
Cu-Fe thermocouple	\(270^\circ C\)

▢ Temperature of Inversion:

❖ Symbol: \(\theta_i\)

❖ Definition: Temperature of hot junction at which thermoemf becomes zero and beyond which thermoemf reverses direction

Table 1: Temperature of Inversion

Point	Answer
Depends on	Nature of thermocouple and temperature of cold junction
Fixed value?	No fixed value; varies with cold junction temperature
	\(540^\circ C\)

❖ Relation:

◉ Formulae:

•
\(\theta_n-\theta_0=\theta_i-\theta_n\)
•

◉ Symbols:

•
•
\(\theta_n\) = neutral temperature
•
\(\theta_i\) = inversion temperature

▢ Seebeck Coefficient:

❖ Also Called: Thermoelectric power

❖ Symbol: \(S\)

❖ Definition: Rate of change of thermoemf with temperature difference of hot and cold junctions

Table 1: Seebeck Coefficient Formulae

Quantity	Formula
	\(E=aT+bT^2\)
Seebeck coefficient	\(S=\frac{dE}{dT}\)
Using \(E=aT+bT^2\)	\(S=a+2bT\)
At neutral temperature	\(\frac{dE}{dT}=0\)
Neutral temperature	\(T_n=-\frac{a}{2b}\)

❖ Constants: a and b depend on nature of metals forming thermocouple

❖ Important Points:

•
Thermoelectric power at neutral temperature is zero
•
Thermoelectric power is independent of cold junction temperature
•
Thermoelectric power is positive when hot junction temperature lies between cold junction temperature and neutral temperature
•
Thermoelectric power is negative when hot junction temperature lies between neutral temperature and inversion temperature
•
If a and b both are positive and cold junction temperature is 0°C or more, neutral and inversion temperatures are not detected

▢ Peltier Effect:

❖ Definition: When current passes through a junction of two metals, heat is evolved or absorbed at that junction

❖ Nature: Reversible effect

❖ Relation with Seebeck Effect: Reverse of Seebeck effect

❖ Reversibility: If current direction is reversed, heat evolution and absorption junctions interchange

Table 1: Peltier Effect Formulae

Quantity	Formula
Heat proportionality	\(H\propto q\)
Using current	\(H\propto It\)
Heat evolved/absorbed	\(H=\pi It\)
Peltier coefficient	\(\pi\)
Relation with Seebeck coefficient	\(\pi=T\frac{dE}{dT}\)
Seebeck coefficient	\(S=\frac{\pi}{T}=\frac{dE}{dT}\)

❖ Peltier Coefficient: Amount of heat evolved or absorbed when 1 A current passes for 1 second through junction of two metals

❖ Use: Thermoelectric refrigerator

▢ Thomson Effect:

❖ Definition: Absorption or evolution of heat along entire length of conductor when electric current passes through a thermocouple circuit with temperature gradient

❖ Nature: Reversible effect

Table 1: Thomson Effect Sign

Metal	Thomson effect
Cu, Sb, Ag, metals after Pb	Positive
Fe, Co, Bi, Pt, metals before Pb	Negative
Pb	Zero / nil

Table 2: Thomson Coefficient

Quantity	Formula / Meaning
Symbol	\(\sigma\)
Definition
Formula	\(\sigma=\frac{dV}{dT}\)
Heat	\(Q=\sigma It\)

❖ Second Definition: Thomson coefficient is heat evolved/absorbed beyond Joule heating between two points of conductor at unit temperature difference when unit current flows for 1 second

▢ Laws of Thermoelectricity:

❖ Law of Successive Metals:

◉ Also Called: Law of intermediate metals

◉ Statement: If metals are in successive contact forming a chain, effective emf between extreme metals equals sum of individual emfs between adjacent metals, provided all junctions are at same temperature

◉ Formula: \(E_A^D=E_A^B+E_B^C+E_C^D\)

❖ Law of Successive Temperatures:

