 ## Seebecks effect, Thermocouples and Variation of Thermo emf with Temperature

Subject: Physics

#### Overview

The phenomenon in which electrical energy produced by means of thermal energy is called thermoelectric effect. This note provides us an information on see beck's effect thermocouples and variation of thermo-emf with temperature.
##### Seebecks effect, Thermocouples and Variation of Thermo emf with Temperature

The phenomenon in which electrical energy produced by means of thermal energy is called thermoelectric effect. This effect involves following three related effects:

1. Seebeck effect
2. Peltier effect
3. Thomson’s effect

#### Seebeck’s effect

If two different metal wires are joined to form a closed circuit and two junctions are kept at different temperatures, a small emf is set up in the circuit in a definite direction. This effect is called thermoelectric effect or Seebeck effect. The emf developed in the circuit is called thermal emf and the current called thermoelectric current.

#### Thermocouples

A couple of wires of dissimilar metals forming a loop and producing thermoelectricity is called thermocouple. The magnitude of emf produced and the direction of current depends on the pair of metals selected from the thermoelectric series and temperature of the junctions. In an iron-copper thermocouple, current flows from iron to copper at the cold junction. The direction of current flow changes if heating and cooling of the junction are reversed.  ##### Thermoelectric series

An arrangement of metals in series in which any two metals can be used to form a thermocouple is called thermoelectric series. When a thermocouple is formed from a pair of metals in the series, the direction of the current flow through the cold junction is from the metal which occurs earlier in the series to the one which occurs later. The greater difference in the order in the series helps to produce a higher value of emf. The thermoelectric series:

1. Antimony
2. Iron
3. Zinc
4. Silver
6. Copper
7. Platinum
8. Cobalt
9. Bismuth

#### Variation of Thermo emf with Temperature

To study the variation of thermo emf with temperature, an iron-copper thermocouple is taken as shown in the figure. One junction is immersed in an oil bath and the other junction is kept at melting ice whose temperature is kept constant. The temperature of oil bath is increased gradually by heating it. The galvanometer shows no deflection as no emf is produced when the temperatures of both junctions are at the same temperature i.e 0o C.

When the temperature of the hot junction is increased, and the cold junction is kept at 0o C, the deflection of the galvanometer is increases i.e emf also increases till it becomes maximum at θn called neutral temperature. The temperature of the hot junction at which the thermo emf becomes maximum is known as neutral temperature (θn).

When the temperature of the hot junction is increased beyond neutral temperature, thermo emf starts to decrease and ultimately becomes zero at temperature θicalled temperature of inversion. The temperature of the hot junction at which thermo emf is zero and changes its polarity is called the temperature of inversion, θi.

If the temperature is increased beyond θi, the direction of thermo emf is reversed. The inversion temperature depends upon the temperature of cold junction and nature of metals used in the thermocouple. For copper-iron thermocouple, the neutral temperature is about 250o and temperature of inversion is about 500oC. the variation of thermo emf with temperature is shown in the figure. The variation of thermo emf with temperature θis given by

$$E = \alpha \theta + \frac 12 \beta \theta ^2$$

Where α and β are constants. The values of these constant depend on the materials of conductor and the temperature difference of two junctions.

If θC is the temperature of the cold junction, then we have

\begin{align*} \theta _1 - \theta _n &= \theta _n - \theta _C \\ \text {or,} \: 2\theta _n &= \theta _C + \theta _ I \\ \text {or,} \: \theta _n &= \frac {\theta _C + \theta _i}{2} \\ \end{align*}

So, the neutral temperature lies between the inversion temperature and temperature of cold junction.

##### Relation Connecting Thermoelectric Constants α, β, θn andθi

The cold junction of thermocouple is kept at 0oC and θis the temperature of the hot junction. The thermo emf is $E = \alpha \theta + \frac 12 \beta \theta ^2$. Differenting this equation with temperature we get

\begin{align*} \frac {dE}{d\theta } &= \alpha + \beta \theta \\ \end{align*} At $\theta = \theta _n,$ E is the maximum and so$\frac {dE}{d\theta } = 0.$ It can be seen that the slope of $E-\theta$ graph, $\frac {dE}{d\theta }$ is zero at point P. So , \begin{align*}0 &= \alpha + \beta \theta _n \\ \text {or,} \theta _n &= -\frac {\alpha }{\beta } \\ \end{align*}

\begin{align*}\text {When,} \: \theta &= \theta _i , \text {then} \: E = 0 \: \text {and} \\ 0 &= \alpha \theta _i + \frac 12 \beta \theta _i^2 \\ \text {or,} \: \theta_i (\alpha + \frac 12 \theta _i) &= 0 \\ \text {Since} \: \theta _i \neq 0, \: \text {then} \: \alpha + \frac 12\beta \theta _1 &= 0.\\ \theta _1 &= - \frac {2\alpha }{\beta } \\ \end{align*}

##### Thermoelectric Power

The ratio of change of thermo emf with temperature is called thermoelectric power. It is denoted by P and given by

$$P = \frac {dE}{dT}$$

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, et al. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.

##### Things to remember

The phenomenon in which electrical energy produced by means of thermal energy is called thermoelectric effect.

A couple of wires of dissimilar metals forming a loop and producing thermoelectricity is called thermocouple.

An arrangement of metals in series in which any two metals can be used to form a thermocouple is called thermoelectric series.

When the temperature of the hot junction is increased, and the cold junction is kept at 0o C, the deflection of the galvanometer is increases i.e emf also increases till it becomes maximum at θn called neutral temperature.

When the temperature of the hot junction is increased beyond neutral temperature, thermo emf starts to decrease and ultimately becomes zero at temperature θcalled temperature of inversion.

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