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 T1 K and T2 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

(ii) Determination of Peltier emf.
Let π1 and π2 be the Peltier coefficient for the junctions of the couple at temperatures T1 and T2 respectively.

The Peltier coefficient at the hot junctions (T2) is
    π1 = T2 (dE/dT)T2 = OB X BD = area OBDF

Similarly, Peltier coefficient at the cold junction (T1) is
    π1 = T2 (dE/dT)T1 = OA X AC = area OACE

π1 and π2 give the Peltier emfs at T1 and T2 respectively.
Peltier emf between temperatures T1 and T2 is
Ep = π2 – π1 = area OBDF – area OACE = area ABDFECA

(iii) Determination of Thomson emf. Total emf developed in a thermocouple between temperatures T and T2 is

Es = (π2 - π1) + ∫(σa – σb) 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 σb = O.
. : Es = (π2 – π1) + ∫(σa dT)
or ∫σa dT = - [(π2 – π1) – E]
Thus, the magnitude of Thomson emf is given by
    Eth = (π2 – π1) – 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 PQB1A1
Emf of Fe – Pb thermocouple = Area PQD1C1
. : the emf of Cu – Fe thermocouple is
EFe the Area PQD1C1 – Area PQB1A1 = Area A1B1D1C1

The emf increases as the temperature of the hot junctions is raised and becomes maximum at the temperature Tn, 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 = Tn, (dE/dT) = 0.

Suppose temperatures of the junctions, T1 and T2, for a Cu – Fe thermocouple are such that the neutral temperatures Tn lies between T1 and T2. Then the thermo emf will be represented by the difference between the area dE/dT A1NC1 and B1D1N1 because these areas represent opposing emf’s. In this case, T2 is the ‘temperatures of inversion’ for the Cu – Fe thermocouple.

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