◉ Also Called: Law of intermediate temperature

◉ Statement: EMF of a thermocouple between temperatures \(T_1\) and \(T_n\) equals sum of emfs for intermediate temperature intervals

◉ Formula: \(E_{T_1}^{T_n}=E_{T_1}^{T_2}+E_{T_2}^{T_3}+...+E_{T_{n-1}}^{T_n}\)

▢ Relations Between Coefficients:

Table 1: Thermoelectric Coefficient Relations

Coefficient / Relation	Formula
Seebeck coefficient	\(S=\frac{dE}{dT}\)
Rate of change of Seebeck coefficient	\(\frac{dS}{dT}=\frac{d^2E}{dT^2}\)
Thomson coefficient	\(\sigma=-T\frac{d^2E}{dT^2}\)
Thomson coefficient	\(\sigma=-T\frac{dS}{dT}\)
Peltier coefficient	\(\pi=TS\)
Peltier coefficient	\(\pi=T\frac{dE}{dT}\)
Thomson coefficient of rod	\(\sigma=\frac{dV}{dT}\)

▢ Read and Digest:

Table 1: Important Points

Fact	Answer
Thermocouple	Two different metals converting heat energy into electrical energy
Charge carriers in thermocouple	Electrons
Thermocouple as AC generator	Cannot act as AC generator
Seebeck effect use	Thermoelectric generator
Peltier effect use	Thermoelectric refrigerator
Thermocouple emf order	Millivolts
Seebeck effect	Resultant of Peltier effect and Thomson effect
Seebeck, Peltier, Thomson effects	Reversible
Joule heating effect	Irreversible
	Straight line
Peltier heat	\(H=\pi It\)
Thomson heat	\(H=\sigma It\)
Joule heat	\(H\propto I^2\)
Thermocouple temperature measurement	Should not be used above neutral temperature
Temperature of inversion	Depends on cold junction temperature
Neutral temperature	Independent of cold junction temperature
Thomson coefficient for lead	Zero
Thermoelectric power positive	Hot junction temperature between cold junction temperature and neutral temperature
Thermoelectric power negative	Hot junction temperature between neutral temperature and inversion temperature
Thermocouple thermometer	Used to measure rapidly changing temperature
Specific heat of electricity	Defined by Thomson coefficient
	\(\pi_2-\pi_1\)

▢ High-Yield Recall:

Table 1: Thermoelectricity One-Liners

Fact	Answer
Seebeck effect	Production of thermoemf due to temperature difference between two junctions
Seebeck effect nature	Reversible
Thermoelectric current	Current induced in thermocouple
Thermoemf depends on	Nature of metals and temperature difference
Seebeck series maximum pair	Sb-Bi
Neutral temperature	Hot junction temperature for maximum thermoemf
Cu-Fe neutral temperature	\(270^\circ C\)
Inversion temperature	Hot junction temperature where thermoemf becomes zero
Cu-Fe inversion temperature at cold junction 0°C	\(540^\circ C\)
Neutral temperature relation
Thermoemf equation	\(E=aT+bT^2\)
Seebeck coefficient	\(S=\frac{dE}{dT}=a+2bT\)
Neutral temperature	\(T_n=-\frac{a}{2b}\)
Thermoelectric power at neutral temperature	Zero
Peltier effect	Heat evolved/absorbed at junction when current passes
Peltier heat	\(H=\pi It\)
Peltier coefficient relation	\(\pi=TS\)
Thomson effect	Heat evolved/absorbed along conductor with temperature gradient
Thomson heat	\(Q=\sigma It\)
Thomson coefficient	\(\sigma=\frac{dV}{dT}\)
Pb Thomson coefficient	Zero
Law of successive metals	\(E_A^D=E_A^B+E_B^C+E_C^D\)
Law of successive temperatures
Seebeck, Peltier, Thomson	Reversible effects
Joule heating	Irreversible effect
Thermocouple emf	Order of millivolts
Thermocouple thermometer	Measures rapidly changing temperature

Q1.

