39Thermoelectricity

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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
Cu-Fe with cold junction at \(0^\circ C\)
\(540^\circ C\)
❖ Relation:
◉ Formulae:
  • •
    \(\theta_n-\theta_0=\theta_i-\theta_n\)
  • •
    \(\theta_n=\frac{\theta_i+\theta_0}{2}\)
◉ Symbols:
  • •
    \(\theta_0\) = cold junction temperature
  • •
    \(\theta_n\) = 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
Thermoemf variation when cold junction at \(0^\circ C\)
\(E=aT+bT^2\)
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:
    ◈ _*type: bullet
  1. Thermoelectric power at neutral temperature is zero
  2. Thermoelectric power is independent of cold junction temperature
  3. Thermoelectric power is positive when hot junction temperature lies between cold junction temperature and neutral temperature
  4. Thermoelectric power is negative when hot junction temperature lies between neutral temperature and inversion temperature
  5. 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:
    ❖ 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:
      ◈ caption: Thomson Coefficient
      ◈ data:
        1. Quantity
        2. Formula / Meaning
        1. Symbol
        2. \(\sigma\)
        1. Definition
        2. EMF between two points of uniform conductor having temperature difference of \(1^\circ C\) or 1 K
        1. Formula
        2. \(\sigma=\frac{dV}{dT}\)
        1. Heat
        2. \(Q=\sigma It\)
    ❖ 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:
      ▢ High-Yield Recall:
      ❖ **table: