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 T₁  and T₂ is

E_s = (π₂ - π₁) + ∫(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 = (π₂ – π₁) + ∫(σ_a dT)
or ∫σ_a dT = - [(π₂ – π₁) – E]
Thus, the magnitude of Thomson emf is given by
    E_th = (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
E^Fe 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 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, T₁ and T₂, for a Cu – Fe thermocouple are such that the neutral temperatures T_n 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.