The neutral temperature is \(\theta_n\), inversion temperature is \(\theta_i\), and cold-junction temperature is \(\theta_0\). What is the relation among them?

📅CEE MBBS 2023

Q2.

Thomson effect is not shown by:

📅CEE BDS 2024

Q3.

A battery is connected in a thermocouple, the two junctions will:

📅CEE BDS 2021

Q4.

The production of emf by maintaining a difference of temperature between the two junctions of dissimilar metals is called:

📅BP 2011•BP 2015•KU 2013

Q5.

The neutral temperature of a thermocouple is \(120^\circ\mathrm{C}\). Its electromotive force changes sign at \(400\ \mathrm{K}\). The temperature of the cold junction will be:

📅MOE 2012

Q6.

Neutral temperature of a thermocouple is \(320^\circ\mathrm{C}\). The cold junction is at \(10^\circ\mathrm{C}\). The inversion temperature is:

📅MOE 2011

Q7.

Thermocouple thermometer is based on principle of:

📅IE 2003

Q8.

Amount of energy absorbed or evolved when \(1\ \mathrm{A}\) of current passes for one second through a junction of two metals is called:

📅BPKIHS 2004

Q9.

A battery is connected in a thermocouple. The two junctions will:

📅BPKIHS 2005

Q10.

Thomson effect is not shown by which element?

📅BPKIHS 1998

Q11.

Which of the following combinations would give maximum e.m.f.?

Q12.

The neutral temperature of a thermocouple is \(300^\circ\mathrm{C}\). What is the inversion temperature if the temperature of cold junction is \(10^\circ\mathrm{C}\)?

📅MOE•IOM

Q13.

The emf in a thermocouple changes sign at \(600\ \mathrm{K}\). If the neutral temperature is \(210^\circ\mathrm{C}\), the temperature of cold junction is:

Q14.

The thermo-emf \(e\) in volts of a certain thermocouple is found to vary with temperature \(\theta\) of hot junction while cold junction is kept at \(0^\circ\mathrm{C}\) as \(e=40\theta-\frac{\theta^2}{20}\). Then the neutral temperature of couple is:

📅BPKIHS

Q15.

The temperature of the cold junction of a thermocouple is \(0^\circ\mathrm{C}\) and the temperature of hot junction is \(T^\circ\mathrm{C}\). The emf is \(E=16T-0.04T^2\ \mu\mathrm{V}\). The inversion temperature \(T_i\) is:

Q16.

For a thermocouple, the temperature of cold junction (\(T_c\)), the neutral temperature (\(T_n\)) and the temperature of inversion (\(T_i\)) are \(0^\circ\mathrm{C}\), \(285^\circ\mathrm{C}\) and \(570^\circ\mathrm{C}\) respectively. If the temperature of cold junction is raised to \(10^\circ\mathrm{C}\), then:

Q17.

A thermo-emf of a thermocouple is \(50\ \mu\mathrm{V/K}\) at room temperature. A galvanometer of resistance \(50\ \Omega\) and capable of detecting a current of order of \(2\ \mu\mathrm{A}\) is used. The smallest temperature difference that can be detected with this galvanometer is:

Q18.

An emf of \(0.9\ \mathrm{V}\) is generated when the temperature difference between hot and cold junctions of a thermocouple is \(75\ \mathrm{K}\). Assuming that the cold junction is heated up by \(15\ \mathrm{K}\), then to what extent will the thermo-emf change?

Q19.

The emf of the battery in a thermocouple is doubled. The rate of heat generated at one of the two junctions will:

39Thermoelectricity

Table 1: Thermoemf Depends On

Table 1: Examples of Current Direction

Table 1: Thermoemf vs Hot Junction Temperature

Table 1: Neutral Temperature

Table 1: Temperature of Inversion

Table 1: Seebeck Coefficient Formulae

Table 1: Peltier Effect Formulae

Table 1: Thomson Effect Sign

Table 2: Thomson Coefficient

Table 1: Thermoelectric Coefficient Relations

Table 1: Important Points

Table 1: Thermoelectricity One-Liners

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