## Uses Of Thermoelectric Diagram

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# Uses of Thermoelectric Diagram

**(i) Determination of Total emf.**MN represents the Thermo-electric power line of a mental like copper couple with lead. MN has a positive slope. Let A and B be two points corresponding to temperatures T

_{1}K and T

_{2}K respectively along the temperature-axis. Consider a small strip abcd of thickness dT with junctions maintained at temperatures T and (T + dT).

The emf developed when the two junctions of the thermocouple differ by dT is

dE = dT(dE/dT) = Area ABDC

**Let π**

(ii) Determination of Peltier emf.

(ii) Determination of Peltier emf.

_{1}and π

_{2}be the Peltier coefficient for the junctions of the couple at temperatures T

_{1}and T

_{2}respectively.

The Peltier coefficient at the hot junctions (T

_{2}) is

π

_{1}= T

_{2 }(dE/dT)T

_{2}= OB X BD = area OBDF

Similarly, Peltier coefficient at the cold junction (T1) is

π

_{1}= T

_{2}(dE/dT)T

_{1}= OA X AC = area OACE

π

_{1}and π

_{2}give the Peltier emfs at T

_{1}and T

_{2}respectively.

Peltier emf between temperatures T

_{1}and T

_{2}is

Ep = π

_{2}– π

_{1}= area OBDF – area OACE = area ABDFECA

**(iii) Determination of Thomson emf.**Total emf developed in a thermocouple between temperatures T

_{1 }and T

_{2 }is

E

_{s}= (π

_{2}- π

_{1}) + ∫(σ

_{a}– σ

_{b}) dT

Here σa and σb represent the Thomson coefficients of two metals constituting the thermocouple.

If the metal A is copper and B is lead, then σ

_{b}= O.

. : E

_{s}= (π

_{2}– π

_{1}) + ∫(σ

_{a}dT)

or ∫σ

_{a}dT = - [(π

_{2}– π

_{1}) – E]

Thus, the magnitude of Thomson emf is given by

E

_{th}= (π

_{2}– π

_{1}) – E = Area ABDFECA – Area ABDC = Area CDFE

**(iv) Thermo emf in a general couple, neutral temperature and temperature of inversion.**In practice, a thermocouple may consist of nay two metals. One of them need not be always lead. Ab and are the thermo-electric power lines for Cu and Fe with respect to lead. Let T1 and T2 be the temperatures of the cold and the junctions corresponding to points P and Q.

Emf of Cu – Pb thermocouple = Area PQB

_{1}A

_{1}

Emf of Fe – Pb thermocouple = Area PQD

_{1}C

_{1 }

. : the emf of Cu – Fe thermocouple is

E

^{Fe}the Area PQD

_{1}C

_{1}– Area PQB

_{1}A

_{1}= Area A

_{1}B

_{1}D

_{1}C

_{1}

The emf increases as the temperature of the hot junctions is raised and becomes maximum at the temperature T

_{n}, where the two thermoelectric power lines intersect each other. The temperature Tn is called the neutral temperature. As the thermo emf becomes maximum at the neutral temperature, at T = T

_{n}, (dE/dT) = 0.

Suppose temperatures of the junctions, T

_{1}and T

_{2}, for a Cu – Fe thermocouple are such that the neutral temperatures T

_{n}lies between T

_{1}and T

_{2}. Then the thermo emf will be represented by the difference between the area dE/dT A

_{1}NC

_{1}and B

_{1}D

_{1}N

_{1}because these areas represent opposing emf’s. In this case, T

_{2}is the ‘temperatures of inversion’ for the Cu – Fe thermocouple.

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