Thermocouple

What is called a Thermocouple?

A thermocouple is defined as a loop made by connecting the ends ( called junctions ) of two different conducting wires whose junctions are maintained at different temperatures for producing thermoelectric effect.

Thermoelectric effect

Consider that, two conducting wires made of two different materials are taken and their ends are joined together to form a loop.
When the junctions of the loop are maintained at different temperature levels, an e.m.f is generated and a current is start to flow through the loop.
This phenomenon is a natural property of materials and is called thermoelectric effect.

Seebeck first explain about the thermoelectric effect of materials and establishes a mathematical relation between generated e.m.f and temperature difference of junctions.

Hence, it is also called a Seebeck effect.

Seebeck Effect

Seebeck effect is the phenomenon of flow of electric current in a wire loop of two different materials if the junctions are maintained at different temperature levels.

Consider that two metallic strips made of different metals are joined at the ends $A$ and $B$ to form a loop as shown in figure.

If the junction $A$ is kept at temperature $( \theta_A )$ and the junction $B$ is kept at temperature $( \theta_B )$ where $( \theta_A > \theta_B )$ , then an e.m.f will generate and there will be a flow of electric current in the loop.

The e.m.f developed in the thermocouple is called Seebeck e.m.f or thermo-e.m.f.

Seebeck e.m.f $( \eta_{AB} )$ produced in a thermocouple is given by the relation –

$\eta_{AB} = a_{AB} ( \theta_A - \theta_B ) + \left ( \frac {1}{2} \right ) b_{AB} ( \theta_A - \theta_B )^2$

Here $( a_{AB} )$ and $( b_{AB} )$ are constants based on given pair of metals in thermocouple.

Therefore, generated e.m.f in a thermocouple depends upon –

The temperature difference $( \theta_A - \theta_B )$ of the junctions $A$ and $B$ .
Nature of material of two wires in thermocouple.

Thermoelectric Series

A thermoelectric series is a list of conducting materials in which the materials are arranged vertically in such a manner that, if two materials are chosen from the list to form a thermocouple then at cold junction the direction of current will be from the material coming earlier of series to the material coming later in the series.

For a given temperature difference of hot and cold junctions of a thermocouple, the direction of flow of current depends upon the materials of wires. Consequently metals are arranged in a series to predict the direction of flow of current.

Thermoelectric series for commonly used conducting metals in a thermocouple is as follows –

Antimony \rightarrow Nichrome \rightarrow Iron \rightarrow Zinc \rightarrow Copper \rightarrow Gold \rightarrow Silver \rightarrow Lead \rightarrow Aluminium \rightarrow Mercury \rightarrow Rhodium \rightarrow Platinum \rightarrow Nickel \rightarrow Costantan \rightarrow Bismuth.

Therefore, a thermoelectric series gives two ideas –

(1) Direction of current – At the cold junction the direction of current is from the metal coming earlier in the series to the metal coming later in the series.

For example – In a thermocouple of Copper & Iron, the direction of current will be from Iron to Copper at the cold junction because Iron is earlier than Copper in the thermoelectric series.

(2) Magnitude of e.m.f – If two metals are chosen which are farther apart in the thermoelectric series then they will produce larger e.m.f.

For example – A thermocouple made of combination of Antimony and Bismuth will produce larger e.m.f than a combination of Antimony and Aluminium because Bismuth is at lower position than Aluminium in thermoelectric series.

Peltier Effect

Peltier effect is the phenomenon of cooling of one junction and heating of the other junction of a thermocouple, if an e.m.f is applied to flow a current through the thermocouple loop.

Peltier effect is a reverse phenomenon of thermoelectric effect. Hence, it is also Reverse thermoelectric effect.
So, it is a reverse phenomenon of Seebeck effect.

Consider that two conducting wires made of two different materials are taken and their ends are joined together to form a loop. Now if an e.m.f is applied to make a flow of current in the loop, then one of the junctions of the loop will become colder than the other junction.

If the direction of current in the loop is reversed, the cooling and heating junctions also get reversed. This means that the junction which was got heated in earlier case is now gets cooled and vice-versa.

In Peltier effect, the heat absorbed or liberated at the junctions is proportional to the charge passed through the junction.

Let, $( \Delta H )$ is the amount of heat produced or absorbed when a charge $( \Delta Q )$ is passed through the junction.

Then Peltier e.m.f is given by the relation –

$\pi_{AB} = \left ( \frac {\Delta H}{\Delta Q} \right ) = \frac {\text {Peltier heat}}{\text {Charge transferred}}$

Heating effect of Current

When electric current passes through a conductor it is get heated. This phenomenon is known as heating effect of electric current.

When a potential difference is applied across the ends of a conductor an electric field is set up in the conductor. Thus the free electrons experience electrostatic forces which produce acceleration in the direction opposite to that of electric field. As a result the free electrons acquire extra kinetic energy. This extra kinetic energy of electrons is imparted to the atoms or ions during collisions.

As a result of this the amplitude of thermal vibrations of the ions and atoms of the lattice increases. So the number of collisions between free electrons and ions in the lattice also increases.

Thus more work is done to carry free electrons from one end of the conductor to the other end. This work done is converted into heat energy of the conductor.

Examples –

Uses of heating effect of electric currents are –

Electric lamp.
Electric heater.
OTG (Oven – Toaster – Griller)
Geyser
Immersion water-heater.
Electric welding.
Arc-furnace.
Electric iron etc.

Joule’s Law of Heating

The heating of a conductor due to flow of electric current is called Joule’s heating effect.

Consider a conductor of resistance $( R )$ . Let $( I )$ be the current flowing through the conductor for time $( t )$ when a potential difference of $( V )$ volt is applied across the ends of the conductor, then heat produced in the conductor is given by Joule’s law as follows :

The heat produced in a conductor is directly proportional to the square of the current flowing through it i.e. $( H \propto I^2 )$
Heat produced in a conductor is directly proportional to the resistance of the conductor i.e. $( H \propto R )$
The heat produced in a conductor is directly proportional to the time for which the current flows through it i.e. $( H \propto t )$

Therefore, combining above equations we get –

$H \propto I^2 R t$

So, $\quad H = k I^2 R t \quad$ where $( k )$ is the constant of proportionality.

In $SI$ units $( k = 1 )$

Therefore, $\quad H = I^2 R t$ ……… (1)

From mechanical equivalent of heat, in $CGS$ units –

$H = \left ( \frac {I^2 R t}{4.186} \right )$

$= 0.24 \left ( I^2 R t \right )$ ……… (2)

In alternatively way we can write –

$H = ( IR )( It ) = V q$

But, $( Vq = W )$ is the amount of work done in carrying charge $( q )$ from one end to other end in conductor when potential difference between ends is $( V )$ .

Then, by the definition of Joule’s mechanical equivalent of heat –

$H = W = I^2 R t$ ……… (3)